Full text of "Lavoisier Fourier Faraday"

OU1 68069

isa^^

BOOKS' OF THE WESTERN WORLD

Introductory Volumes:

1. A Liberal Education

2. The Great Ideas I

4. HOMER

5. AESCHYLUS
SOPHOCLES
EURIPIDES
ARISTOPHANES

6. HERODOTUS
THUCYD1DES

7. PLATO

9. ARISTOTLE II

10. HIPPOCRATES
GALEN

ARCHIMEDES
APOLLONIUS
NICOMACHUS

12. LUCRETIUS
EPICTETUS
MARCUS AURELIUS

13. VIRGIL

14. PLUTARCH

15. TACITUS

16. PTOLEMY
COPERNICUS
KEPLER

17. PLOTINUS

18. AUGUSTINE

19. THOMAS AQUINAS I

20. THOMAS AQUINAS II
2 I.DANTE

22. CHAUCER

23. MACHIAVELLI
HOBBES

24. RABELAIS

25. MONTAIGNE

26. SHAKESPEARE I

27. SHAKESPEARE II

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^f

$S^^^5^$3>53^^5^35&=

V3tJ^-iV=Ar-

^;5y5^gi^=?5^^

?2&2&2&g^&&&?5&^^

^v5Ki^^y^^^

GREAT BOOKS OF THE WESTERN WORLD

^5g&^&&^&?&^^

^f^?^

^5^

28. GILBERT
GALILEO
HARVEY

29. CERVANTES

30. FRANCIS BACON

31. DESCARTES
SPINOZA

32. MILTON

33. PASCAL

34. NEWTON
HUYGENS

35. LOCKE
BERKELEY
HUME

36. SWIFT
STERNE

37. FIELDING

38. MONTESQUIEU
ROUSSEAU

39- ADAM SMITH
40. GIBBON I

41. GIBBON II

42. KANT

43. AMERICAN STATE

PAPERS

THE FEDERALIST
J. S. MILL

44. BOSWELL

45. LAVOISIER
FOURIER
FARADAY

46. HEGEL

47. GOETHE

48. MELVILLE

49. DARWIN

50. MARX
ENGELS

51. TOLSTOY

52. DOSTOEVSKY

53. WILLIAM JAMES

54. FREUD

?y^*t
ga^^>

S?&5>

^^^^

?^v2^^

^^^
^v^g^

GREAT BOOKS
OF THE WESTERN WORLD

ROBERT MAYNARD HUTCHINS, EDITOR IN CHIEF

LAVOISIER

FOURIER

FARADAY

MORTIMER J. ADLER, Associate Editor

Members of the Advisory Board: STRING FELLOW BARR, SCOTT BUCHANAN, JOHN ERSKINE,

CLARENCE H. FAUST, ALEXANDER MEIKLEJOHN, JOSEPH J. SCHWAB, MARK VAN DOREN.

Editorial Consultants: A. F. B. CLARK, F. L. LUCAS, WALTER MURDOCH.

WALLACE BROCKWAY, Executive Editor

ELEMENTS OF CHEMISTRY

BY ANTOINE LAURENT LAVOISIER

ANALYTICAL THEORY OF HEAT

BY JEAN BAPTISTE JOSEPH FOURIER

EXPERIMENTAL RESEARCHES
IN ELECTRICITY

BY MICHAEL FARADAY

\YILLIAM BENTOX, Publisher

ENCYCLOPAEDIA BRITANNICA, INC.
CHICAGO LONDON TORONTO

GENERAL CONTENTS

ELEMENTS OF CHEMISTRY, Page 1

By ANTOINE LAURENT LAVOISIER

Translated by ROBKKT KERR

ANALYTICAL THEORY OF HEAT, Page 169

By JEAN BAPTIST i: JOSEPH FOURIER

Translated by ALEXANDER FREKMAN

EXPER IMENTA L RESEARCHES

IN ELECTRICITY, Page 261

By MICHAEL FARADAY

ELEMENTS OF CHEMISTRY

BIOGRAPHICAL NOTE

ANTOINE LAVOISIER, 1743-1794

LAVOISIER was born in Paris, August 26, 1743.
His father was attorney to the Parliament of
Paris. His mother was the daughter of the sec-
retary to the Vice-Admiral of France and heir-
ess to a considerable fortune.

After completing his elementary education
Lavoisier was sent to the College Mazarin. His
early ambitions were literary rather than Sci-
entific, and in 1760 he won second prize in a
rhetorical contest. Although on leaving the
college he went on to prepare for law, and re-
ceived his Licentiate in 1764, he devoted him-
self to science, studying, with well-known
teachers of the time, mathematics, astronomy,
botany, mineralogy, geology, and chemistry.
He also began to conduct experiments arid ob-
servations of his own. One of the earliest was
in meteorology; he made barometrical obser-
vations several times daily and engaged others
in the same pursuit with the aim of discovering
the laws governing the weather. His zeal for
investigation was so great that at the age of
nineteen he decided to cut himself off from all
social activity; he gave ill-health as an excuse
and for several months lived in retirement on
a diet of milk.

His formal career as a scientist began in 1763
when he was invited by Guettard, his teacher
in geology, to collaborate in preparing the first
rnineralogical atlas of France. Lavoisier's part
of the project consisted largely of collecting
data; he kept elaborate notebooks which indi-
cate that he was not only amassing material
but analysing and developing ideas for later re-
search. While engaged in this work, he entered
the contest held by the French Academy of
Science for the best essay on methods for light-
ing the streets of a large city at night. The es-
says were divided into two groups, practical
and scientific, and while the prize was given to
entries in the first group, Lavoisier alone was
singled out from the second for special mention
and a gold medal from the King. The work with
Guettard also yielded material which Lavoisier
worked up in the form of memoires to be pre-
sented to the Academy of Science. In 1768,

after he had presented four such papers, two
on hydrometry and two on gypsum, he was
elected a member of the Academy. His youth
excited comment, and, as a friend of the family
remarked, at the age of twenty-five he had ob-
tained "a position which is usually won, with
great difficulty, by men past their fiftieth year."

Desirous of securing a larger income for re-
search, Lavoisier, shortly after his nomination
to the Academy, bought an interest in the
Ferme, an association of financiers who had the
privilege of collecting the national taxes in re-
turn for a fixed annual sum paid in advance to
the Government. His friends at the Academy
did not entirely approve of this association,
but it did provide him with the money he
sought, and it also made him acquainted with
Farmer-General Paulze, whose daughter he
married in 1771.

Lavoisier entered further into public life
when the Government took over the manufac-
ture of gunpowder. Upon his suggestion, Tur-
got, Minister of the Treasury, canceled the
private production of gunpowder and estab-
lished the Regie des poudres, a four-man admin-
istrative committee headed by Lavoisier.
With this appointment he was assigned a house
at the Arsenal, where with his own funds he
established a fully-equipped laboratory, which
he made available to all scientists interested in
his work. As his scientific fame increased, the
laboratory became a meeting place for promi-
nent scientists, and among his guests he num-
bered Priestley, Franklin, Watt, Tennant, and
Arthur Young. Lavoisier always retained an
interest in younger scientists, providing finan-
cial assistance for many and making laboratory
assistants of others, among whom was the Du-
pont who later went to America and founded
the munitions firm.

Although occupied with many practical con-
cerns in connection with the Ferme and the
Regie des poudres, Lavoisier reserved six hours
a day, from six to nine in the morning and from
seven to ten at night, for his scientific work,
and one full day each week for experiments.

BIOGRAPHICAL NOTE

His wife, who was fourteen at the time of her
marriage, became an active partner in his re-
search. She assisted in the laboratory, learned
English so as to translate the technical works
of Priestley and Cavendish, and drew the illus-
trations for the Traitt EUmentaire de Chimie
(1789). He also engaged in many works of phil-
anthropic nature, starting a model farm to
demonstrate the advantages of scientific agri-
culture, and planning the establishment of sav-
ings banks, insurance societies, canals, and work
houses for improving the conditions of the com-
munity.

When the Revolution occurred, Lavoisier had
long been a national figure. He was Director of
the Academy of Sciences, deputy to the States-
General of 1789, and a prominent member of
the club founded to promote the cause of con-
stitutional monarchy. For some years after

1789 Lavoisier continued to work as secretary
and treasurer of the commission to secure uni-
formity of weights and measures. In 1791 he
was made a member of the commission on arts
and professions; his report for this commission,
Reflexions sur l f instruction publique (1793),
presented a detailed scheme for public free ed-
ucation. But almost from the beginning of the
Revolution, Lavoisier had been under suspi-
cion because of his association with the Fernie
and R6gie des poudres, and from early 1791 he
was subjected to vitriolic attack from Marat.
In 1794 he and the other farmers-general were
placed on trial by the Revolutionary Tribunal
and condemned to death. Lavoisier and his fa-
ther-in-law were guillotined May 8, 1794, at the
Place de la Revolution and their bodies thrown
into nameless graves in the cemetery of La
Madeleine.

CONTENTS

BIOGRAPHICAL NOTE, ix
PREFACE, 1

PART I. Of the Formation and Decomposition of
Aeriform Fluids, of the Combustion of Simple
Bodies, and the Formation of Adds

I. Of the Combinations of Caloric, and the Forma-
tion of Elastic Aeriform Fluids or Oases, 9

II. General Views Relative to the Formation and
Composition of our Atmosphere, 16

III. Analysis of Atmospheric Air, and its Division
into Two Elastic Fluids; One Fit for Respira-
tion, the Other Incapable of Being Respired, 16

IV. Nomenclature of the Several Constituent Parts
of Atmospheric Air, 21

V. Of the Decomposition of Oxygen Gas by Sul-
phur, Phosphorus, and Charcoal, and of the
Formation of Acids in General, 22

VI. Of the Nomenclature of Acids in general, and
particularly of those drawn from Nitre and Sea
Salt, 25

VII. Of the Decomposition of Oxygen Gas by means
of Metals, and the Formation of Metallic
Oxides, 28

VIII. Of the Radical Principle of Water, and of its
Decomposition by Charcoal and Iron, 29

IX. Of the Quantities of Caloric disengaged from dif-
ferent Species of Combustion, 33
SECT. i. Combustion of Phosphorus, 34
SECT. ii. Combustion of Charcoal, 34
SECT. in. Combustion of Hydrogen Gas, 34
SECT. iv. Formation of Nitric Acid, 34
SECT. v. Combustion of Wax, 35
SECT. vi. Combustion of Olive Oil, 35
X. Of the Combination of Combustible Substances
with each other, 36

XI. Observations upon Oxides and Acids with sev-
eral Bases, and upon the Composition of Ani-
mal and Vegetaole Substances, 37
XII. Of the Decomposition of Vegetable and Animal
Substances by the Action of Fire, 39

XIII. Of the Decomposition of Vegetable Oxides by
the Vinous Fermentation, 41

XIV. Of the Putrefactive Fermentation, 44
XV. Of the Acetous Fermentation, 46

XVI. Of the Formation of Neutral Salts, and of their
Bases, 46

SECT. i. Of Potash, 47
SECT. ii. Of Soda, 48
SECT. in. Of Ammonia, 48
SECT. iv. Of Lime, Magnesia, Barytes, and
Argill, 48

SECT. v. Of Metallic Bodies, 49
XVII. Continuation of the Observations upon Salifi-
able Bases, and the Formation of Neutral Salts,
49

PART II. Of the Combination of Acids with Sali-
fiable Bases, and of the Formation of Neutral Salts

INTRODUCTION, 43

TABLE of Simple Substances, 53

SECT, i Observations upon Simple Substances, 54

TABLE of Compound Oxidabls and Acidifiable Bases,

SECT. ii. Observations upon Compound Radicals, 55

TABLE of the Combinations of Oxygen with the Simple
Substances, 56

SECT. in. Observations upon the Combinations of Light
and Caloric with different Substances, 57

SECT. iv. Observations upon these Combinations, 57

TABLE of the Combinations of Oxygen with Compound
Radicals, 58

SECT. v. Observations upon these Combinations, 59

TABLE of the Combinations of Azote with the Simple
Substances, 60

SECT. vi. Observations upon these Combinations of
Azote, 60

TABLE of the Binary Combinations of Hydrogen with
Simple Substances, 61

SECT. vn. Observations upon Hydrogen, and its Com-
binations, 61

TABLE of the Binary Combinations of Sulphur with
the Simple Substances, 62

SECT. viii. Observations upon Sulphur, and its Com-
binations, 63

TABLE of the Combinations of Phosphorus with Simple
Substances, 63

SECT. ix. Observations upon Phosphorus and its Com-
binations, 63

TABLE of the Binary Combinations of Charcoal, 64

SECT. x. Observations upon Charcoal, and its Combi-
nations, 64

SECT. xi. Observations upon the Muriatic, Fluoric, and
Boracic Radicals, and their Combinations, 64

SECT. xn. Observations upon the Combinations of
Metals with each other, 65

TABLE of the Combinations of Azote, in the State of
Nitrous Acid, with the SaUfiable Bases, 65

TABLE of the Combinations of Azote, in the State of
Nitric Acid, with the SaUfiable Bases, 66

SECT. xin. Observations upon Nitrous and Nitric
Acids, and their Combinations with SaUfiable Bases,
66

TABLE of the Combinations of Sulphuric Acid with
the SaUfiable Bases, 67

SECT. xiv. Observations upon Sulphuric Acid, and its
Combinations, 68

TABLE of the Combinations of Sulphurous Acid, 68

SECT. xv. Observations upon Sulphurous Acid, and
its Combinations with SaUfiable Bases, 69

TABLE of the Combinations of Phosphorous and Phos-
phoric Acids, 69

SECT. xvi. Observations upon Phosphorous and Phos-
phoric Acids, and their Combinations with SaUfi-
able Bases, 70

TABLE of the Combinations of Carbonic Add, 70

SECT. xyn. Observations upon Carbonic Add, and its
Combinations with SaUfiable Bases, 71

TABLE of the Combinations of Oxygenated Muriatic
Acid, 71

TABLE of the Combinations of Muriatic Acid, 72

SECT. xvin. Observations upon Muriatic and Oxyge-
nated Muriatic Acid, ana their Combinations with
SaUfiable Bases, 72

TABLE of the Combinations of Nitro-Muriatic Acid, 73

SECT. xix. Observations upon Nitro-Muriatic Add,
and its Combinations with SaUfiable Bases, 73

TABLE of the Combinations of Fluoric Add, 74

SECT. xx. Observations upon Fluoric Add, and its
Combinations with Scdifiable Bases, 74

TABLE of the Combinations of Boracic Add, 74

SECT. xxi. Observations upon Boracic Add, and its
Combinations with SaUfiable Bases, 74

xii LAVOISIER

TABLE of the Combinations of Arseniac Acid, 75
SECT. xxn. Observations upon Arseniac Acid, and its

Combinations with Salifiable Bases, 75
SECT. xxni. Observations upon Molibdic Acid, and

its Combinations unth Salifiable Bases, 76
SECT. xxiv. Observations upon Tungstic Acid, and its

Combinations with Salifiable Bases, and a Table of

these in the order of their Affinity, 76
TABLE of the Combinations of Tartarous Acid, 77
SECT. xxv. Observations upon Tartarous Acid, and its

Combinations with Salifiable Bases, 77
SECT. xxvi. Observations upon Malic Acid, and its

Combinations with Salifiable Bases, 77
TABLE of the Combinations of Citric Acid, 78
SECT, xxvii. Observations upon Citric Acid, and its

Combinations with Salifiable Bases, 78
TABLE of the Combinations of Pyro-lignous Acid, 78
SECT, xxvin. Observations upon Pyro-lignous Acid,

and its Combinations with Salifiable Bases, 78
SECT. xxix. Observations upon Pyro-tartarous Add,

and its Combinations with Salifiable Bases, 79
TABLE of the Combinations of Pyro-mucous Acid, 79
SECT. xxx. Observations upon Pyro-mucou* Acid, and

its Combinations with Salifiable Bases, 79
SECT. xxxi. Observations upon Oxalic Acid, and its

Combinations with Salifiable Bases, 79
TABLE of the Combinations of Oxalic Acid, 79
TABLE of the Combinations of Acetous Acid

80
SECT, xxxii. Observations upon Acetous Acid, and its

Combinations with the Salifiable Bases, 81
TABLE of the Combinations of Acetic Acid, 81
SECT, xxxiii. Observations upon Acetic Acid, and its

Combinations with Salifiable Bases, 82
TABLE of the Combinations of Succinic Add, 82
SECT, xxxiv. Observations upon Sucdnic Add, and

its Combinations with Salifiable Bases, 82
SECT. xxxv. Observations upon Benstoic Add, and its

Combinations with Salifiable Bases, 82
SECT, xxxvi. Observations upon Camphoric Add, and

its Combinations with Salifiable Bases, 83
SECT. XXXVII, Observations upon Gallic Add, and its

Combinations with Salifiable Bases, 83
SECT, xxxyin. Observations upon Lactic Add, and

its Combinations with Salifiable Bases, 83
TABLE of the Combinations of Saccho-Lactic Add, 83
SECT, xxxix. Observations upon Saccho4actic Add,

and its Combinations with Salifiable Bases, 84
TABLE of the Combinations of Formic Add, 84
SECT. XL. Observations upon Formic Add, and its

Combinations with the Salifiable Bases, 84
SECT. XLI. Observations upon the Bombic Add, and

Us Combinations with the Salifiable Bases, 84
TABLE of the Combinations of the Sebadc Add, 84
SECT. XLII. Observations upon the Sebadc Add, and

its Combinations with the Salifiable Bases, 85
SECT. XLIII. Observations upon the Lithic Add, and

its Combinations with the Salifiable Bases, 85
TABLE of the Combinations of the Prussic Add, 85
SECT. XLIV. Observations upon the Prussic Add, and

its Combinations with the Salifiable Bases, 85

PART III. Description of the Instruments and
Operations of Chemistry

INTRODUCTION, 87

I. Of the Instruments necessary for determining
the Absolute and Specific Gravities of Solid and
Liquid Bodies, 87

II. Of Gazometry, or the Measurement of the
Weight and Volume of Aeriform Substances, 90
SECT. i. Of the Pneumato-chemical Apparatus,
90

SECT. ii. Of the Gazometer, 91
i SECT. in. Some other methods for Measuring
the Volume of Gasses, 94

SECT. iv. Of the method of Separating the differ-
ent Gasses from each other, 95
SECT. v. Of the necessary Corrections of the
volume of Uases, according to the Pressure of
the Atmosphere, 96

SECT. vi. Of the Correction relative to the De-
grees of the Thermometer, 98
SECT. vn. Example for Calculating the Correc-
tions relative to the Variations of Pressure and
Temperature, 98

SECT. yiii. Method of determining the Weight
of the different Gasses, 99

III. Description of the Calorimeter, or Apparatus
for measuring Caloric, 99

IV. Of the Mechanical Operations for Division of
Bodies, 103

SECT. i. Of Trituration, Levigation, and Pul-
verization, 103
SECT. ii. Of Sifting and Washing Powdered

Substances, 104
SECT. iii. Of Filtration, 104
SECT. iv. Of Decantation, 105
V. Of Chemical means for Separating the Particles
of Bodies from each other without Decomposi-
tion, and for Uniting them again, 105
SECT. i. Of the Solution of Salts, 106
SECT. ii. Of Lixiviation r 107
SECT. in. Of Evaporation, 107
SECT. iv. Of Crystallization, 108
SECT. v. Of Simple Distillation, 110
SECT. vi. Of Sublimation, 111
VI. Of Pneumato-chemical Distillations, Metallic
Dissolutions, and some other operations which
require very complicated instruments, 111
SECT. i. Of Compound and Pneumato-chemical
Distillations 111

SECT. ii. Of Metallic Dissolutions, 113
SECT. iii. Apparatus necessary in Experiments
upon Vinous and Putrefactive Fermentations,
114

SECT. iv. Apparatus for the Decomposition of
Water, 114

VII. Of the Composition and Use of Lutes, 115
VIII. Of Operations upon Combustion and Deflagra-
tion, 117

SECT. i. Of Combustion in general, 117
SECT. n. Of the Combustion of Phosphorus, 118
SECT. in. Of the Combustion of Charcoal, 119
SECT. iv. Of the Combustion of Oils, 120
SECT. v. Of the Combustion of Alcohol, 122
SECT. vi. Of the Combustion of Ether, }22
SECT. vn. Of the Combustion of Hydrogen
Gas, and the Formation of Water, 123
SECT. vin. Of the Oxidation of Metals, 124
IX. Of Deflagration, 126

X. Of the Instruments necessary for Operating
upon Bodies in very high Temperatures, 128
SECT. i. Of Fusion, 128
SECT. n. Of Furnaces, 129
SECT. in. Of increasing the Action of Fire, by
using Oxygen Gaa instead of Atmospheric
Air, 132

PLATES I XIII, 135

PREFACE

WHEN I began the following work, my only
object was to extend and explain more fully the
memoir which I read at the public meeting of
the Academy of Sciences in the month of April,
1787, on the necessity of reforming and com-
pleting the nomenclature of chemistry. While
engaged in this employment, I perceived, bet-
ter than I had ever done before, the justice of
the following maxims of the Abb de Condillac,
in his Logic, and some other of his works.

"We think only through the medium of
words. Languages are true analytical meth-
ods. Algebra, which is adapted to its purpose
in every species of expression, in the most sim-
ple, most exact, and best manner possible, is at
the same time a language and an analytical
method. The art of reasoning is nothing more
than a language well arranged."

Thus, while I thought myself employed only
in forming a nomenclature, and while I propos-
ed to myself nothing more than to improve the
chemical language, my work transformed itself
by degrees, without my being able to prevent it,
into a treatise upon the elements of chemistry.

The impossibility of separating the nomen-
clature of a science from the science itself is
owing to this, that every branch of physical
science must consist of three things : the series
of facts which are the objects of the science,
the ideas which represent these facts, and the
words by which these ideas are expressed. Like
three impressions of the same seal, the word
ought to produce the idea, and the idea to be a
picture of the fact. And, as ideas are preserved
and communicated by means of words, it nec-
essarily follows that we cannot improve the
language of any science without at the same
time improving the science itself; neither can
we, on the other hand, improve a science with-
out improving the language or nomenclature
which belongs to it. However certain the facts
of any science may be and however just the
ideas we may have formed of these facts, we

can only communicate false impressions to
others while we want words by which these
may be properly expressed.

To those who will consider it with attention,
the first part of this treatise will afford frequent
proofs of the truth of the above observations.
But as, in the conduct of my work, I have been
obliged to observe an order of arrangement es-
sentially differing from what has been adopted
in any other chemical work yet published, it is
proper that I should explain the motives which
have led me to do so.

It is a maxim universally admitted in geom-
etry, and indeed in every branch of knowledge,
that, in the progress of investigation, we should
proceed from known facts to what is unknown.
In early infancy, our ideas spring from our
wants; the sensation of want excites the idea of
the object by which it is to be gratified. In this
manner, from a series of sensations, observa-
tions, and analyses, a successive train of ideas
arises, so linked together that an attentive ob-
server may trace back to a certain point the
order and connection of the whole sum of hu-
man knowledge.

When we begin the study of any science, we
are in a situation, respecting that science, simi-
lar to that of children; and the course by which
we have to advance is precisely the same which
nature follows in the formation of their ideas.
In a child, the idea is merely an effect produced
by a sensation; and, in the same manner, in
commencing the study of a physical science,
we ought to form no idea but what is a neces-
sary consequence, and immediate effect, of an
experiment or observation. Besides, he that en-
ters upon the career of science is in a less ad-
vantageous situation than a child who is ac-
quiring his first ideas. To the child, nature
gives various means of rectifying any mistakes
he may commit respecting the salutary or hurt-
ful qualities of the objects which surround him.
On every occasion his judgments are corrected

LAVOISIER

by experience; want and pain are the necessary
consequences arising from false judgment ; grat-
ification and pleasure are produced by judging
aright. Under such masters, we cannot fail to
become well informed; and we soon learn to
reason justly, when want and pain are the
necessary consequences of a contrary conduct.
. In the study and practice of the sciences it is
quite different; the false judgments we form
neither affect our existence nor our welfare;
and we are not forced by any physical neces-
sity to correct them. Imagination, on the con-
trary, which is ever wandering beyond the
bounds of truth, joined to self-love and that
self-confidence we are so apt to indulge, prompts
us to draw conclusions which are not immedi-
ately derived from facts; so that we become in
some measure interested in deceiving ourselves.
Hence, it is by no means to be wondered that, in
the science of physics in general, men have
often made suppositions instead of forming
conclusions. These suppositions, handed down
from one age to another, acquire additional
weight from the authorities by which they are
supported, till at last they are received, even
by men of genius, as fundamental truths.

The only method of preventing such errors
from taking place, and of correcting them when
formed, is to restrain and simplify our reason-
ing as much as possible. This depends entirely
upon ourselves, and the neglect of it is the only
source of our mistakes. We must trust to noth-
ing but facts : these are presented to us by na-
ture and cannot deceive. We ought, in every
instance, to submit our reasoning to the test of
experiment and never to search for truth but
by the natural road of experiment and observa-
tion. Thus mathematicians obtain the solution
of a problem by the mere arrangement of data
and by reducing their reasoning to such simple
steps, to conclusions so very obvious, as never
to lose sight of the evidence which guides them.

Thoroughly convinced of these truths, I have
imposed upon myself, as a law, never to ad-
vance but from what is known to what is un-
known; never to form any conclusion which is
not an immediate consequence necessarily
flowing from observation and experiment; and
always to arrange the facts, and the conclu-
sions which are drawn from them, in such an
order as shall render it most easy for beginners

in the study of chemistry thoroughly to under-
stand them. Hence, I have been obliged to de-
part from the usual order of courses of lectures
and of treatises upon chemistry, which always
assume the first principles of the science as
known, when the pupil or the reader should
never be supposed to know them till they have
been explained in subsequent lessons. In al-
most every instance, these begin by treating of
the elements of matter and by explaining the
table of affinities, without considering that, in
so doing, they must bring the principal phe-
nomena of chemistry into view at the very out-
set: they make use of terms which have not
been defined and suppose the science to be un-
derstood by the very persons they are only be-
ginning to teach. It ought likewise to be con-
sidered that very little of chemistry can be
learned in a first course, which is hardly suffi-
cient to make the language of the science famil-
iar to the ears or the apparatus familiar to
the eyes. It is almost 4 impossible to become a
chemist in less than three or four years of con-
stant application.

These inconveniences are occasioned not so
much by the nature of the subject as by the
method of teaching it; and, to avoid them, I
was chiefly induced to adopt a new arrange-
ment of chemistry, which appeared to me more
consonant to the order of nature. I acknowl-
edge, however, that in thus endeavouring to
avoid difficulties of one kind I have found my-
self involved in others of a different species,
some of which I have not been able to remove;
but I am persuaded that such as remain do not
arise from the nature of the order I have
adopted, but are rather consequences of the
imperfection under which chemistry still la-
bours. This science still has many chasms,
which interrupt the series of facts and often
render it extremely difficult to reconcile them
with each other: it has not, like the elements
of geometry, the advantage of being a com-
plete science, the parts of which are all closely
connected together: its actual progress, how-
ever, is so rapid, and the facts, under the mod-
ern doctrine, have assumed so happy an ar-
rangement that we have ground to hope, even
in our own times, to see it approach near to the
highest state of perfection of which it is sus-
ceptible.

PREFACE

The rigorous law from which I have never
deviated, of forming no conclusions which are
not fully warranted by experiment, and of nev-
er supplying the absence of facts, has prevent-
ed me from comprehending in this work the
branch of chemistry which treats of affinities,
although it is perhaps the best calculated of
any part of chemistry for being reduced into a
completely systematic- foody. MM. Geoffrey,
Gellert, Bergman, Scheele, de Morveau, Kir-
wan, and many others, have collected a num-
ber of particular facts upon this subject, which
only wait for a proper arrangement; but the
principal data are still wanting, or, at least,
those we have are either not sufficiently de-
fined or not sufficiently proved to become the
foundation upon which to build so very impor-
tant a branch of chemistry. This science of af-
finities, or elective attractions, holds the same
place with regard to the other branches of
chemistry as the higher or transcendental ge-
ometry does with respect to the simpler and
elementary part; and I thought it improper
to involve those simple and plain elements,
which I flatter myself the greatest part of my
readers will easily understand, in the obscurities
and difficulties which still attend that other
very useful and necessary branch of chemical
science.

Perhaps a sentiment of self-love may, with-
out my perceiving it, have given additional
force to these reflections. Mr. de Morveau is at
present engaged in publishing the article Affin-
ity in the Methodical Encyclopedia and I had
more reasons than one to decline entering upon
a work in which he is employed.

It will, no doubt, be a matter of surprise,
that in a treatise upon the elements of chem-
istry there should be no chapter on the con-
stituent and elementary parts of matter; but I
shall take occasion, in this place, to remark
that the fondness for reducing all the bodies in
nature to three or four elements proceeds from
a prejudice which has descended to us from the
Greek philosophers. The notion of four ele-
ments, which, by the variety of their propor-
tions, compose all the known substances in na-
ture, is a mere hypothesis, assumed long before
the first principles of experimental philosophy
or of chemistry had any existence. In those
days, without possessing facts, they framed

systems; while we, who have collected facts,
seem determined to reject them when they do
not agree with our prejudices. The authority
of these fathers of human philosophy still carry
great weight, and there is reason to fear that it
will even bear hard upon generations yet to
come.

It is very remarkable that, notwithstanding
the number of philosophical chemists who have
supported the doctrine of the four elements,
there is not one who has not been led by the
evidence of facts to admit a greater number of
elements into their theory. The first chemists
that wrote after the revival of letters consid-
ered sulphur and salt elementary substances
entering into the composition of a great num-
ber of substances; hence, instead of four, they
admitted the existence of six elements. Beccher
assumes the existence of three kinds of earth,
from the combination of which, in different
proportions, he supposed all the varieties of
metallic substances to be produced. Stahl gave
a new modification to this system; and suc-
ceeding chemists have taken the liberty to
make or to imagine changes and additions of a
similar nature. All these chemists were carried
along by the influence of the genius of the age
in which they lived, which contented itself with
assertions without proofs; or, at least, often ad-
mitted as proofs the slightest degrees of prob-
ability, unsupported by that strictly rigorous
analysis required by modern philosophy.

All that can be said upon the number and na-
ture of elements is, in my opinion, confined to
discussions entirely of a metaphysical nature.
The subject only furnishes us with indefinite
problems, which may be solved in a thousand
different ways, not one of which, in ail proba-
bility, is consistent with nature. I shall there-
fore only add upon this subject that if by the
term elements we mean to express those simple
and indivisible atoms of which matter is com-
posed, it is extremely probable we know noth-
ing at all about them; but, if we apply the term
elements, or principles of bodies, to express our
idea of the last point which analysis is capable
of reaching, we must admit, as elements, all the
substances into which we are capable, by any
means, to reduce bodies by decomposition. Not
that we are entitled to affirm that these sub-
stances we consider as simple may not be com-

LAVOISIER

pounded of two, or even of a greater number of
principles; but, since these principles cannot be
separated, or rather since we have not hitherto
discovered the means of separating them, they
act with regard to us as simple substances, and
we ought never to suppose them compounded
until experiment and observation has proved
them to be so.

The foregoing reflections upon the progress
of chemical ideas naturally apply to the words
by which these ideas are to be expressed. Guid-
ed by the work which, in the year 1787, Messrs.
de Morveau, Berthoiiet, de Fourcroy, and I
composed upon the nomenclature of chemistry,
I have endeavoured, as much as possible, to de-
nominate simple bodies by simple terms, and I
was naturally led to name these first. It will be
recollected that we were obliged to retain that
name of any substance by which it had been
long known in the world, and that in two cases
only we took the liberty of making alterations ;
first, in the case of those which were but newly
discovered and had not yet obtained names, or
at least which had been known but for a short
time and the names of which had not yet re-
ceived the sanction of the public; and, second-
ly, when the names which had been adopted,
whether by the ancients or the moderns, ap-
peared to us to express evidently false ideas,
when they confounded the substances to which
they were applied with others possessed of dif-
ferent or perhaps opposite qualities. We made
no scruple, in this case, of substituting other
names in their room, and the greatest number
of these were borrowed from the Greek lan-
guage. We endeavoured to frame them in such
a manner as to express the most general and
the most characteristic quality of the sub-
stances; and this was attended with the addi-
tional advantage both of assisting the memory
of beginners, who find it difficult to remember
a new word which has no meaning, and of
accustoming them early to admit no word
without connecting with it some determinate
idea.

To those bodies which are formed by the un-
ion of several simple substances we gave new
names, compounded in such a manner as the
nature of the substances directed; but, as the
number of double combinations is already very
considerable, the only method by which we

could avoid confusion was to divide them into
classes. In the natural order of ideas, the name
of the class or genus is that which expresses a
quality common to a great number of individ-
uals : the name of the species, on the contrary,
expresses a quality peculiar to certain individ-
uals only.

These distinctions are not, as some may imag-
ine, merely metaphysical, but are established
by nature. "A child," says the Abbe* de Con-
dillac, " is taught to give the name tree to the
first one which is pointed out to him. The next
one he sees presents the same idea, and he gives
it the same name. This he does likewise to a
third and a fourth, till at last the word tree,
which he first applied to an individual, comes
to be employed by him as the name of a class
or a genus, an abstract idea, which comprehends
all trees in general. But, when he learns that all
trees serve not the same purpose, that they do
not all produce the same kind of fruit, he will
soon learn to distinguish them by specific and
particular names." This is the logic of all the
sciences and is naturally applied to chemistry.

The acids, for example, are compounded of
two substances, of the order of those which we
consider as simple; the one constitutes acidity,
and is common to all acids, and, from this sub-
stance, the name of the class or the genus ought
to be taken; the other is peculiar to each acid,
and distinguishes it from the rest, and from this
substance is to be taken the name of the spe-
cies. But, in the greatest number of acids, the
two constituent elements, the acidifying prin-
ciple and that which it acidifies, may exist in
different proportions, constituting all the pos-
sible points of equilibrium or of saturation. This
is the case in the sulphuric and the sulphurous
acids; and these two states of the same acid we
have marked by varying the termination of the
specific name.

Metallic substances which have been exposed
to the joint action of the air and of fire lose
their metallic lustre, increase in weight, and as-
sume an earthy appearance. In this state, like
the acids, they are compounded of a principle
which is common to all and one which is pecu-
liar to each. In the same way, therefore, we
have thought proper to class them under a ge-
neric name, derived from the common princi-
ple; for which purpose, we adopted the term ox-

PREFACE

ide; and we distinguish them from each other
by the particular name of the metal to which
each belongs.

Combustible substances, which in acids and
metallic oxides are a specific and particular
principle, are capable of becoming, in their turn
common principles of a great number of sub-
stances. The sulphurous combinations have
been long the only known ones in this kind.
Now, however, we know, from the experiments
of Messrs. Vandermonde, Monge, and Berthol-
let, that charcoal may be combined with iron,
and perhaps with several other metals, and that,
from this combination, according to the pro-
portions, may be produced steel, plumbago, &c.
We know likewise, from the experiments of M.
Pelletier, that phosphorus may be combined
with a great number of metallic substances.
These different combinations we have classed
under generic names taken from the common
substance, with a termination which marks
this analogy, specifying them by another name
taken from that substance which is proper
to each.

The nomenclature of bodies compounded of
three simple substances was attended with still
greater difficulty, not only on account of their
number, but, particularly, because we cannot
express the nature of their constituent princi-
ples without employing more compound names.
In the bodies which form this class, such as the
neutral salts for instance, we had to consider,
1st, the acidifying principle, which is common
to them all; 2nd, the acidifiable principle which
constitutes their peculiar acid; 3rd, the saline,
earthy, or metallic basis, which determines the
particular species of salt. Here we derived the
name of each class of salts from the name of the
acidifiable principle common to all the individ-
uals of that class and distinguished each spe-
cies by the name of the saline, earthy, or metal-
lic basis, which is peculiar to it.

A salt, though compounded of the same three
principles, may, nevertheless, by the mere dif-
ference of their proportion, be in three different
states. The nomenclature we have adopted
would have been defective had it not expressed
these different states ; and this we attained chief-
ly by changes of termination uniformly applied
to the same state of the different salts.

In short, we have advanced so far that from

the name alone may be instantly found what
the combustible substance is which enters into
any combination; whether that combustible
substance be combined with the acidifying prin-
ciple, and in what proportion; what is the state
of the acid ; with what basis it is united; wheth-
er the saturation be exact, or whether the acid
or the basis be in excess.

It may be easily supposed that it was not
possible to attain all these different obj ects with-
out departing, in some instances, from estab-
lished custom and adopting terms which at first
sight will appear uncouth and barbarous. But
we considered that the ear is soon habituated
to new words, especially when they are con-
nected with a general and rational S3 r stem. The
names, besides, which were formerly employed,
such as powder ofalgarothj salt ofalembroth, pom-
pholix, phagadenic water, turbith mineral, colco-
thar, and many others, were neither less bar-
barous nor less uncommon. It required a great
deal of practice, and no small degree of mem-
ory, to recollect the substances to which they
were applied, much more to recollect the genus
of combination to which they belonged. The
names of oil of tartar per deliquium, oil of vitriol,
butter of arsenic and of antimony, flowers of zinc>
&c. were still more improper, because they sug-
gested false ideas: for, in the whole mineral
kingdom, and particularly in the metallic class,
there exist no such things as gutters, oils, or
flowers; and, in short, the substances to which
they give these fallacious names are nothing
less than rank poisons.

When we published our essay on the nomen-
clature of chemistry, we were reproached for
having changed the language which was spok-
en by our masters, which they distinguished by
their authority and handed down to us. But
those who reproach us on this account have for-
gotten that it was Bergman and Macquer them-
selves who urged us to make this reformation.
In a letter which the learned Professor of Upp-
sala, M. Bergman, wrote, a short time before
he died, to M. de Morveau, he bids him spare
no improper names; those who are learned will al-
ways be learned, and those who are ignorant will
thus karn sooner.

There is an objection to the work which I am
going to present to the public, which is perhaps
better founded, that I have given no account of

LAVOISIER

the opinion of those who have gone before me;
that I have stated only my own opinion, with-
out examining that of others. By this I have
been prevented from doing that justice to my
associates, and more especially to foreign chem-
ists, which I wished to render them. But I be-
seech the reader to consider that, if I had filled
an elementary work with a multitude of quota-
tions, if I had allowed myself to enter into long
dissertations on the history of the science and
the works of those who have studied it, I must
have lost sight of the true object I had in view
and produced a work the reading of which must
have been extremely tiresome to beginners. It
is not to the history of the science, or of the hu-
man mind, that we are to attend in an elemen-
tary treatise : our only aim ought to be ease and
perspicuity and with the utmost care to keep
everything out of view which might draw aside
the attention of the student; it is a road which
we should be continually rendering more
smooth, and from which we should endeavour
to remove every obstacle which can occasion
delay. The sciences, from their own nature, pre-
sent a sufficient number of difficulties, though
we add not those which are foreign to them.
But, besides this, chemists will easily perceive
that, in the first part of my work, I make very
little use of any experiments but those which
were made by myself: if at any time I have
adopted, without acknowledgment, the experi-
ments or the opinions of M. Berthollet, M.
Fourcroy, M. de la Place, M. Monge, or, in
general, of any of those whose principles are the
same as my own, it is owing to this circum-
stance, that frequent intercourse, and the hab-
it of communicating our ideas, our observa-
tions, and our way of thinking to each other,
has established between us a sort of community
of opinions in which it is often difficult for every
one to know his own.

The remarks I have made on the order which
I thought myself obliged to follow in the ar-
rangement of proofs and ideas are to be applied
only to the first part of this work. It is the only
one which contains the general sum of the doc-
trine I have adopted and to which I wished to
give a form completely elementary.

The second part is composed chiefly of tables
of the nomenclature of the neutral salts. To
these I have only added general explanations,

the object of which was to point out the most
simple processes for obtaining the different
kinds of known acids. This part contains noth-
ing which I can call my own and presents only
a very short abridgment of the results of these
processes, extracted from the works of different
authors.

In the third part, I have given a description,
in detail, of all the operations connected with
modern chemistry. I have long thought that a
work of this kind was much wanted, and I am
convinced it will not be without use. The meth-
od of performing experiments, and particularly
those of modern chemistry, is not so generally
known as it ought to be; and had I, in the dif-
ferent Mtmoires which I have presented to the
Academy, been more particular in the detail of
the manipulations of my experiments, it is prob-
able I should have made myself better under-
stood, and the science might have made a more
rapid progress. The order of the different mat-
ters contained in this third part appeared to me
to be almost arbitrary; and the only one I have
observed was to class together, in each of the
chapters of which it is composed, those opera-
tions which are most connected with one an-
other. I need hardly mention that this part
could not be borrowed from any other work,
and that, in the principal articles it contains, I
could not derive assistance from anything but
the experiments which I have made myself.

I shall conclude this preface by transcribing,
literally, some observations of the Abb6 de
Condillac, which I think describe, with a good
deal of truth, the state of chemistry at a
period not far distant from our own. These
observations were made on a different sub-
ject; but they will not, on this account, have
less force, if the application of them be thought
just.

"Instead of applying observation to the
things we wished to know, we have chosen
rather to imagine them. Advancing from one ill-
founded supposition to another, we have at last
bewildered ourselves amidst a multitude of er-
rors. These errors becoming prejudices, are, of
course, adopted as principles, and we thus be-
wilder ourselves more and more. The method,
too, by which we conduct our reasonings is as
absurd; we abuse words which we do not un-
derstand, and call this the art of reasoning.

PREFACE

When matters have been brought this length,
when errors have been thus accumulated, there
is but one remedy by which order can be re-
stored to the faculty of thinking; this is to for-
get all that we have learned, to trace back our
ideas to their source, to follow the train in
which they rise, and, as Bacon says, to frame
the human understanding anew.

"This remedy becomes the more difficult in
proportion as we think ourselves more learned.
Might it not be thought that works which treat-
ed of the sciences with the utmost perspicuity,
with great precision and order, must be under-

stood by everybody? The fact is, those who
have never studied anything will understand
them better than those who have studied a
great deal, and especially than those who have
written a great deal."

At the end of the fifth chapter, the Abb6 de
Condillac adds: "But, after all, the sciences
have made progress, because philosophers have
applied themselves with more attention to ob-
serve and have communicated to their lan-
guage that precision and accuracy which they
have employed in their observations. In cor-
recting their language they reason better."

FIRST PART

OF THE FORMATION AND DECOMPOSITION OF AERIFORM

FLUIDS OF THE COMBUSTION OF SIMPLE BODIES,

AND THE FORMATION OF ACIDS

CHAPTER I

Of the Combinations of Caloric, and the Forma-
tion of Elastic Aeriform Fluids or gases

THAT every body, whether solid or fluid, is aug-
mented in all its dimensions by any increase of
its sensible heat was long ago fully established
as a physical axiom, or universal proposition,
by the celebrated Boerhaave. Such facts as
have been adduced for controverting the gen-
erality of this principle offer only fallacious re-
sults, or, at least, such as are so complicated
with foreign circumstances as to mislead the
j udgment : but, when we separately consider the
effects, so as to deduce each from the cause to
which they separately belong, it is easy to per-
ceive that the separation of particles by heat is
a constant and general law of nature.

When we have heated a solid body to a cer-
tain degree and have thereby caused its parti-
cles to separate from each other, if we allow
the body to cool, its particles again approach
each other in the same proportion in which
they were separated by the increased tempera-
ture; the body returns through the same de-
grees of expansion which it before extended
through; and, if it be brought back to the same
temperature from which we set out at the com-
mencement of the experiment, it recovers ex-
actly the same dimensions which it formerly oc-
cupied. But, as we are still very far from being
able to arrive at the degree of absolute cold, or
deprivation of all heat, being unacquainted with
any degree of coldness which we cannot sup-
pose capable of still further augmentation, it
follows that we are still incapable of causing
the ultimate particles of bodies to approach each
other as near as is possible and, consequently,
that the particles of all bodies do not touch
each other in any state hitherto known, which,
tho' a very singular conclusion, is yet impossi-
ble to be denied.

It is supposed that, since the particles of bo-
dies are thus continually impelled by heat to

separate from each other, they would have no
connection between themselves and, of conse-
quence, that there could be no solidity in na-
ture, unless they were held together by some
other power which tends to unite them, and,
so to speak, to chain them together ; which pow-
er, whatever be its cause or manner of opera-
tion, we name attraction.

Thus the particles of all bodies may be con-
sidered as subjected to the action of two oppo-
site powers, the one repulsive, the other attrac-
tive, between which they remain in equilibrio.
So long as the attractive force remains strong-
er, the body must continue in a state of solid-
ity; but if, on the contrary, heat has so far
removed these particles from each other as to
place them beyond the sphere of attraction,
they lose the adhesion they before had with each
other, and the body ceases to be solid.

Water gives us a regular and constant ex-
ample of these facts; whilst below zero 1 of the
French thermometer, or 32 of Fahrenheit, it
remains solid, and is called ice. Above that de-
gree of temperature, its particles being no long-
er held together by reciprocal attraction, it
becomes liquid ; and, when we raise its tempera-
ture above 80 (212), its particles, giving way
to the repulsion caused by the heat, assume the
state of vapour or gas, and the water is changed
into an aeriform fluid.

The same may be affirmed of all bodies in
nature: they are either solid or liquid, or in the
state of elastic aeriform vapour, according to
the proportion which takes place between the
attractive force inherent in their particles, and
the repulsive power of the heat acting upon
these; or, which amounts to the same thing, in
proportion to the degree of heat to which they
are exposed.

It is difficult to comprehend these phenom-

1 Whenever the degree of heat occurs in this work,
it is stated by the author according to Reaumur's
scale. The degrees within parentheses are the corre-
spondent degrees of Fahrenheit's scale, added by the
translator. TRANSLATOB.

LAVOISIER

ena, without admitting them as the effects of a
real and material substance, or very subtile
fluid, which, insinuating itself between the par-
ticles of bodies, separates them from each
other; and, even allowing the existence of this
fluid to be hypothetical, we shall see in the se-
quel that it explains the phenomena of nature
in a very satisfactory manner.

This substance, whatever it is, being the
cause of heat, or, in other words, the sensation
which we call warmth being caused by the ac-
cumulation of this substance, we cannot, in
strict language, distinguish it by the term heat;
because the same name would then very im-
properly express both cause and effect. For
this reason, in the Memoir which I published
in 1777 1 , I gave it the names of igneous fluid
and matter of heat: And, since that time, in the
work 2 published by M. de Morveau, M. Ber-
thollet, M. de Fourcroy, and myself, upon the
reformation of chemical nomenclature, we
thought it necessary to banish all periphrastic
expressions, which both lengthen physical lan-
guage and render it more tedious and less dis-
tinct, and which even frequently does not con-
vey sufficiently just ideas of the subject in-
tended. Wherefore, we have distinguished the
cause of heat, or that exquisitely elastic fluid
which produces it, by the term of caloric. Be-
sides that this expression fulfils our object in
the system which we have adopted, it possesses
this further advantage, that it accords with
every species of opinion, since, strictly speak-
ing, we are not obliged to suppose this to be a
real substance; it being sufficient, as will more
clearly appear in the sequel of this work, that
it be considered as the repulsive cause, what-
ever that may be, which separates the particles
of matter from each other, so that we are still
at liberty to investigate its effects in an ab-
stract and mathematical manner.

In the present state of our knowledge, we
are unable to determine whether light be a
modification of caloric, or if caloric be, on the
contrary, a modification of light. This, how-
ever, is indisputable, that, in a system where
only decided facts are admissible, and where
we avoid, as far as possible, to suppose any
thing to be that is not really known to exist,
we ought provisionally to distinguish, by dis-
tinct terms, such things as are known to
produce different effects. We therefore distin-
guish light from caloric ; though we do not there-

1 Collections of the French Academy of Sciences
for that year, p. 420.
8 Chemical Nomenclature.

fore deny that these have certain qualities in
common, and that, in certain circumstances,
they combine with other bodies almost in the
same manner, and produce, in part, the same
effects.

What I have already said may suffice to de-
termine the idea affixed to the word caloric;
but there remains a more difficult attempt,
which is to give a just conception of the man-
ner in which caloric acts upon other bodies.
Since this subtile matter penetrates through
the pores of all known substances ; since there
are no vessels through which it cannot escape,
and, consequently, as there are none which are
capable of retaining it, we can only come at
the knowledge of its properties by effects
which are fleeting and with difficulty ascer-
tainable. It is in these things which we neither
see nor feel that it is especially necessary to
guard against the extravagance of our imagi-
nation, which forever inclines to step beyond the
bounds of truth and is with great difficulty re-
strained within the narrow line of facts.

We have already seen that the same body be-
comes solid, or fluid, or aeriform, according to
the quantity of caloric by which it is penetrat-
ed; or, to speak more strictly, according as the
repulsive force exerted by the caloric is equal
to, stronger, or weaker, than the attraction of
the particles of the body it acts upon.

But, if these two powers only existed, bodies
would become liquid at an indivisible degree of
the thermometer and would almost instan-
taneously pass from the solid state of aggrega-
tion to that of aeriform elasticity. Thus water,
for instance, at the very moment when it
ceases to be ice, would begin to boil, and would
be transformed into an aeriform fluid, having
its particles scattered indefinitely through the
surrounding space. That this does not happen
must depend upon the action of some third
power. The pressure of the atmosphere pre-
vents this separation, and causes the water to
remain in the liquid state till it be raised to 80
of temperature (212) above zero of the French
thermometer, the quantity of caloric which it
receives in the lowest temperature being insuf-
ficient to overcome the pressure of the atmos-
phere.

Whence it appears that, without this atmos-
pheric pressure, we should not have any per-
manent liquid and should only be able to see
bodies in that state of existence in the very in-
stant of melting, as the smallest additional
caloric would instantly separate their particles
and dissipate them through the surrounding

CHEMISTRY

medium. Besides, without this atmospheric
pressure we should not even have any aeriform
fluids, strictly speaking, because the moment
the force of attraction is overcome by the re-
pulsive power of the caloric the particles would
separate themselves indefinitely, having noth-
ing to give limits to their expansion, unless
their own gravity might collect them together,
so as to form an atmosphere.

Simple reflection upon the most common ex-
periments is sufficient to evince the truth of
these positions. They are more particularly
proved by the following experiment, which I
published in the Recueil de V Acadtmie for
1777, p. 426.

Having filled with sulphuric ether 1 a small
narrow glass vessel A (Plate vu, Fig. 77),
standing upon its stalk P, the vessel, which is
from twelve to fifteen lines 2 diameter, is to be
covered by a wet bladder, tied round its neck
with several turns of strong thread; for greater
security, fix a second bladder over the first. The
vessel should be filled in such a manner with
the ether as not to leave the smallest portion of
air between the liquor and the bladder. It is
now to be placed under the recipient BCD of
an air-pump, of which the upper part B ought
to be fitted with a leathern lid, through which
passes a wire EF, having its point F very sharp;
and in the same receiver there ought to be
placed the barometer GH. The whole being
thus disposed, let the recipient be exhausted,
and then, by pushing down the wire EF, we
make a hole in the bladder. Immediately the
ether begins to boil with great violence and is
changed into an elastic aeriform fluid which
fills the receiver. If the quantity of ether be
sufficient to leave a few drops in the phial after
the evaporation is finished, the elastic fluid pro-
duced will sustain the mercury in the barom-
eter attached to the airpump, at eight or ten
inches in winter, and from twenty to twenty-
five in summer. To render this experiment more
complete, we may introduce a small thermom-
eter into the phial A, containing the ether, which
will descend considerably during the evapora-
tion.

The only effect produced in this experiment
is the taking away the weight of the atmos-
phere, which, in its ordinary state, presses on

1 As I shall afterwards give a definition, and ex-
plain the properties of the liquor called ether, I shall
only premise here, that it is a very volatile in-
flammable liquor, having a considerably smaller
specific gravity than water, or even spirit of wine.
AUTHOB.

> Line (from the French ligne) equals one-twelfth
of an inch. EDITOB.

the surface of the ether; and the effects result-
ing from this removal evidently prove that, in
the ordinary temperature of the earth, ether
would always exist ifr an aeriform state, but
for the pressure of the atmosphere, and that
the passing of the ether from the liquid to the
aeriform state is accompanied by a consider-
able lessening of heat; because, during the
evaporation, a part of the caloric, which was
before in a free state, or at least in equili-
brio in the surrounding bodies, combines with
the ether and causes it to assume the aeriform
state.

The same experiment succeeds with ail evap-
orable fluids, such as alcohol, water, and even
mercury with this difference, that the atmos-
phere formed in the receiver by alcohol only
supports the attached barometer about one
inch in winter, and about four or five inches in
summer; that formed by water, in the same
situation, raises the mercury only a few lines,
and that by quicksilver but a few fractions of
a line. There is therefore less fluid evaporated
from alcohol than from ether, less from water
than from alcohol, and still less from mercury
than from either; consequently there is less
caloric employed, and less cold produced, which
quadrates exactly with the results of these
experiments.

Another species of experiment proves very
evidently that the aeriform state is a modifica-
tion of bodies dependent on the degree of tem-
perature and on the pressure which these bod-
ies undergo. In a Memoire read by M. de La*
place and me to the Academy in 1777, which
has not been printed, we have shown that,
when ether is subjected to a pressure equal
to twenty-eight inches of the barometer or
about the medium pressure of the atmosphere,
it boils at the temperature of about 32 P (104),
or 33 (106.25), of the thermometer. M. de
Luc, who has made similar experiments with
spirit of wine, finds it boils at 67 (182.75).
And all the world knows that water boils at 80
(212) . Now, boiling being only the evaporation
of a liquid, or the moment of its passing frbm
the fluid to the aeriform state, it is evident
that, if we keep ether continually at the tem-
perature of 33 (106.25), and under the com-
mon pressure of the atmosphere, we shall have
it always in an elastic aeriform state; and that
the same thing will happen with alcohol when
above 67 (182.75), and with water when
above 80 (212); all which are perfectly con-
formable to the following experiment. 8

a Vid* Recueil de V Academic, 1780, p. 335.

LAVOISIER

I filled a large vessel ABCD (Plate vn, Fig.
16) with water at 35 (110.75), or 36 (113);
I suppose the vessel transparent, that we may
see what takes place in the experiment; and we
can easily hold the hands in water at that tem-
perature without inconvenience. Into it I
plunged some narrow necked bottles F, G,
which were filled with the water, after which
they were turned up, so as to rest on their
mouths on the bottom of the vessel. Having
next put some ether into a very small matrass,
with its neck a b c, twice bent as in the Plate, I
plunged this matrass into the water so as to
have its neck inserted into the mouth of one of
the bottles F. Immediately upon feeling the ef-
fects of the heat communicated to it by the
water in the vessel ABCD it began to boil ; and
the caloric, entering into combination with it,
changed it into elastic aeriform fluid, with
which I filled several bottles successively, F,
G, &c.

This is not the place to enter upon the ex-
amination of the nature and properties of this
aeriform fluid, which is extremely inflammable ;
but, confining myself to the object at present
in view, without anticipating circumstances
which I am not to suppose the reader to know,
I shall only observe that the ether, from this
experiment, is almost only capable of existing
in the aeriform state in our world; for, if the
weight of our atmosphere was only equal to
between 20 and 24 inches of the barometer, in-
stead of 28 inches, we should never be able to
obtain ether in the liquid state, at least in sum-
mer; and the formation of ether would conse-
quently be impossible upon mountains of a
moderate degree of elevation, as it would be
converted into gas immediately upon being
produced, unless we employed recipients of ex-
traordinary strength, together with refrigera-
tion and compression. And, lastly, the temper-
ature of the blood being nearly that at which
ether passes from the liquid to the aeriform
state, it must evaporate in the primae viae,
and consequently it is very probable the medi-
cal properties of this fluid depend chiefly upon
its mechanical effect.

These experiments succeed better with ni-
trous ether, because it evaporates in a lower
temperature than sulphuric ether. It is more
difficult to obtain alcohol in the aeriform state
because, as it requires 67 (182.75) to reduce
it to vapour, the water of the bath must be
almost boiling, and consequently it is impos-
sible to plunge the hands into it at that temper-
ature.

It is evident that, if water were used in the
foregoing experiment, it would be changed into
gas when exposed to a temperature superior to
that at which it boils. Although thoroughly
convinced of this, M. de Laplace and myself
judged it necessary to confirm it by the follow-
ing direct experiment. We filled a glass jar A
(Plate vn, Fig. 5.} with mercury, and placed
it with its mouth downwards in a dish B, like-
wise filled with mercury, and having intro-
duced about two gross of water into the jar,
which rose to the top of the mercury at CD,
we then plunged the whole apparatus into an
iron boiler, EFGH, full of boiling sea-water of
the temperature of 85 (123.25), placed upon
the furnace GHIK. Immediately upon the wa-
ter over the mercury attaining the tempera-
ture of 80 (212), it began to boil ; and, instead
of only filling the small space ACD, it was con-
verted into an aeriform fluid which filled the
whole jar; the mercury even descended below
the surface of that in the dish B; and the jar
must have been overturned if it had not been
very thick and heavy and fixed to the dish by
means of iron wire. Immediately after with-
drawing the apparatus from the boiler, the va-
pour in the jar began to condense, and the mer-
cury rose to its former station; but it returned
again to the aeriform state a few seconds after
replacing the apparatus in the boiler.

We have thus a certain number of sub-
stances, which are convertible into elastic aeri-
form fluids by degrees of temperature not much
superior to that of our atmosphere. We shall
afterwards find that there are several others
which undergo the same change in similar cir-
cumstances, such as muriatic or marine acid,
ammonia or volatile alkali, carbonic acid or
fixed air, sulphurous acid, <fec. All of these are
permanently elastic in or about the mean tem-
perature of the atmosphere and under its com-
mon pressure.

All these facts, which could be easily multi-
plied if necessary, give me full right to assume,
as a general principle, that almost every body
in nature is susceptible of three several states
of existence, solid, liquid, and aeriform, and
that these three states of existence depend
upon the quantity of caloric combhnd with
the body. Henceforwards I shall express these
elastic aeriform fluids by the generic term gas;
and in each species of gas I shall distinguish
between the caloric, which in some measure
serves the purpose of a solvent, and the sub-
stance, which in combination with the caloric,
forms the base of the gas.

CHEMISTRY

To these bases of the different gases, which
are but little known, we have been obliged to
assign names; these I shall point out in Chap-
ter IV of this work, when I have previously
given an account of the phenomena attendant
upon the heating and cooling of bodies, and
when I have established precise ideas concern-
ing the composition of our atmosphere.

We have already shown, that the particles
of every substance in nature exist in a certain
state of equilibrium, between that attraction
which tends to unite and keep the particles to-
gether and the effects of the caloric which
tends to separate them. Hence the caloric not
only surrounds the particles of all bodies on
every side but fills up every interval which the
particles of bodies leave between each other.
We may form an idea of this by supposing a
vessel filled with small spherical leaden bullets,
into which a quantity of fine sand is poured,
which, insinuating into the intervals between
the bullets, will fill up every void. The balls, in
this comparison, are to the sand which sur-
rounds them exactly in the same situation as
the particles of bodies are with respect to the
caloric; with this difference only, that the balls
are supposed to touch each other, whereas the
particles of bodies are not in contact, being re-
tained at a small distance from each other by
the caloric.

If, instead of spherical balls, we substitute
solid bodies of a hexahedral, octahedral, or any
other regular figure, the capacity of the inter-
vals between them will be lessened and conse-
quently will no longer contain the same quan-
tity of sand. The same thing takes place, with
respect to natural bodies; the intervals left be-
tween their particles are not of equal capacity
but vary in consequence of the different figures
and magnitude of their particles, and of the
distance at which these particles are main-
tained, according to the existing proportion
between their inherent attraction and the re-
pulsive force exerted upon them by the caloric.

In this manner we must understand the fol-
lowing expression, introduced by the English
philosophers, who have given us the first pre-
cise ideas upon this subject: the capacity of
bodies for containing the matter of heat. As com-
parisons with sensible objects are of great use
in assisting us to form distinct notions of ab-
stract ideas, we shall endeavour to illustrate
this by instancing the phenomena which take
place between water and bodies which are
wetted and penetrated by it, with a few reflec-
tions.

If we immerge equal pieces of different kinds
of wood, suppose cubes of one foot each, into
water, the fluid gradually insinuates itself into
their pores and the pieces of wood are aug-
mented both in weight and magnitude: but
each species of wood will imbibe a different
quantity of water ; the lighter and more porous
woods will admit a larger, the compact and
closer grained will admit of a lesser quantity;
for the proportional quantities of water im-
bibed by the pieces will depend upon the na-
ture of the constituent particles of the wood
and upon the greater or lesser affinity sub-
sisting between them and water. Very resinous
wood, for instance, though it may be at the
same time very porous, will admit but little
water. We may therefore say that the different
kinds of wood possess different capacities for
receiving water; we may even determine, by
means of the augmentation of their weights,
what quantity of water they have actually ab-
sorbed; but, as we are ignorant how much wa-
ter they contained previous to immersion, we
cannot determine the absolute quantity they
contain after being taken out of the water.

The same circumstances undoubtedly take
place with bodies that are immersed in caloric;
taking into consideration, however, that water
is an incompressible fluid, whereas caloric is,
on the contrary, endowed with very great elas-
ticity; or, in other words, the particles of ca-
loric have a great tendency to separate from
each other, when forced by any other power to
approach; this difference must of necessity oc-
casion very considerable diversities in the re-
sults of experiments made upon these two sub-
stances.

Having established these clear and simple
propositions, it will be very easy to explain the
ideas which ought to be affixed to the follow-
ing expressions, which are by no means syn-
onimous, but possess each a strict and deter-
minate meaning, as in the following definitions :

Free caloric is that which is not combined in
any manner with any other body. But, as we
live in a system to which caloric has a very strong
adhesion, it follows that we are never able to
obtain it in the state of absolute freedom.

Combined caloric is that which. is fixed in
bodies by affinity or elective attraction, so as
to form part of the substance of the body, even
part of its solidity.

By the expression specific caloric of bodies
we understand the respective quantities of ca-
loric requisite for raising a number of bodies of
the same weight to an equal degree of tempera-

LAVOISIER

ture. This proportional quantity of caloric de-
pends upon the distance between the constitu-
ent particles of bodies and their greater or less-
er degrees of cohesion ; and this distance, or rath-
er the space or void resulting from it, is, as I
have already observed, called the capacity of
bodies for containing caloric.

Heat, considered as a sensation, or, in other
words, sensible heat, is only the effect pro-
duced upon our sentient organs by the motion
or passage of caloric, disengaged from the sur-
rounding bodies. In general, we receive im-
pressions only in consequence of motion, and
we might establish it as an axiom that, WITH-
OUT MOTION, THERE IS NO SENSATION. This

general principle applies very accurately to the
sensations of heat and cold: when we touch a
cold body, the caloric which always tends to
become in equilibrio in all bodies, passes from
our hand into the body we touch, which gives
us the feeling or sensation of cold. The direct
contrary happens, when we touch a warm
body, the caloric then passing from the body
into our hand produces the sensation of heat.
If the hand and the body touched be of the
same temperature, or very nearly so, we re-
ceive no impression, either of heat or cold, be-
cause there is no motion or passage of caloric;
and thus no sensation can take place without
some correspondent motion to occasion it.

When the thermometer rises, it shows that
free caloric is entering into the surrounding
bodies : the thermometer, which is one of these,
receives its share in proportion to its mass and
to the capacity which it possesses for contain-
ing caloric. The change therefore which takes
place upon the thermometer only announces a
change of place of the caloric in those bodies
of which the thermometer forms one part; it
only indicates the portion of caloric received,
without being a measure of the whole quantity
disengaged, displaced, or absorbed.

The most simple and most exact method for
determining this latter point is that described
by M. de Laplace, in the Recueil de VAcaM-
mie 1780, p. 364, a summary explanation of
which will be found towards the conclusion of
this work. This method consists in placing a
body, or a combination of bodies, from which
caloric is disengaging, in the midst of a hollow
sphere of ice; and the quantity of ice melted
becomes an exact measure of the quantity of
caloric disengaged. It is possible, by means of
the apparatus which we have caused to be con-
structed upon this plan, to determine not, as
has been pretended, the capacity of bodies for

containing heat, but the ratio of the increase
or diminution of capacity produced by deter-
minate degrees of temperature. It is easy with
the same apparatus, by means of divers com-
binations of experiments, to determine the
quantity of caloric requisite for converting sol-
id substances into liquids, and liquids into elas-
tic aeriform fluids; and, vice versa, what quan-
tity of caloric escapes from elastic vapours in
changing to liquids, and what quantity escapes
from liquids during their conversion into sol-
ids. Perhaps, when experiments have been made
with sufficient accuracy, we may one day be
able to determine the proportional quantity of
caloric necessary for producing the several spe-
cies of gases. I shall hereafter, in a separate
chapter, give an account of the principal results
of such experiments as have been made upon
this head.

It remains, before finishing this article, to
say a few words relative to the cause of the
elasticity of gases and of fluids in the state of
vapour. It is by no means difficult to perceive
that this elasticity depends upon that of ca-
loric, which seems to be the most eminently
elastic body in nature. Nothing is more readily
conceived than that one body should become
elastic by entering into combination with an-
other body possessed of that quality. We must
allow that this is only an explanation of elastic-
ity, by an assumption of elasticity, and that
we thus only remove the difficulty one step
further, and that the nature of elasticity, and
the reason for caloric being elastic, remains
still unexplained. Elasticity in the abstract is
nothing more than that quality of the particles
of bodies by which they recede from each other
when forced together. This tendency in the
particles of caloric to separate, takes place
even at considerable distances. We shall be
satisfied of this, when we consider that air is
susceptible of undergoing great compression,
which supposes that its particles were pre-
viously very distant from each other; for the
power of approaching together certainly sup-
poses a previous distance, at least equal to the
degree of approach. Consequently, those par-
ticles of the air, which are already considerably
distant from each other, tend to separate still
farther. In fact, if we produce Boyle's vacuum
in a large receiver, the very last portion of air
which remains spreads itself uniformly through
the whole capacity of the vessel, however
large, fills it completely throughout, and presses
everywhere against its sides. We cannot, how-
ever, explain this effect without supposing that

CHEMISTRY

the particles make an effort to separate them-
selves on every side, and we are quite ignorant
at what distance, or what degree of rarefaction,
this effort ceases to act.

Here, therefore, exists a true repulsion be-
tween the particles of elastic fluids; at least,
circumstances take place exactly as if such a
repulsion actually existed; and we have very
good right to conclude that the particles of
caloric mutually repel ^ach other. When we are
once permitted to suppose this repelling force,
the rationale of the formation of gases, or
aeriform fluids becomes perfectly simple; tho'
we must, at the same time, allow that it is ex-
tremely difficult to form an accurate concep-
tion of this repulsive force acting upon very
minute particles placed at great distances from
each other.

It is, perhaps, more natural to suppose that
the particles of caloric have a stronger mutual
attraction than those of any other substance
and that these latter particles are forced
asunder in consequence of this superior attrac-
tion between the particles of the caloric, which
forces them between the particles of other
bodies that they may be able to reunite with
each other. We have somewhat analogous to
this idea in the phenomena which occur when
a dry sponge is dipped into water: the sponge
swells; its particles separate from each other;
and all its intervals are filled up by the water.
It is evident that the sponge in the act of
swelling, has acquired a greater capacity for
containing water than it had when dry. But we
cannot certainly maintain that the introduc-
tion of water between the particles of the
sponge has endowed them with a repulsive
power, which tends to separate them from each
other; on the contrary, the whole phenomena
are produced by means of attractive powers;
and these are, 1st, the gravity of the water,
and the power which it exerts on every side, in
common with all other fluids; 2nd, the force
of attraction which takes place between the
particles of the water, causing them to unite
together; 3rd, the mutual attraction of the
particles of the sponge with each other; and,
lastly, the reciprocal attraction which exists
between the particles of the sponge and those
of the water. It is easy to understand that the
explanation of this fact depends upon properly
appreciating the intensity of, and connection
between, these several powers. It is probable
that the separation of the particles of bodies,
occasioned by caloric, depends in a similar
manner upon a certain combination of differ-

ent attractive powers, which, in conformity
with the imperfection of our knowledge, we
endeavour to express by saying that caloric
communicates a power of repulsion to the par-
ticles of bodies.

CHAPTER II

General Views Relative to 'the Formation and
Composition of our Atmosphere

THESE views which I have taken of the forma-
tion of elastic aeriform fluids or gases throw
great light upon the original formation of the
atmospheres of the planets and particularly
that of our earth. We readily conceive that it
must necessarily consist of a mixture of the
following substances: 1st, of all bodies that are
susceptible of evaporation, or, more strictly
speaking, which are capable of retaining the
state of aeriform elasticity in the temperature
of our atmosphere, and under a pressure equal
to that of a column of twenty-eight inches of
quicksilver in the barometer; and, 2nd, of all
substances, whether liquid or solid, which are
capable of being dissolved by this mixture of
different gases.

The better to determine our ideas relating to
this subject, which has not hitherto been suf-
ficiently considered, let us, for a moment, con-
ceive what change would take place in the var-
ious substances which compose our earth, if its
temperature were suddenly altered. If, for
instance, we were suddenly transported into
the region of the planet Mercury, where prob-
ably the common temperature is much superior
to that of boiling water, the water of the earth
and all the other fluids which are susceptible of
the gaseous state at a temperature near to
that of boiling water, even quicksilver itself,
would become rarified;and all these substances
would be changed into permanent aeriform
fluids or gases, which would become part of
the new atmosphere. These new species of airs
or gases would mix with those already exist-
ing, and certain reciprocal decompositions and
new combinations would take place, until such
time as all the elective attractions or affinities
subsisting amongst all these new and old gase-
ous substances had operated fully; after which,
the elementary principles composing these
gases, being saturated, would remain at rest.
We must attend to this, however, that, even
in the above hypothetical situation, certain
bounds would occur to the evaporation of these
substances, produced by that very evapora-
tion itself; for as, in proportion to the increase

LAVOISIER

of elastic fluids, the pressure of the atmosphere
would be augmented, as every degree of pres-
sure tends, in some measure, to prevent evap-
oration, and as even the most evaporable
fluids can resist the operation of a very high
temperature without evaporating, if prevented
by a proportionally stronger compression, wa-
ter and all other liquids being able to sustain a
red heat in Papin's digester; we must admit
that the new atmosphere would at last arrive
at such a degree of weight that the water which
had not hitherto evaporated would cease to
boil and, of consequence, would remain liquid;
so that, even upon this supposition as in ail
others of the same nature, the increasing grav-
ity of the atmosphere would find certain limits
which it could not exceed. We might even ex-
tend these reflections greatly further, and ex-
amine what change might be produced in such
situations upon stones, salts, and the greater
part of the fusible substances which compose
the mass of our earth. These would be softened,
fused, and changed into fluids, &c. : but these
speculations carry me from my object, to
which I hasten to return.

By a contrary supposition to the one we
have been forming, if the earth were suddenly
transported into a very cold region, the water
which at present composes our seas, rivers, and
springs, and probably the greater number of
the fluids we are acquainted with, would be
converted into solid mountains and hard rocks,
at first diaphanous and homogeneous, like rock
crystal, but which, in time, becoming mixed
with foreign and heterogeneous substances,
would become opaque stones of various colours.
In this case, the air, or at least some part of the
aeriform fluids which now compose the mass of
our atmosphere, would doubtless lose its elas-
ticity for want of a sufficient temperature to
retain it in that state: it would return to the
liquid state of existence, and new liquids would
be formed, of whose properties we cannot, at
present, form the most distant idea.

These two opposite suppositions give a dis-
tinct proof of the following corollaries: 1st that
solidity, liquidity, and aeriform elasticity, are
only three different states of existence of the
same matter, or three particular modifications
which almost all substances are susceptible of
assuming successively, and which solely depend
upon the degree of temperature to which they
are exposed ; or, in other words, upon the quanti-
ty of caloric with which they are penetrated.
2nd, that it is extremely probable that air is a
Quid naturally existing in a state of vapour;

or, as we may better express it, that our atmos-
phere is a compound of all the fluids which are
susceptible of the vaporous or permanently
elastic state, in the usual temperature and un-
der the common pressure. 3rd, that it is not
impossible we may discover, in our atmos-
phere, certain substances naturally very com-
pact, even metals themselves; as a metallic
substance, for instance, only a little more vol-
atile than mercury, might exist in that sit-
uation,

Amongst the fluids with which we are ac-
quainted, some, as water and alcohol, are
susceptible of mixing with each other in all pro-
portions; whereas others, on the contrary, as
quicksilver, water, and oil, can only form a
momentary union; and, after being mixed to-
gether, separate and arrange themselves ac-
cording to their specific gravities. The same
thing ought to, or at least may, take place in
the atmosphere. It is possible, and even ex-
tremely probable, that, both at the first crea-
tion and every day, gases are formed, which
are with difficulty miscible with atmospheric
air and are continually separating from it. If
these gases bo specifically lighter than the gen-
eral atmospheric mass, they must, of course,
gather in the higher regions and form strata that
float upon the common air. The phenomena
which accompany igneous meteors induce me
to believe that there exists in the upper parts of
our atmosphere a stratum of inflammable fluid
in contact with those strata of air which pro-
duce the phenomena of the aurora borealis and
other fiery meteors. I mean hereafter to pur-
sue this subject in a separate treatise.

CHAPTER III

Analysis of Atmospheric Air, and its Division
into Two Elastic Fluids; the One Fit for Res-
piration, the Other Incapable of Being Respired.

FROM what has been premised, it follows that
our atmosphere is composed of a mixture of
every substance capable of retaining the gas-
eous or aeriform state in the common temper-
ature, and under the usual pressure which it
experiences. These fluids constitute a mass, in
some measure homogeneous, extending from
the surface of the earth to the greatest height
hitherto attained, of which the density contin-
ually decreases in the inverse ratio of the super-
incumbent weight. But, as I have before ob-
served, it is possible that this first stratum is
surmounted by several others consisting of
very different fluids.

CHEMISTRY

Our business, in this place, is to endeavour
to determine, by experiments, the nature of
the elastic fluids which compose the inferior
stratum of air which we inhabit. Modern chem-
istry has made great advances in this research;
and it will appear by the following details that
the analysis of atmospherical air has been more
rigorously determined than that of any other
substance of the class, phemistry affords two
general methods of determining the constitu-
ent principles of bodies, the method of analysis,
and that of synthesis. When, for instance, by
combining water with alcohol we form the
species of liquor called, in commercial lan-
guage, brandy or spirit of wine, we certainly
have a right to conclude that brandy, or spirit
of wine, is composed of alcohol combined with
water. We can produce the same result by the
analytical method; and in general it ought to
be considered as a principle in chemical science
never to rest satisfied without both these spe-
cies of proofs.

We have this advantage in the analysis of
atmospherical air, being able both to decom-
pound it, and to form it anew in the most sat-
isfactory manner. I shall, however, at present
confine myself to recount such experiments as
are most conclusive upon this head ; and I may
consider most of these as my own, having
either first invented them or having repeated
those of others, with the intention of analysing
atmospherical air t in perfectly new points of
view.

I took a matrass A (Plate n, Fig. 14) of
about 36 cubic inches capacity, having a long
neck BCDE of six or seven lines internal diam-
eter, and having bent the neck as in Plate IV,
Fig. 2, so as to allow of its being placed in the
furnace MMNN, in such a manner that the
extremity of its neck E might be inserted under
a bell-glass FG, placed in a trough of quick-
silver RRSS; I introduced four ounces of pure
mercury into the matrass and, by means of a
siphon, exhausted the air in the receiver FG,
so as to raise the quicksilver to LL, and I care-
fully marked the height at which it stood by
pasting on a slip of paper. Having accurately
noted the height of the thermometer and ba-
rometer, I lighted a fire in the furnace MMNN,
which I kept up almost continually during
twelve days, so as to keep the quicksilver al-
ways almost at its boiling point. Nothing re-
markable took place during the first day: the
mercury, though not boiling, was continually
evaporating and covered the interior surface of
the vessels with small drops, at first very mi-

nute, which, gradually augmenting to a suffi-
cient size, fell back into the mass at the bottom
of the vessel. On the second day, small red
particles began to appear on the surface of the
mercury, which, during the four or five follow-
ing days, gradually increased in size and num-
ber, after which they ceased to increase in
either respect. At the end of twelve days, see-
ing that the calcination of the mercury did not
at all increase, I extinguished the fire, and al-
lowed the vessels to cool. The bulk of air in the
body and neck of the matrass, and in the bell-
glass, reduced to a medium of 28 inches of the
barometer and 10 (54.5) of the thermometer,
at the commencement of the experiment was
about 50 cubic inches. At the end of the ex-
periment the remaining air, reduced to the
same medium pressure and temperature, was
only between 42 and 43 cubic inches; conse-
quently it had lost about % of its bulk. After-
wards, having collected all the red particles
formed during the experiment from the run-
ning mercury in which they floated, I found
these to amount to 45 grains.

I was obliged to repeat this experiment seve-
ral times, as it is difficult in one experiment
both to preserve the whole air upon which we
operate and to collect the whole of the red
particles, or calx of mercury, which is formed
during the calcination. It will often happen in
the sequel that I shall, in this manner, give in
one detail the results of two or three experi-
ments of the same nature.

The air which remained after the calcination
of the mercury in this experiment, and which
was reduced to % of its former bulk, was no
longer fit either for respiration or for combus-
tion; animals being introduced into it were
suffocated in a few seconds, and when a taper
was plunged into it, it was extinguished as if it
had been immersed into water.

In the next place, I took the 45 grains of red
matter formed during this experiment, which I
put into a small glass retort, having a proper
apparatus for receiving such liquid, or gaseous
product, as might be extracted : having applied
a fire to the retort in a furnace, I observed that,
in proportion as the red matter became heated,
the intensity of its colour augmented. When the
retort was almost red hot, the red matter began
gradually to decrease in bulk, and a few min-
utes afterwards, it disappeared altogether; at
the same time 41 J^ grains of running mercury
were collected in the recipient, and 7 or 8 cubic
inches of elastic fluid, greatly more capable of
supporting both respiration and combustion

LAVOISIER

than atmospherical air, were collected in the
bell-glass.

A part of this air being put into a glass tube
of about an inch diameter showed the follow-
ing properties: a taper burned in it with a daz-
zling splendour and charcoal, instead of con-
suming quietly as it does in common air, burnt
with a flame, attended with a decrepitating
noise, like phosphorus, and threw out such a
brilliant light that the eyes could hardly en-
dure it. This species of air was discovered al-
most at the same time by M. Priestley, M.
Scheele, and myself. M. Priestley gave it the
name of dephlogisticated air, M. Scheele called
it empyreal air. At first I named it highly res-
pirable air, to which has since been substituted
the term of vital air. We shall presently see
what we ought to think of these denomina-
tions.

In reflecting upon the circumstances of this
experiment, we readily perceive that the mer-
cury, during its calcination, absorbs the salu-
brious and respirable part of the air, or, to
speak more strictly, the base of this respirable
part; that the remaining air is a species of me-
phitis, incapable of supporting combustion or
respiration ; and consequently that atmospheric
air is composed of two elastic fluids of different
and opposite qualities. As a proof of this im-
portant truth, if we recombine these two elastic
fluids, which we have separately obtained in
the above experiment, viz., the 42 cubic inches
of mephitis, with the 8 cubic inches of respir-
able air, we reproduce an air precisely similar
to that of the atmosphere and possessing nearly
the same power of supporting combustion and
respiration, and of contributing to the calcina-
tion of metals.

Although this experiment furnishes us with
a very simple means of obtaining the two prin-
cipal elastic fluids which compose our atmos-
phere separate from each other, yet it does not
give us an exact idea of the proportion in which
these two enter into its composition: for the
attraction of mercury to the respirable part of
the air, or rather to its base, is not sufficiently
strong to overcome all the circumstances which
oppose this union. These obstacles are the mu-
tual adhesion of the two constiutent parts of
the atmosphere for each other and the elective
attraction which unites the base of vital air
with caloric ; in consequence of these, when the
calcination ends, or is at least carried as far as
is possible in a determinate quantity of atmos-
pheric air, there still remains a portion of
respirable air united to the mephitis, which

the mercury cannot separate. I shall after-
wards show that, at least in our climate,
the atmospheric air is composed of respir-
able, and mephitic airs, in the proportion
of 27 and 73; and I shall then discuss the
causes of the uncertainty which still exists
with respect to the exactness of that propor-
tion.

Since, during the calcination of mercury, air
is decomposed, and the base of its respirable
part is fixed and combined with the mercury,
it follows, from the principles already estab-
lished, that caloric and light must be disen-
gaged during the process: but the two follow-
ing causes prevent us from being sensible of
this taking place: as the calcination lasts dur-
ing several days, the disengagement of caloric
and light, spread out in a considerable space of
time, becomes extremely small for each par-
ticular moment of that time, so as not to be
perceptible; and, in the next place, the opera-
tion being carried on by means of fire in a fur-
nace, the heat produced by the calcination it-
self becomes confounded with that proceeding
from the furnace. I might add the respirable
part of the air, or rather its base, in entering
into combination with the mercury, does not
part with all the caloric which it contained but
still retains a part of it after forming the new
compound; but the discussion of this point,
and its proofs from experiment, do not belong
to this part of our subject.

It is, however, easy to render this disengage-
ment of caloric and light evident to the senses,
by causing the decomposition of air to take
place in a more rapid manner. And for this
purpose, iron is excellently adapted, as it pos-
sesses a much stronger affinity for the base of
respirable air than mercury. The elegant ex-
periment of M. Ingenhouz, upon the combus-
tion of iron, is well known. Take a piece of
fine iron wire twisted into a spiral BC (Plate
iv, Fig. 17), fix one of its extremities B into
the cork A, adapted to the neck of the bottle
DEFG, and fix to the other extremity of the
wire C a small morsel of tinder. Matters being
thus prepared, fill the bottle DEFG with air
deprived of its mephitic part; then light the
tinder and introduce it quickly, with the wire
upon which it is fixed, into the bottle which
you stop up with the cork A, as is shown in the
figure (17, Plate iv). The instant the tinder
comes into contact with the vital air it begins
to burn with great intensity; and, communi-
cating the inflammation to the iron-wire, it too
takes fire and burns rapidly, throwing out

CHEMISTRY

brilliant sparks, which fall to the bottom of the
vessel in rounded globules, which become black
in cooling but retain a degree of metallic splen-
dour. The iron thus burnt is more brittle even
than glass and is easily reduced into powder,
and is still attractable by the magnet, though
not so powerfully as it was before combustion.
As M. Ingenhouz has neither examined the
change produced on iron nor upon the air by
this operation, I have repeated the experiment
under different circumstances, in an apparatus
adapted to answer my particular views, as
follows.

Having filled a bell-glass A (Plate iv, Fig. 3)
of about six pints measure with pure air, or the
highly respirable part of air, I transported this
jar by means of a very flat vessel, into a quick-
silver bath in the basin BC, and I took care to
render the surface of the mercury perfectly dry
both within and without the jar with blotting
paper. I then provided a small capsule of china-
ware D, very flat and open, in which I placed
some small pieces of iron, turned spirally and
arranged in such a way as seemed most favour-
able for the combustion being communicated
to every part. To the end of one of these pieces
of iron was fixed a small morsel of tinder, to
which was added about the sixteenth part of a
grain of phosphorus, and, by raising the bell-
glass a little, the china capsule, with its con-
tents, were introduced into the pure air. I know
that, by this means, some common air must
mix with the pure air in the glass; but this,
when it is done dexterously, is so very trifling
as not to injure the success of the experiment.
This being done, a part of the air is sucked out
from the bell-glass, by means of a siphon GHI,
so as to raise the mercury within the glass to
EF; and, to prevent the mercury from getting
into the siphon, a small piece of paper is twist-
ed round its extremity. In sucking out the air,
if the motion of the lungs only be used,
we cannot make the mercury rise above an
inch or an inch and a half; but, by properly
using the muscles of the mouth, we can, with-
out difficulty, cause it to rise six or seven
inches.

I next took an iron wire, (MN, Plate iv, Fig.
16) properly bent for the purpose, and making
it red hot in the fire passed it through the mer-
cury into the receiver and brought it in contact
with the small piece of phosphorus attached to
the tinder. The phosphorus instantly takes
fire, which communicates to the tinder, and
from that to the iron. When the pieces have
been properly arranged, the whole iron burns,

even to the last particle, throwing out a white
brilliant light similar to that of Chinese fire-
works. The great heat produced by this com-
bustion melts the iron into round globules of
different sizes, most of which fall into the china
cup; but some are thrown out of it and swim
upon the surface of the mercury. At the begin-
ning of the combustion, there is a slight aug-
mentation in the volume of the air in the bell-
glass, from the dilatation caused by the heat;
but, presently afterwards, a rapid diminution
of the air takes place and the mercury rises in
the glass; insomuch that, when the quantity of
iron is sufficient, and the air operated upon is
very pure, almost the whole air employed is
absorbed.

It is proper to remark in this place that, un-
less in making experiments for the purpose of
discovery, it is better to be contented with
burning a moderate quantity of iron; for, when
this experiment is pushed too far, so as to ab-
sorb much of the air, the cup D, which floats
upon the quicksilver, approaches too near the
bottom of the bell-glass; and the great heat
produced, which is followed by a very sudden
cooling, occasioned by the contact of the cold
mercury, is apt to break the glass. In which
case, the sudden fall of the column of mercury,
which happens the moment the least flaw is
produced in the glass, causes such a wave as
throws a great part of the quicksilver from
the basin. To avoid this inconvenience, and
to ensure success to the experiment, one
gross and a half of iron is sufficient to burn
in a bell-glass, which holds about eight pints
of air. The glass ought likewise to be strong,
that it may be able to bear the weight of
the column of mercury which it has to sup-
port.

By this experiment, it is not possible to de-
termine, at one time, both the additional weight
acquired by the iron, and the changes which
have taken place in the air. If it is wished to
ascertain what additional weight has been
gained by the iron, and the proportion be-
tween that and the air absorbed, we must
carefully mark upon the bell-glass, with a dia-
mond, the height of the mercury, beth before
and after the experiment. After this, the si-
phon GH (Plate iv, Fig. 8) guarded, as before,
with a bit of paper, to prevent its filling with
mercury, is to be introduced under the bell-
glass, having the thumb placed upon the ex-
tremity, G, of the siphon, to regulate the pas-
sage of the air; and by this means the air is
gradually admitted, so as to let the mercury

LAVOISIER

fall to its level. This being done, the bell-glasa
is to be carefully removed, the globules of
melted iron contained in the cup, and those
which have been scattered about, and swim
upon the mercury are to be accurately col-
lected, and the whole is to be weighed. The iron
will be found in that state called martial ethiops
by the old chemists, possessing a degree of me-
tallic brilliancy,, very friable, and readily re-
ducible into powder under the hammer or with
a pestle and mortar. If the experiment has suc-
ceeded well, from 100 grains of iron will be ob-
tained 135 or 136 grains of ethiops, which is an
augmentation of 35 per cent.

If all the attention has been paid to this ex-
periment which it deserves, the air will be
found diminished in weight exactly equal to
what the iron has gained. Having therefore
burnt 100 grains of iron, which has acquired an
additional weight of 35 grains, the diminution
of air will be found exactly 70 cubic inches;
and it will be found, in the sequel, that the
weight of vital air is pretty nearly half a grain
for each cubic inch; so that, in effect, the aug-
mentation of weight in the one exactly coin-
cides with the loss of it in the other.

I shall observe here, once for all, that, in
every experiment of this kind, the pressure and
temperature of the air, both before and after
the experiment, must be reduced, by calcula-
tion, to a common standard of 10 (54.5) of
the thermometer and 28 inches of the barom-
eter. Towards the end of this work, the manner
of performing this very necessary reduction
will be found accurately detailed.

If it be required to examine the nature of the
air which remains after this experiment, we
must operate in a somewhat different manner.
After the combustion is finished, and the ves-
sels have cooled, we first take out the cup, and
the burnt iron, by introducing the hand through
the quicksilver under the bell-glass; we next
introduce some solution of potash, or caustic
alkali, or of the sulphuret of potash, or such
other substance as is judged proper for exam-
ining their action upon the residuum of air. I
shall, in the sequel, give an account of these
methods of analysing air, when I have ex-
plained the nature of these different substances,
which are only here in a manner accidentally
mentioned. After this examination, so much
water must be let into the glass as will displace
the quicksilver, and then, by means of a shal-
low dish placed below the bell-glass, it is to be
removed into the common watej pneumato-
chemical apparatus, where the air remaining

may be examined at large and with great fa-
cility.

When very soft and very pure iron has been
employed in this experiment, and, if the com-
bustion has been performed in the purest respir-
able or vital air, free from all admixture of the
noxious or mephitic part, the air which remains
after the combustion will be found as pure as it
was before; but it is difficult to find iron en-
tirely free from a small portion of charry mat-
ter, which is chiefly abundant in steel. It is
likewise exceedingly difficult to procure the
pure air perfectly free from some admixture of
mephitis, with which it is almost always con-
taminated ; but this species of noxious air does
not in the smallest degree disturb the result of
the experiment, as it is always found at the
end exactly in the same proportion as at the
beginning.

I mentioned before that we have two ways
of determining the constituent parts of atmos-
pheric air, the method of analysis, and that by
synthesis. The calcination of mercury has fur-
nished us with an example of each of these
methods, since, after having robbed the respir-
able part of its base, by means of the mercury,
we have restored it, so as to recompose an air
precisely similar to that of the atmosphere.
But we can equally accomplish this synthetic
composition of atmospheric air by borrowing
the materials of which it is composed from dif-
ferent kingdoms of nature. We shall see here-
after that when animal substances are dis-
solved in the nitric acid a great quantity of gas
is disengaged, which extinguishes light and
is unfit for animal respiration, being exactly
similar to the noxious or mephitic part of at-
mospheric air. And, if we take 73 parts, by
weight, of this elastic fluid, and mix it with 27
parts of highly respirable air, procured from
calcined mercury, we will form an elastic fluid
precisely similar to atmospheric air in all its
properties.

There are many other methods of separating
the respirable from the noxious part of the at-
mospheric air, which cannot be taken notice of
in this part without anticipating information
which properly belongs to the subsequent
chapters. The experiments already adduced
may suffice for an elementary treatise; and, in
matters of this nature, the choice of our evi-
dences is of far greater consequence than their
number.

I shall close this article by pointijig out the
property which atmospheric air, and all the
known gases, possess of dissolving water, which

CHEMISTRY

is of great consequence to be attended to in all
experiments of this nature. M. Saussure found,
by experiment, that a cubic foot of atmos-
pheric air is capable of holding 12 grains of
water in solution: other gases, as carbonic acid,
appear capable of dissolving a greater quan-
tity; but experiments are still wanting by
which to determine their several proportions.
This water, held in solution by gases, gives rise
to particular phenomena in many experiments
which require great attention and which has
frequently proved the source of great errors to
chemists in determining the results of their
experiments.

CHAPTER IV

Nomenclature of the Several Constituent Parts of
Atmospheric Air

HITHERTO I have been obliged to make use of
circumlocution to express the nature of the
several substances which constitute our at-
mosphere, having provisionally used the terms
of respirable and noxious, or non-respirable
parts of the air. But the investigations I mean
to undertake require a more direct mode of
expression; and, having now endeavoured to
give simple and distinct ideas of the different
substances which enter into the composition of
the atmosphere, I shall henceforth express
these ideas by words equally simple.

The temperature of our earth being very
near to that at which water becomes solid and
reciprocally changes from solid to fluid, and as
this phenomenon takes place frequently under
our observation, it has very naturally fol-
lowed that, in the languages of at least every
climate subjected to any degree of winter, a
term has been used for signifying water in the
state of solidity when deprived of its caloric.
The same, however, has not been found neces-
sary with respect to water reduced to the state
of vapour by an additional dose of caloric;
since those persons who do not make a partic-
ular study of objects of this kind are still ig-
norant that water, when in a temperature only
a little above the boiling heat, is changed into
an elastic aeriform fluid, susceptible, like all
other gases, of being received and contained in
vessels and preserving its gaseous form so long
as it remains at the temperature of 80 (212)
and under a pressure not exceeding 28 inches
of the mercurial barometer. As this phenom-
enon has not been generally observed, no lan-
guage has used a particular term for express-
ing water in this state; and the same thing

occurs with all fluids and all substances which
do not evaporate in the common temperature
and under the usual pressure of our atmos-
phere.

For similar reasons, names have not been
given to the liquid or concrete states of most of
the aeriform fluids: these were not known to
arise from the combination of caloric with cer-
tain bases; and, as they had not been seen
either in the liquid or solid states, their exist-
ence, under these forms, was even unknown to
natural philosophers.

We have not pretended to make any altera-
tion upon such terms as are sanctified by an-
cient custom and, therefore, continue to use
the words water and ice in their common accep-
tation. We likewise retain the word air to ex-
press that collection of elastic fluids which com-
poses our atmosphere ; but we have not thought
it necessary to preserve the same respect for
modern terms, adopted by latter philosophers,
having considered ourselves as at liberty to
reject such as appeared liable to occasion er-
roneous ideas of the substances they are meant
to express, and either to substitute new terms,
or to employ the old ones after modifying them
in such a manner as to convey more determi-
nate ideas. New words have been drawn, chiefly
from the Greek language, in such a manner as
to make their etymology convey some idea of
what was meant to be represented; and these
we have always endeavoured to make short
and of such a nature as to be changeable into
adjectives and verbs.

Following these principles, we have, after
M. Macquer's example, retained the term gas
employed by van Helmont, having arranged
the numerous classes of elastic aeriform fluids
under that name, excepting only atmospheric
air. Gas, therefore, in our nomenclature be-
comes a generic term, expressing the fullest
degree of saturation in any body with caloric ;
being, in fact, a term expressive of a mode of
existence. To distinguish each species of gas,
we employ a second term from the name of the
base, which, saturated with caloric, forms each
particular gas. Thus, we name water combined
to saturation with caloric, so as to form an
elastic fluid, aqueous gas; ether, combined in
the same manner, etherial gas; the combination
of alcohol with caloric becomes alcoholic gas;
and, following the same principles, we have
muriatic acid gas, ammoniacal gas, and so on of
every substance susceptible of being combined
with caloric, in such a manner as to assume the
gaseous or elastic aeriform state.

LAVOISIER

We have already seen that the atmospheric
air is composed of two gases, or aeriform fluids,
one of which is capable, by respiration, of con-
tributing to animal life, and in which metals
are calcinable and combustible bodies may
burn; the other, on the contrary, is endowed
with directly opposite qualities; it cannot be
breathed by animals, neither will it admit of
the combustion of inflammable bodies, nor of
the calcination of metals. We have given to
the base of the former, or respirable portion of
the air, the name of oxygen, from ovs, acidum,
and ydvopai, gignor; because, in reality, one
of the most general properties of this base is to
form acids by combining with many different
substances. The union of this base with caloric
we term oxygen gas, which is the same with
what was formerly called pure or vital air. The
weight of this gas, at the temperature of 10
(54.50), and under a pressure equal to 28
inches of the barometer, is half a grain for each
cubic inch, or an ounce and a half to each
cubic foot.

The chemical properties of the noxious por-
tion of atmospheric air being hitherto but little
known, we have been satisfied to derive the
name of its base from its known quality of kill-
ing such animals as are forced to breathe it,
giving it the name of azote, from the Greek
privative particle a and fan), vita; hence the
name of the noxious part of atmospheric air is
azotic gas; the weight of which, in the same
temperature and under the same pressure, is
1 oz. 2 gros 1 and 48 grs. to the cubic foot, or
0.4444 of a grain to the cubic inch. We cannot
deny that this name appears somewhat ex-
traordinary; but this must be the case with all
new terms, which cannot be expected to be-
come familiar until they have been some time
in use. We long endeavoured to find a more
proper designation without success; it was at
first proposed to call it alkaligen gas, as, from
the experiments of M. Berthollet, it appears
to enter into the composition of ammonia, or
volatile alkali; but then, we have as yet no
proof of its making one of the constituent ele-
ments of the other alkalies; beside, it is proved
to compose a part of the nitric acid, which
gives as good reason to have called it nitrogen.
For these reasons, finding it necessary to reject
any name upon systematic principles, we have
considered that we run no risk of mistake in
adopting the terms of azote and azotic gas,
which only express a matter of fact, or that
property which it possesses, of depriving such

1 Gros equals one-eighth of an ounce. EDITOR.

animals as breathe it of their lives.

I should anticipate subjects more properly
reserved for the subsequent chapters were I in
this place to enter upon the nomenclature of
the several species of gases: it is sufficient, in
this part of the work, to establish the prin-
ciples upon which their denominations are
founded. The principal merit of the nomen-
clature we have adopted is that, when once
the simple elementary substance is distin-
guished by an appropriate term, the names of
all its compounds derive readily, and neces-
sarily, from this first denomination.

CHAPTER V

Of the Decomposition of Oxygen Gas by Sulphur,
Phosphorus, and Charcoal, and of the Forma-
tion of Acids in General

IN performing experiments, it is a necessary
principle, which ought never to be deviated
from, that they be simplified as much as pos-
sible, and that every circumstance capable of
rendering their results complicated be carefully
removed. Wherefore, in the experiments which
form the object of this chapter, we have never
employed atmospheric air, which is not a sim-
ple substance. It is true that the azotic gas,
which forms a part of its mixture, appears to
be merely passive during combustion and cal-
cination; but, besides that it retards these
operations very considerably, we are not cer-
tain but it may even alter their results in some
circumstances; for which reason I have thought
it necessary to remove even this possible cause
of doubt, by only making use of pure oxygen
gas in the following experiments which show
the effects produced by combustion in that
gas; and I shall advert to such differences as
take place in the results of these, when the
oxygen gas, or pure vital air, is mixed, in dif-
ferent proportions, with azotic gas.

Having filled a bell-glass A (Plate iv, Fig. 8),
of between five and six pints measure, with
oxygen gas, I removed it from the water
trough, where it was filled, into the quicksilver
bath by means of a shallow glass dish slipped
underneath, and having dried the mercury I
introduced 61 J^ grains of Kunkel's phosphorus
in two little china cups, like that represented
at D (Fig. 8), under the glass A; and that I
might set fire to each of the portions of phos-
phorus separately, and to prevent the one from
catching fire from the other, one of the dishes
was covered with a piece of flat glass. I next

CHEMISTRY

raised the quicksilver in the bell-glass up to
EF, by sucking out a sufficient portion of the
gas by means of the siphon GHI. After this,
by means of the crooked iron wire (Fig. 16),
made red hot, I set fire to the two portions of
phosphorus successively, first burning that
portion which was not covered with the piece
of glass. The combustion was extremely rapid,
attended with a very brilliant flame and con-
siderable disengagement of light and heat. In
consequence of the great heat induced, the gas
was at first much dilated, but soon after the
mercury returned to its level and a consider-
able absorption of gas took place; at the same
time, the whole inside of the glass became
covered with white light flakes of concrete
phosphoric acid.

At the beginning of the experiment, the
quantity of oxygen gas, reduced, as above di-
rected, to a common standard, amounted to
162 cubic inches; and, after the combustion
was finished, only 23J4 cubic inches, likewise
reduced to the standard, remained ; so that the
quantity of oxygen gas absorbed during the
combustion was 138% cubic inches, equal to
69.375 grains.

A part of the phosphorus remained uncon-
sumed in the bottom of the cups, which being
washed on purpose to separate the acid weighed
about 16J4 grains; so that about 45 grains of
phosphorus had been burned: but, as it is
hardly possible to avoid an error of one or two
grains, I leave the quantity so far qualified.
Hence, as nearly 45 grains of phosphorus had,
in this experiment, united with 69.375 grains
of oxygen, and as no gravitating matter could
have escaped through the glass, we have a
right to conclude that the weight of the sub-
stance resulting from the combustion in form
of white flakes must equal that of the phos-
phorus and oxygen employed, which amounts
to 114.375 grains. And we shall presently find
that these flakes consisted entirely of a solid or
concrete acid. When we reduce these weights
to hundredth parts, it will be found that 100
parts of phosphorus require 154 parts of oxy-
gen for saturation and that this combination
will produce 254 parts of concrete phosphoric
acid, in form of white fleecy flakes.

This experiment proves, in the most con-
vincing manner, that, at a certain degree of
temperature, oxygen possesses a stronger elec-
tive attraction, or affinity, for phosphorus than
for caloric; that, in consequence of this, the
phosphorus attracts the base of oxygen gas
from the caloric, which, being set free, spreads

itself over the surrounding bodies. But, though
this experiment be so far perfectly conclusive,
it is not sufficiently rigorous, as, in the appa-
ratus described, it is impossible to ascertain
the weight of the flakes of concrete acid which
are formed; we can therefore only determine
this by calculating the weights of oxygen and
phosphorus employed; but as, in physics
and in chemistry, it is not allowable to sup-
pose what is capable of being ascertained by
direct experiment, I thought it necessary to
repeat this experiment as follows, upon a
larger scale and by means of a different appa-
ratus.

I took a large glass balloon A (Plate iv, Fig.
4) with an opening three inches diameter, to
which was fitted a crystal stopper ground with
emery, and pierced with two holes for the
tubes yyy, xxx. Before shutting the balloon
with its stopper, I introduced the support BC,
surmounted by the china cup D, containing
150 grs. of phosphorus; the stopper was then
fitted to the opening of the balloon, luted with
fat lute, and covered with slips of linen spread
with quicklime and white of eggs: when the
lute was perfectly dry, the weight of the whole
apparatus was determined to within a grain or
a grain and a half. I next exhausted the balloon,
by means of an air pump applied to the tube
xxx, and then introduced oxygen gas by means
of the tube yyy, having a stop-cock adapted to
it. This kind of experiment is most readily and
most exactly performed by means of the hydro-
pneumatic machine described by M. Meus-
nier and me in the Recueil de I AcaMmie for
1782, page 466, and explained in the latter
part of this work, with several important addi-
tions and corrections since made to it by M.
Meusnier. With this instrument we can readily
ascertain, in the most exact manner, both the
quantity of oxygen gas introduced into the
balloon and the quantity consumed during the
course of the experiment.

When all things were properly disposed, I
set fire to the phosphorus with a burning glass.
The combustion was extremely rapid, accom-
panied with a bright flame and much heat; as
the operation went on, large quantities of white
flakes attached themselves to the inner surface
of the balloon, so that at last it was rendered
quite opaque. The quantity of these flakes at
last became so abundant that although fresh
oxygen gas was continually supplied, which
ought to have supported the combustion, yet
the phosphorus was soon extinguished. Having
allowed the apparatus to cool completely, I

LAVOISIER

first ascertained the quantity of oxygen gas
employed, and weighed the balloon accurately,
before it was opened. I next washed, dried, and
weighed the small quantity of phosphorus re-
maining in the cup, on purpose to determine
the whole quantity of phosphorus consumed in
the experiment; this residuum of the phos-
phorus was of a yellow ochre colour. It is evi-
dent that by these several precautions I could
easily determine, 1st, the weight of the phos-
phorus consumed; 2nd, the weight of the flakes
produced by the combustion; and, 3rd, the
weight of the oxygen which had combined with
the phosphorus. This experiment gave very
nearly the same results with the former, as it
proved that the phosphorus, during its com-
bustion, had absorbed a little more than one
and a half its weight of oxygen; and I learned
with more certainty that the weight of the new
substance produced in the experiment exactly
equalled the sum of the weights of the phos-
phorus consumed and oxygen absorbed, which
indeed was easily determinable a priori. If the
oxygen gas employed be pure, the residuum
after combustion is as pure as the gas em-
ployed; this proves that nothing escapes from
the phosphorus capable of altering the purity
of the oxygen gas, and that the only action
of the phosphorous is to separate the oxygen
from the caloric with which it was before
united.

I mentioned above, that when any combus-
tible body is burnt in a hollow sphere of ice, or
in an apparatus properly constructed upon
that principle, the quantity of ice melted dur-
ing the combustion is an exact measure of the
quantity of caloric disengaged. Upon this head,
the Mtmoire given by M. de Laplace and me,
1780, p. 355, may be consulted. Having sub-
mitted the combustion of phosphorus to this
trial, we found that one pound of phosphorus
melted a little more than 100 pounds of ice
during its combustion.

The combustion of phosphorus succeeds
equally well in atmospheric air as in oxygen
gas, with this difference, that the combustion
is vastly slower, being retarded by the large
proportion of azotic gas mixed with the oxy-
gen gas, and that only about one-fifth part of
the air employed is absorbed, because as the
oxygen gas only is absorbed the proportion of
the azotic gas becomes so great toward the
close of the experiment as to put an end to the
combustion.

I have already shown that phosphorus is
changed by combustion into an extremely light,

white, flaky matter; and its properties are
entirely altered by this transformation: from
being insoluble in water, it becomes not only
soluble, but so greedy of moisture as to attract
the humidity of the air with astonishing rapid-
ity; by this means it is converted into a liquid
considerably more dense and of more specific
gravity than water. In the state of phos-
phorus before combustion, it had scarcely any
sensible taste; by its union with oxygen it
acquires an extremely sharp and sour taste:
in a word, from one of the class of combustible
bodies it is changed into an incombustible
substance and becomes one of those bodies
called acids.

This property of a combustible substance to
be converted into an acid, by the addition of
oxygen, we shall presently find belongs to a
great number of bodies: wherefore, strict logic
requires that we should adopt a common term
for indicating all these operations which pro-
duce analogous results; this is the true way to
simplify the study of science, as it would be
quite impossible to bear all its specific details
in the memory if they were not classically ar-
ranged. For this reason, we shall distinguish
this conversion of phosphorus into an acid by
its union with oxygen, and in general every
combination of oxygen with a combustible
substance, by the term of oxygenation: from
which I shall adopt the verb to oxygenate, and
of consequence shall say, that in oxygenating
phosphorus we convert it into an acid.

Sulphur is likewise a combustible body or, in
other words, it is a body which possesses the
power of decomposing oxygen gas by attract-
ing the oxygen from the caloric with which it
was combined. This can very easily be proved
by means of experiments quite similar to those
we have given with phosphorus ; but it is neces-
sary to premise that in these operations with
sulphur the same accuracy of result is not to be
expected as with phosphorus; because the acid
which is formed by the combustion of sulphur
is difficultly condensible, and because sulphur
burns with more difficulty, and is soluble in
the different gases. But I can safely assert,
from my own experiments, that sulphur in
burning absorbs oxygen gas; that the resulting
acid is considerably heavier than the sulphur
burnt; that its weight is equal to the sum of
the weights of the sulphur which has been
burnt and of the oxygen absorbed; and, lastly,
that this acid is weighty, incombustible, and
miscible with water in all proportions: the only
uncertainty remaining upon this head is with

CHEMISTRY

regard to the proportions of sulphur and of
oxygen which enter into the composition of the
acid.

Charcoal, which, from all our present knowl-
edge regarding it, must be considered as a sim-
ple combustible body, has likewise the prop-
erty of decomposing oxygen gas by absorbing
its base from the caloric : but the acid resulting
from this combustion does not condense in the
common temperature; under the pressure of
our atmosphere, it remains in the state of
gas, and requires a large proportion of water
to combine with or be dissolved in. This
acid has, however, all the known properties
of other acids, though in a weaker degree,
and combines, like them, with all the bases
which are susceptible of forming neutral
salts.

The combustion of charcoal in oxygen gas
may be effected like that of phosphorus in the
bell-glass A (Plate iv, Fig. 3) placed over mer-
cury: but, as the heat of red hot iron is not suf-
ficient to set fire to the charcoal, we must add
a small morsel of tinder with a minute particle
of phosphorus, in the same manner as directed
in the experiment for the combustion of iron.
A detailed account of this experiment will be
found in the Recueil de I' Academic for 1781, p.
448. By that experiment it appears that 28
parts by weight of charcoal require 72 parts of
oxygen for saturation and that the aeriform
acid produced is precisely equal in weight to
the sum of the weights of the charcoal and
oxygen gas employed. This aeriform acid was
called fixed or fixable air by the chemists who
first discovered it; they did not then know
whether it was air resembling that of the at-
mosphere or some other elastic fluid, vitiated
and corrupted by combustion; but since it is
now ascertained to be an acid, formed like all
others by the oxygenation of its peculiar base,
it is obvious that the name of fixed air is quite
ineligible.

By burning charcoal in the apparatus men-
tioned, p. 24, M. de Laplace and I found that
one Ib. of charcoal melted 96 Ibs. 6 oz. of ice;
that, during the combustion, 2 Ibs. 9 oz. 1 gros
10 grs. of oxygen were absorbed, and that 3 Ibs.
9 oz. 1 gros 10 grs. of acid gas were formed. This
gas weighs 0.695 parts of a grain for each cubic
inch, in the common standard temperature and
pressure mentioned above, so that 34,242 cubic
inches of acid gas are produced by the com-
bustion of one pound of charcoal.

I might multiply these experiments and show
by a numerous succession of facts that all acids

are formed by the combustion of certain sub-
stances; but I am prevented from doing so in
this place by the plan which I have laid down,
of proceeding only from facts already ascer-
tained to such as are unknown and of drawing
my examples only from circumstances already
explained. In the mean time, however, the
three examples above cited may suffice for
giving a clear and accurate conception of the
manner in which acids are formed. By these it
may be clearly seen that oxygen is an element
common to them all which constitutes their
acidity, and that they differ from each other
according to the nature of the oxygenated or
acidified substance. We must therefore, in
every acid, carefully distinguish between the
acidifiable base, which M. de Morveau calls
the radical, and the acidifying principle or
oxygen.

CHAPTER VI

Of the Nomenclature of Acids in General , and
Particularly of Those Drawn from Nitre and
Sea-Salt

IT becomes extremely easy, from the principles
laid down in the preceding chapter, to establish
a systematic nomenclature for the acids: the
word acid being used as a generic term, each
acid falls to be distinguished in language, as
in nature, by the name of its base or radical.
Thus, we give the generic name of acids to the
products of the combustion or oxygenation of
phosphorus, of sulphur, and of charcoal; and
these products are respectively named the
phosphoric acid, the sulphuric add, and the
carbonic acid.

There is, however, a remarkable circum-
stance in the oxygenation of combustible
bodies, and of a part of such bodies as are con-
vertible into acids, that they are susceptible of
different degrees of saturation with oxygen,
and that the resulting acids, though formed by
the union of the same elements, are possessed
of different properties, depending upon that
difference of proportion. Of this, the phos-
phoric acid, and more especially the sulphuric,
furnishes us with examples. When sulphur is
combined with a small proportion of oxygen,
it forms, in this first or lower degree of oxy-
genation, a volatile acid, having a penetrating
odour and possessed of very particular qual-
ities. By a larger proportion of oxygen, it is
changed into a fixed, heavy acid, without any
odour, and which, by combination with other
bodies, gives products quite different from

LAVOISIER

those furnished by the former. In this instance,
the principles of our nomenclature seem to
fail; and it seems difficult to derive such terms
from the name of the acidifiable base as shall
distinctly express these two degrees of satura-
tion, or oxygenation, without circumlocution.
By reflection, however, upon the subject, or
perhaps rather from the necessity of the case,
we have thought it allowable to express these
varieties in the oxygenation of the acids by
simply varying the termination of their spe-
cific names. The volatile acid produced from
sulphur was anciently known to Stahl under
the name of sulphurous acid. We have pre-
served that term for this acid from sulphur
under-saturated with oxygen; and distinguish
the other, or completely saturated or oxygen-
ated acid, by the name of sulphuric acid. We
shall therefore say, in this new chemical lan-
guage, that sulphur, in combining with oxygen,
is susceptible of two degrees of saturation ; that
the first or lesser degree constitutes sulphurous
acid, which is volatile and penetrating; whilst
the second or higher degree of saturation pro-
duces sulphuric acid, which is fixed and inodor-
ous. We shall adopt this difference of termina-
tion for all the acids which assume several
degrees of saturation. Hence we have a phos-
phorous and a phosphoric acid, an acetous and
an acetic acid; and so on, for others in similar
circumstances.

This part of chemical science would have
been extremely simple, and the nomenclature
of the acids would not have been at all per-
plexed as it is now in the old nomenclature, if
the base or radical of each acid had been known
when the acid itself was discovered. Thus, for
instance, phosphorus being a known substance
before the discovery of its acid, this latter was
rightly distinguished by a term drawn from
the name of its acidifiable base. But when, on
the contrary, an acid happened to be discov-
ered before its base, or rather when the acidi-
fiable base from which it was formed remained
unknown, names were adopted for the two,
which have not the smallest connection; and
thus, not only the memory, became burdened
with useless appellations, but even the minds
of students, nay even of experienced chemists,
became filled with false ideas, which time and
reflection alone are capable of eradicating. We
may give an instance of this confusion with
respect to the acid sulphur: the former chem-
ists having procured this acid from the vitriol
of iron gave it the name of the vitriolic acid

from the name of the substance which pro-
duced it; and they were then ignorant that the
acid procured from sulphur by combustion was
exactly the same.

The same thing happened with the aeriform
acid formerly called fixed air; it not being
known that this acid was the result of combin-
ing charcoal with oxygen, a variety of denom-
inations have been given to it, not one of which
conveys just ideas of its nature or origin. We
have found it extremely easy to correct and
modify the ancient language with respect to
these acids proceeding from known bases, hav-
ing converted the name of vitriolic add into
that of sulphuric, and the name of fixed air
into that of carbonic acid; but it is impossible
to follow this plan with the acids whose bases
are still unknown; with these we have been
obliged to use a contrary plan and, instead of
forming the name of the acid from that of its
base, have been forced to denominate the un-
known base from the name of the known acid,
as happens in the case of the acid which is pro-
cured from sea-salt.

To disengage this acid from the alkaline
base with which it is combined, we have only
to pour sulphuric acid upon sea-salt; imme-
diately a brisk effervescence takes place, white
vapours arise, of a very penetrating odour,
and, by only gently heating the mixture, all
the acid is driven off. As in the common tem-
perature and pressure of our atmosphere this
acid is naturally in the state of gas, we must
use particular precautions for retaining it in
proper vessels. For small experiments, the
most simple and most commodious apparatus
consists of a small retort G (Plate v, Fig. 5\
into which the sea-salt is introduced, well
dried; we then pour on some concentrated sul-
phuric acid, and immediately introduce the
beak of the retort under little jars or bell-
glasses A (same Plate and Fig.), previously
filled with quicksilver. In proportion as the
acid gas is disengaged, it passes into the jar
and gets to the top of the quicksilver, which it
displaces. When the disengagement of the gas
slackens, a gentle heat is applied to the retort
and gradually increased till nothing more
passes over. This acid gas has a very strong
affinity with water, which absorbs an enor-
mous quantity of it, as is proved by introduc-
ing a very thin layer of water into the glass
which contains the gas; for, in an instant, the
whole acid gas disappears and combines with
the water.

CHEMISTRY

This latter circumstance is taken advantage
of in laboratories and manufactures on purpose
to obtain the acid of sea-salt in a liquid form;
and for this purpose the apparatus (Plate iv,
Fig. 1) is employed. It consists, 1st, of a tabu-
lated retort A, into which the sea-salt, and after
it the sulphuric acid, are introduced through the
opening II ; 2nd, of the balloon or recipient c, b,
intended for containing the small quantity of
liquid which passes over during the process;
and, 3rd, of a set of bottles, with two mouths,
L,L,L,L, half filled with water, intended for
absorbing the gas disengaged by the distilla-
tion. This apparatus will be more amply de-
scribed in the latter part of this work.

Although we have not yet been able, either
to compose or to decompound this acid of sea-
salt, we cannot have the smallest doubt that it,
like all other acids, is composed by the union
of oxygen with an acidifiable base. We have
therefore called this unknown substance the
muriatic base, or muriatic radical, deriving this
name, after the example of M. Bergman and
M. de Morveau, from the Latin word muria,
which was anciently used to signify sea-salt.
Thus, without being able exactly to determine
the component parts of muriatic acid, we de-
sign by that term a volatile acid, which retains
the form of gas in the common temperature
and pressure of our atmosphere, which com-
bines with great facility, and in great quantity,
with water, and whose acidifiable base adheres
so very intimately with oxygen that no method
has hitherto been devised for separating them.
If ever this acidifiable base of the muriatic
acid is discovered to be a known substance,
though now unknown in that capacity, it
will be requisite to change its present denom-
ination for one analogous with that of its
base.

In common with sulphuric acid, and several
other acids, the muriatic is capable of different
degrees of oxygenation; but the excess of oxy-
gen produces quite contrary effects upon it
from what the same circumstance produces
upon the acid of sulphur. The lower degree of
oxygenation converts sulphur into a volatile
gaseous acid, which only mixes in small pro-
portions with water, whilst a higher oxygena-
tion forms an acid possessing much stronger
acid properties, which is very fixed and cannot
remain in the state of gas but in a very high
temperature, which has no smell, and which
mixes in large proportion with water. With
muriatic acid, the direct reverse takes place;

an additional saturation with oxygen renders
it more volatile, of a more penetrating odour,
less miscible with water, and diminishes its
acid properties. We were at first inclined to
have denominated these two degrees of satura-
tion in the same manner as we had done with
the acid of sulphur, calling the less oxygen-
ated muriatous acid, and that which is more
saturated with oxygen muriatic acid: but, as
this latter gives very particular results in
its combinations, and as nothing analo-
gous to it is yet known in chemistry, we have
left the name of muriatic acid to the less
saturated and given the latter the more com-
pounded appellation of oxygenated muriatic
acid.

Although the base or radical of the acid
which is extracted from nitre or saltpetre be
better known, we have judged proper only to
modify its name in the same manner with that
of the muriatic acid. It is drawn from nitre by
the intervention of sulphuric acid, by a process
similar to that described for extracting the
muriatic acid, and by means of the same ap-
paratus (Plate iv, Fig. l).ln proportion as the
acid passes over, it is in part condensed in
the balloon or recipient and the rest is ab-
sorbed by the water contained in the bottles
L, L, L, L; the water becomes first green, then
blue, and at last yellow, in proportion to the
concentration of the acid. During this opera-
tion, a large quantity of oxygen gas, mixed
with a small proportion of azotic gas, is dis-
engaged.

This acid, like all others, is composed of oxy-
gen, united to an acidifiable base, and is even
the first acid in which the existence of oxygen
was well ascertained. Its two constituent ele-
ments are but weakly united and are easily
separated by presenting any substance with
which oxygen has a stronger affinity than with
the acidifiable base peculiar to this acid. By
some experiments of this kind, it was first dis-
covered that azote, or the base of mephitis or
azotic gas, constituted its acidifiable base or
radical, and consequently that the acid of nitre
was really an azotic acid, having azote for its
base, combined with oxygen. For these rea-
sons, that we might be consistent with our
principles, it appeared necessary either to call
the acid by the name of azotic or to name the
base nitric radical; but from either of these 1 we !
were dissuaded by the following considerations.
In the first place, it seemed difficult to change
the name of nitre or saltpetre, which has been

LAVOISIER

universally adopted in society, in manufac-
tures, and in chemistry; and, on the other
hand, azote having been discovered by M.
Berthollet to be the base of volatile alkali, or
ammonia, as well as of this acid, we thought it
improper to call it nitric radical. We have
therefore continued the term of azote to the
base of that part of atmospheric air which is
likewise the nitric and ammoniacal radical;
and we have named the acid of nitre, in its
lower and higher degrees of oxygenation, ni-
trous add in the former and nitric acid in the
latter state; thus preserving its former appella-
tion properly modified.

Several very respectable chemists have dis-
approved of this deference for the old terms
and wished us to have persevered in perfecting
a new chemical language, without paying any
respect for ancient usage; so that, by thus
steering a kind of middle course, we have ex-
posed ourselves to the censures of one sect of
chemists, and to the expostulations of the op-
posite party.

The acid of nitre is susceptible of assuming a
great number of separate states, depending up-
on its degree of oxygenation or upon the pro-
portions in which azote and oxygen enter into
its composition. By a first or lowest degree of
oxygenation it forms a particular species of
gas, which we shall continue to name nitrous
gas; this is composed nearly of two parts, by
weight, of oxygen combined with one part of
azote; and in this state it is not miscible with
water. In this gas, the azote is by no means
saturated with oxygen, but, on the contrary,
has still a very great affinity for that element
and even attracts it from atmospheric air, im-
mediately upon getting into contact with it.
This combination of nitrous gas with atmos-
pheric air has even become one of the methods
for determining the quantity of oxygen con-
tained in air and consequently for ascertaining
its degree of salubrity.

This addition of oxygen converts the nitrous
gas into a powerful acid, which has a strong
affinity with water and which is itself suscep-
tible of various additional degrees of oxygena-
tion. When the proportions of oxygen and
azote is below three parts, by weight, of the
former to one of the latter, the acid is red col-
oured and emits copious fumes. In this state,
by the application of a gentle heat, it gives out
nitrous gas, and we term it, in this degree of
oxygenation, nitrous acid. When four parts, by
weight, of oxygen are combined with one part

of azote, the acid is clear and colourless, more
fixed in the fire than the nitrous acid, has less
odour, and its constituent elements are more
firmly united. This species of aeid, in conform-
ity with our principles of nomenclature, is
called nitric acid.

Thus, nitric acid is the acid of nitre, sur-
charged with oxygen; nitrous &cid is the acid
of nitre surcharged with azote or, what is the
same thing, with nitrous gas; and this latter is
azote not sufficiently saturated with oxygen to
possess the properties of an acid. To this de-
gree of oxygenation, we have afterwards, in
the course of this work, given the generical
name of oxide.

CHAPTER VII

Of the Decomposition of Oxygen Gas by Means of
Metals and the Formation of Metallic Oxides

OXYGEN has a stronger affinity with metals
heated to a certain degree than with caloric;
in consequence of which, ail metallic bodies,
excepting gold, silver, and platinum, have the
property of decomposing oxygen gas, by at-
tracting its base from the caloric with which it
was combined. We have already shown in what
manner this decomposition takes place, by
means of mercury and iron; having observed,
that, in the case of the first, it must be consid-
ered as a kind of gradual combustion, whilst,
in the latter, the combustion is extremely
rapid and attended with a brilliant flame. The
use of the heat employed in these operations
is to separate the particles of the metal from
each other and to diminish their attraction
of cohesion or aggregation or, which is the
same thing, their mutual attraction for each
other.

The absolute weight of metallic substances
is augmented in proportion to the quantity of
oxygen they absorb; they, at the same time,
lose their metallic splendour, and are reduced
into an earthy pulverulent matter. In this state
metals must not be considered as entirely sat-
urated with oxygen, because their action upon
this element is counterbalanced by >the power
of affinity between it and caloric. During the
calcination of metals the oxygen is, therefore,
acted upon by two separate and opposite pow-
ers, that of its attraction for caloric and that
exerted by the metal, and only tends to unite
with the latter in consequence of the excess of
the latter over the former, which is, in general,

CHEMISTRY

very inconsiderable. Wherefore, when metallic
substances are oxygenated in atmospheric air
or in oxygen gas, they are not converted into
acids like sulphur, phosphorus, and charcoal,
but are only changed into intermediate sub-
stances, which, though approaching to the
nature of salts, have not acquired all the saline
properties. The old chemists have affixed the
name of calx not only to metals in this state
but to every body which has been long exposed
to the action of fire without being melted.
They have converted this word calx into a
generical term, under which they confound
calcareous earth, which, from a neutral salt,
which it really was before calcination, has been
changed by fire into an earthy alkali, by losing
half of its weight, with metals which, by the
same means, have joined themselves to a new
substance, whose quantity often exceeds half
their weight, and by which they have been
changed almost into the nature of acids. This
mode of classifying substances of so very op-
posite natures under the same generic name
would have been quite contrary to our prin-
ciples of nomenclature, especially as, by re-
taining the above term for this state of metal-
lic substances, we must have conveyed very
false ideas of its nature. We have, therefore,
laid aside the expression metallic calx alto-
gether and have substituted in its place the
term oxide, from the Greek word ous.

By this may be seen that the language we
have adopted is both copious and expressive.
The first, or lowest, degree of oxygenation in
bodies converts them into oxides; a second de-
gree of additional oxygenation constitutes the
class of acids, of which the specific names,
drawn from their particular bases, terminate
in ous, as the nitrous and sulphurous acids; the
third degree of oxygenation changes these into
the species of acids distinguished by the term-
ination in ic, as the nitric and sulphuric acids;
and, lastly, we can express a fourth, or highest
degree of oxygenation, by adding the word
oxygenated to the name of the acid, as has been
already done with the oxygenated muriatic
acid.

We have not confined the term oxide to ex-
pressing the combinations of metals with oxy-
gen, but have extended it to signify that first
degree of oxygenation in all bodies, which,
without converting them into acids, causes
them to approach to the nature of salts. Thus,
we give the name of oxide of sulphur to that
soft substance into which sulphur is converted

by incipient combustion; and we call the yel-
low matter left by phosphorus, after combus-
tion, by the name of oxide of phosphorus. In
the same manner, nitrous gas, which is azote
in its first degree of oxygenation, is the oxide of
azote. We have likewise oxides in great num-
bers from the vegetable and animal kingdoms;
and I shall show, in the sequel, that this new
language throws great light upon all the oper-
ations of art and nature.

We have already observed that almost all
the metallic oxides have peculiar and perma-
nent colours. These vary not only in the differ-
ent species of metals, but even according to
the various degrees of oxygenation in the same
metal. Hence we are under the necessity of
adding two epithets to each oxide, one of which
indicates the metal oxidated, while the other
indicates the peculiar colour of the oxide. Thus,
we have the black oxide of iron, the red oxide
of iron, and the yellow oxide of iron; which
expressions respectively answer to the old
unmeaning terms of martial ethiops, colco-
thar, and rust of iron, or ochre. We have like-
wise the gray, yellow, and red oxides of lead,
which answer to the equally false or insig-
nificant terms, ashes of lead, massicot, and
minium.

These denominations sometimes become ra-
ther long, especially when we mean to indicate
whether the metal has been oxidated in the
air, by detonation with nitre, or by means of
acids; but then they always convey just and
accurate ideas of the corresponding object
which we wish to express by their use. All this
will be rendered perfectly clear and distinct by
means of the tables which are added to this
work.

CHAPTER VIII

Of the Radical Principle of Water and of its De-
composition by Charcoal and Iron

UNTIL very lately, water has always been
thought a simple substance, insomuch that the
older chemists considered it as an element.
Such it undoubtedly was to them, as they were
unable to decompose it; or, at least, since the
decomposition which took place daily before
their eyes was entirely unnoticed. But we
mean to prove that water is by no means a
simple or elementary substance. I shall not
here pretend to give the history of this recant
and hitherto contested discovery, which is de-
tailed in the Recueil de V Academic for 1781, but

LAVOISIER

shall only bring forwards the principal proofs
of the decomposition and composition of wa-
ter; and I may venture to say that these will be
convincing to such as consider them impartially.

First Experiment

Having fixed the glass tube EF (Plate vn,
Fig. 11) of from 8 to 12 lines diameter across a
furnace, with a small inclination from E to F,
lute the superior extremity E to the glass re-
tort A, containing a determinate quantity of
distilled water, and to the inferior extremity F
the worm SS fixed into the neck of the doubly
tubulated bottle H, which has the bent tube
KK adapted to one of its openings, in such a
manner as to convey such aeriform fluids or
gases as may be disengaged, during the exper-
iment, into a proper apparatus for determining
their quantity and nature.

To render the success of this experiment cer-
tain, it is necessary that the tube EF be made
of well annealed and difficultly fusible glass,
and that it be coated with a lute composed of
clay mixed with powdered stone- ware; besides
which, it must be supported about its middle
by means of an iron bar passed through the
furnace, lest it should soften and bend during
the experiment. A tube of chinaware, or por-
celain, would answer better than one of glass
for this experiment, were it not difficult to pro-
cure one so entirely free from pores as to pre-
vent the passage of air or of vapours.

When things are thus arranged, a fire is
lighted in the furnace EFCD, which is sup-
ported of such a strength as to keep the tube
EF red hot but not to make it melt; and, at
the same time, such a fire is kept up in the fur-
nace WXX as to keep the water in the retort
A continually 'boiling.

In proportion as the water in the retort A is
evaporated it fills the tube EF, and drives out
the air it contained by the tube KK; the aque-
ous gas formed by evaporation is condensed by
cooling in the worm SS and falls, drop by drop,
into the tubulated bottle H. Having continued
this operation until all the water be evaporated
from the retort, and having carefully emptied
ail the vessels employed, we find that a quan-
tity of water has passed over into the bottle H
exactly equal to what was before contained in
the retort A, without any disengagement of
gas whatsoever: so that this experiment turns
out to be a simple distillation, and the result
would have been exactly the same, if the water
had been run from one vessel into the other,

through the tube EF, without having under-
gone the intermediate incandescence.

Second Experiment

The apparatus being disposed, as in the for-
mer experiment, 28 grs. of charcoal, broken into
moderately small parts and which have pre-
viously been exposed for a long time to a red
heat in close vessels, are introduced into the
tube EF. Everything else is managed as in the
preceding experiment.

The water contained in the retort A is dis-
tilled, as in the former experiment, and, being
condensed in the worm, falls into the bottle H;
but, at the same time, a considerable quantity
of gas is disengaged, which, escaping by the
tube KK, is received in a convenient apparatus
for that purpose. After the operation is fin-
ished, we find nothing but a few atoms of ashes
remaining in the tube EF, the 28 grs. of char-
coal having entirely disappeared.

When the disengaged gases are carefully ex-
amined, they are found to weigh 113.7 grs.; 1
these are of two kinds, viz., 144 cubic inches of
carbonic acid gas weighing 100 grs. and 380
cubic inches of a very light gas weighing only
13.7 grs. y which takes fire when in contact with
air, by the approach of a lighted body; and,
when the water which has passed over into the
bottle H is carefully examined, it is found to
have lost 85.7 grs. of its weight. Thus, in this
experiment, 85.7 grs. of water, joined to 28 grs.
of charcoal, have combined in such a way as to
form 100 grs. of carbonic acid, and 13.7 grs. of
a particular gas capable of being burnt.

I have already shown, that 100 grs. of car-
bonic acid gas consists of 72 grs. of oxygen
combined with 28 grs. of charcoal; hence the 28
grs. of charcoal placed hi the glass tube have
acquired 72 grs. of oxygen from the water; and
it follows that 85.7 grs. of water are composed
of 72 grs. of oxygen combined with 13.7 grs. of a
gas susceptible of combustion. We shall see pres-
ently that this gas cannot possibly have been
disengaged from the charcoal and must, con-
sequently, have been produced from the water.

I have suppressed some circumstances in the
above account of this experiment, which would
only have complicated and obscured its results
hi the minds of the reader. For instance, the
inflammable gas dissolves a very small part of

1 In the latter part of this work will be found a
particular account of the processes necessary for
separating the different kinds of gases, and for deter-
mining their quantities. AUTHOR.

CHEMISTRY

the charcoal, by which means its weight is
somewhat augmented and that of the carbonic
gas proportionally diminished. Altho' the al-
teration produced by this circumstance is very
inconsiderable, yet I have thought it necessary
to determine its effects by rigid calculation,
and to report, as above, the results of the ex-
periment in its simplified state, as if this cir-
cumstance had not happened. At any rate,
should any doubts remain respecting the con-
sequences I have drawn from this experiment,
they will be fully dissipated by the following
experiments, which I am going to adduce in
support of my opinion.

Third Experiment

The apparatus being disposed exactly as in
the former experiment, with this difference,
that instead of the 28 grs. of charcoal the tube
EF is filled with 274 grs. of soft iron in thin
plates, rolled up spirally. The tube is made red
hot by means of its furnace, and the water in
the retort A is kept constantly boiling till it be
all evaporated, and has passed through the
tube EF so as to be condensed in the bottle H.

No carbonic acid gas is disengaged in this
experiment, instead of which we obtain 416
cubic inches, or 15 grs. of inflammable gas,
thirteen times lighter than atmospheric air. By
examining the water which has been distilled,
it is found to have lost 100 grs. and the 274 grs.
of iron confined in the tube are found to have
acquired 85 grs. additional weight and its mag-
nitude is considerably augmented. The iron is
now hardly at all attractable by the magnet;
it dissolves in acids without effervescence; and,
in short, it is converted into a black oxide, pre-
cisely similar to that which has been burnt in
oxygen gas.

In this experiment we have a true oxidation
of iron, by means of water, exactly similar to
that produced in air by the assistance of heat.
One hundred grains of water having been de-
composed, 85 grs. of oxygen have combined
with the iron, so as to convert it into the state
of black oxide, and 15 grs. of a peculiar inflam-
mable gas are disengaged: from all this it clear-
ly follows that water is composed of oxygen
combined with the base of an inflammable gas,
in the respective proportions of 85 parts, by
weight of the former, to 15 parts of the latter,

Thus water, besides the oxygen which is one
of its elements in common with many other
substances, contains another element as its
constituent base or radical and for which we

must find an appropriate term. None that we
could think of seemed better adapted than the
word hydrogen, which signifies the generative
principle of water, from vBop aqua, and 7ewo-
/*eu gignor. 1 We call the combination of this
element with caloric hydrogen gas; and the
term hydrogen expresses the base of that gas,
or the radical of water.

This experiment furnishes us with a new
combustible body, or, in other words, a body
which has so much affinity with oxygen as to
draw it from its connection with caloric and to
decompose air or oxygen gas. This combustible
body has itself so great affinity with caloric
that, unless when engaged in a combination
with some other body, it always subsists in the
aeriform or gaseous state, in the usual temper-
ature and pressure of our atmosphere. In this
state of gas it is about YIS of the weight of an
equal bulk of atmospheric air; it is not ab-
sorbed by water, though it is capable of hold-
ing a small quantity of that fluid in solution,
and it is incapable of being used for respiration.

As the property this gas possesses, in com-
mon with all other combustible bodies, is no-
thing more than the power of decomposing air
and carrying off its oxygen from the caloric
with which it was combined, it is easily under-
stood that it cannot burn unless in contact
with air or oxygen gas. Hence, when we set fire
to a bottle full of this gas, it burns gently, first
at the neck of the bottle, and then in the inside
of it, in proportion as the external air gets in.
This combustion is slow and successive and only
takes place at the surface of contact between
the two gases. It is quite different when the
two gases are mixed before they are set on fire:
if, for instance, after having introduced one
part of oxygen gas into a narrow mouthed bot-
tle, we fill it up with two parts of hydrogen gas
and bring a lighted taper or other burning
body to the mouth of the bottle, the combus-
tion of the two gases takes place instantaneously
with a violent explosion. This experiment
ought only to be made in a bottle of very strong
green glass, holding not more than a pint, and
wrapped round with twine, otherwise the oper-
ator will be exposed to great danger from the

1 This expression hydrogen has been very severely
criticised by some, who pretend that it signifies en-
gendered by water and not that which engenders
water. The experiments related in this chapter prove
that when water is decomposed hydrogen is pro-
duced, and that when hydrogen is combined with
oxygen water is produced : so that we may say, with
equal truth, that water is produced from hydrogen,
or hydrogen is produced from water. AUTHOK.

LAVOISIER

rupture of the bottle, of which the fragments
will be thrown about with great force.

If all that has been related above, concern-
ing the decomposition of water, be exactly con-
formable to truth; if, as I have endeavoured
to prove, that substance be really composed of
hydrogen, as its proper constituent element,
combined with oxygen, it ought to follow that,
by reuniting these two elements together, we
should recompose water; and that this actually
happens may be judged of by the following
experiment.

Fourth Experiment

I took a large crystal balloon A (Plate iv, Fig.
6) holding about 30 pints, having a large open-
ing, to which was cemented the plate of copper
BC pierced with four holes in which four tubes
terminate. The first tube, H^, is intended to
be adapted to an air pump, by which the balloon
is to be exhausted of its air. The second ture
gg, communicates, by its extremity MM, with
a reservoir of oxygen gas, with which the bal-
loon is to be filled. The third tube dDd' com-
municates, by its extremity dNN, with a res-
ervoir of hydrogen gas. The extremity d' of
this tube terminates in a capillary opening,
through which the hydrogen gas contained in
the reservoir is forced, with a moderate degree
of quickness, by the pressure of one or two
inches of water. The fourth tube contains a
metallic wire GL, having a knob at its extrem-
ity L, intended for giving an electrical spark
from L to d', on purpose to set fire to the hy-
drogen gas: this wire is moveable in the tube,
that we may be able to separate the knob L
from the extremity d' of the tube Dd f . The
three tubes dDd', gg, and H/i, are all provided
with stop-cocks.

That the hydrogen gas and oxygen gas may
be as much as possible deprived of water, they
are made to pass, in their way to the baloon A,
through the tubes MM, NN, of about an inch
diameter, and filled with salts, which, from
their deliquescent nature, greedily attract the
moisture of the air: such are the acetite of
potash, and the muriate or nitrate of lime. 1
These salts must only be reduced to a coarse
powder, lest they run into lumps, and prevent
the gases from getting through their inter-
stices.

We must be provided beforehand with a
sufficient quantity of oxygen gas, carefully
purified from all admixture of carbonic acid by

1 See the nature of these salts in the second part of
this book. AUTHOR.

long contact with a solution of potash. 2

We must likewise have a double quantity of
hydrogen gas, carefully purified in the same
manner by long contact with a solution of pot-
ash in water. The best way of obtaining this
gas free from mixture is by decomposing water
with very pure soft iron, as directed in Exp. 3
of this chapter.

Having adjusted everything properly, as
above directed, the tube HA is adapted to an
air-pump, and the balloon A is exhausted of its
air. We next admit the oxygen gas so as to fill
the balloon and then, by means of pressure as
is before mentioned, force a small stream of
hydrogen gas through its tube Dd 1 , which we
immediately set on fire by an electric spark.
By means of the above described apparatus,
we can continue the mutual combustion of
these two gases for a long time, as we have the
power of supplying them to the balloon from
their reservoirs, in proportion as they are con-
sumed. I have in another place 3 given a de-
scription of the apparatus used in this experi-
ment and have explained the manner of ascer-
taining the quantities of the gases consumed
with the most scrupulous exactitude.

In proportion to the advancement of the
combustion, there is a deposition of water upon
the inner surface of the balloon or matrass A :
the water gradually increases in quantity and,
gathering into large drops, runs down to the
bottom of the vessel. It is easy to ascertain the
quantity of water collected, by weighing the
balloon both before and after the experiment.
Thus we have a twofold verification of our ex-
periment, by ascertaining both the quantities
of the gases employed and of the water formed
by their combustion : these two quantities must
be equal to each other. By an operation of this
kind, M. Meusnier and I ascertained that it
required 85 parts, by weight, of oxygen, united
to 15 parts of hydrogen, to compose 100 parts
of water. This experiment, which has not
hitherto been published, was made in pres-
ence of a numerous committee from the Royal
Academy. We exerted the most scrupulous
attention to its accuracy and have reason to
believe that the above propositions cannot vary
a two-hundredth part from absolute truth.

From these experiments, both analytical and
synthetic, we may now affirm that we have
ascertained, with as much certainty as is pos-

1 The method of obtaining this pure alkali of pot-
ash will be given in the sequel. AUTHOR.
8 See the third part of this work. AUTHOR.

CHEMISTRY

sible in physical or chemical subjects, that
water is not a simple elementary substance
but is composed of two elements, oxygen and
hydrogen; which elements, when existing
separately, have so strong affinity for caloric
as only to subsist under the form of gas in the
common temperature and pressure of our
atmosphere.

This decomposition and recomposition of
water is perpetually operating before our eyes,
in the temperature of the atmosphere, by
means of compound elective attraction. We
shall presently see that the phenomena attend-
ant upon vinous fermentation, putrefaction,
and even vegetation, are produced, at least in
a certain degree, by decomposition of water.
It is very extraordinary that this fact should
have hitherto been overlooked by natural phi-
losophers and chemists: indeed, it strongly
proves that, in chemistry as in moral philos-
ophy, it is extremely difficult to overcome prej-
udices imbibed in early education and to search
for truth in any other road than the one we
have been accustomed to follow.

I shall finish this chapter by an experiment
much less demonstrative than those already
related, but which has appeared to make more
impression than any other upon the minds of
many people. When 16 ounces of alcohol are
burnt in an apparatus 1 properly adapted for
collecting all the water disengaged during the
combustion, we obtain from 17 to 18 ounces of
water. As no substance can furnish a product
larger than its original bulk, it follows that
something else has united with the alcohol dur-
ing its combustion; and I have already shown
that this must be oxygen, or the base of air.
Thus alcohol contains hydrogen, which is one
of the elements of water; and the atmospheric
air contains oxygen, which is the other element
necessary to the composition of water. This
experiment is a new proof that water is a com-
pound substance.

CHAPTER IX

Of the Quantities of Caloric Disengaged from
Different Species of Combustion

WE have already mentioned that, when any
body is burnt in the center of a hollow sphere
of ice and supplied with air at the temperature
of zero (32), the quantity of ice melted from
the inside of the sphere becomes a measure of

* See an aocount of this apparatus in the third part
of this work. AUTHOR.

the relative quantities of caloric disengaged.
M. de Laplace and I gave a description of the
apparatus employed for this kind of experiment
in the Recueil de I'Academie for 1780, p. 355;
and a description and plate of the same appa-
ratus will be found in the third part of this work.
With this apparatus, phosphorus, charcoal, and
hydrogen gas, gave the following results:

one pound of phosphorus melted 1 00 Ibs . of ice ;

one pound of charcoal melted 96 Ibs. 8 oz;

one pound of hydrogen gas melted 295 Ibs.
9 oz. %y<i gros.

As a concrete acid is formed by the combus-
tion of phosphorus, it is probable that very
little caloric remains in the acid and, conse-
quently, that the above experiment gives us
very nearly the whole quantity of caloric con-
tained in the oxygen gas. Even if we suppose
the phosphoric acid to contain a good deal of
caloric, yet, as the phosphorus must have con-
tained nearly an equal quantity before com-
bustion, the error must be very small, as it will
only consist of the difference between what
was contained in the phosphorus before, and
in the phosphoric acid after combustion.

I have already shown in Chapter V that one
pound of phosphorus absorbs one pound eight
ounces of oxygen during combustion; and
since, by the same operation, 100 Ibs. of ice are
melted, it follows that the quantity of caloric
contained in one pound of oxygen gas is ca-
pable of melting 66 Ibs. 10 oz.5gros 24 grs. of ice.

One pound of charcoal during combustion
melts only 96 Ibs. 8 oz. of ice, whilst it absorbs
2 Ibs. 9 oz. 1 gros 10 grs. of oxygen. By the ex-
periment with phosphorus, this quantity of
oxygen gas ought to disengage a quantity of
caloric sufficient to melt 171 Ibs. 6 oz. 5 gros of
ice; consequently, during this experiment, a
quantity of caloric sufficient to melt 74 Ibs. 14
oz. 5 gros of ice disappears. Carbonic acid is
not, like phosphoric acid, in a concrete state
after combustion but in the state of gas and re-
quires to be united with caloric to enable it to
subsist in that state; the quantity of caloric
missing in the last experiment is evidently em-
ployed for that purpose. When we divide that
quantity by the weight of carbonic acid formed
by the combustion of one pound of charcoal,
we find that the quantity of caloric necessary
for changing one pound of carbonic acid from
the concrete to the gaseous state would be ca-
pable of melting 20 Ibs. 15 oz. 5 gros of ice.

We may make a similar calculation with the
combustion of hydrogen gas and the conse-

LAVOISIER

quent formation of water. During the combus-
tion of one pound of hydrogen gas, 5 Ibs. 10 oz.
5 gros 24 grs. of oxygen gas are absorbed, and
295 Ibs. 9 oz. 3J/ gros of ice are melted. But 5
Ibs. 10 oz. 5 gros 24 grs. of oxygen gas, in chang-
ing from the aeriform to the solid state, loses,
according to the experiment with phosphorus,
enough of caloric to have melted 377 /6s. 12 oz.
3 gros of ice. There is only disengaged from the
same quantity of oxygen, during its combus-
tion with hydrogen gas, as much caloric as
melts 295 Ibs. 2 oz. 3% gros; wherefore there
remains in the water at zero (32), formed,
during this experiment, as much caloric as
would melt 82 Ibs. 9 oz. 7 % gros of ice.

Hence, as 6 Ibs. 10 oz. 5 gros 24 grs. of water
are formed from the combustion of one pound
of hydrogen gas with 5 Ibs. 10 oz. 5 gros 24 grs.
of oxygen, it follows that in each pound of
water, at the temperature of zero (32), there
exists as much caloric as would melt 12 Ibs.
5 oz. 2 gros 48 grs. of ice, without taking into
account the quantity originally contained in the
hydrogen gas, which we have been obliged to
omit for want of data to calculate its quantity.
From this it appears that water, even in the
state of ice, contains a considerable quantity
of caloric, and that oxygen, in entering into that
combination, retains likewise a good proportion.

From these experiments, we may assume the
following results as sufficiently established.

Combustion of phosphorus

From the combustion of phosphorus, as re-
lated in the foregoing experiments, it appears
that one pound of phosphorus requires 1 Ib. 8 oz.
of oxygen gas for its combustion and that 2 /6s.
8 oz. of concrete phosphoric acid are produced.

The quantity of caloric disengaged by
the combustion of one pound of phos-
phorus, expressed by the number of
pounds of ice melted during that op-
eration, is 100.00000
The quantity disengaged from each
pound of oxygen during the combus-
tion of phosphorus, expressed in the
same manner, is 66.66667
The quantity disengaged during the
formation of one pound of phosphoric
acid 40.00000
The quantity remaining in each pound
of phosphoric acid O.OOOOO 1

1 We here suppose the phosphoric acid not to con-
tain any caloric, which is not strictly true; but, as
I have before observed, the quantity it really con-
tains is probably very small, and we have not given
it a value, for want of sufficient data to go upon.
AUTHOR.

Combustion of charcoal

In the combustion of one pound of charcoal,
2 Ibs. 9 oz. 1 gros 10 grs. of oxygen gas are ab-
sorbed, and 3 Ibs. 9 oz. 1 gros 10 grs. of carbonic
acid gas are formed.

Caloric disengaged during the combus-
tion of one pound of charcoal 96.50000
Caloric disengaged during the combus-
tion of charcoal, from each pound of
oxygen gas absorbed 37.52823
Caloric disengaged during the formation
of one pound of carbonic acid gas 27.02024
Caloric retained by each pound of oxy-
gen after the combustion 29.13844
Caloric necessary for supporting one
pound of carbonic acid in the state of
gas 20.97960

Combustion of hydrogen gas

In the combustion of one pound of hydrogen
gas, 5 Ibs. 10 oz. 5 gros 24 grs. of oxygen gas are
absorbed and 6 Ibs. 10 oz. 5 gros 24 grs. of water
are formed.

Caloric from each Ib. of hydrogen gas 295.58950
Caloric from each Ib. of oxygen gas 52.16280
Caloric disengaged during the forma-
tion of each pound of water 44.33840
Caloric retained by each Ib. of oxygen
after combustion with hydrogen 14.50386
Caloric retained by each Ib. of water at
the temperature of zero (32) 12.32823

Formation of nitric add

When we combine nitrous gas with oxygen
gas so as to form nitric or nitrous acid a degree
of heat is produced which is much less consid-
erable than what is evolved during the other
combinations of oxygen; whence it follows
that oxygen, when it becomes fixed in nitric
acid, retains a great part of the heat which it
possessed in the state of gas. It is certainly pos-
sible to determine the quantity of caloric which
is disengaged during the combination of these
two gases and consequently to determine what
quantity remains after the combination takes
place. The first of these quantities might be
ascertained by making the combination of the
two gases in an apparatus surrounded by ice;
but, as the quantity of caloric disengaged is
very inconsiderable, it would be necessary to
operate upon a large quantity of the two gases
in a very troublesome and complicated appa-
ratus. By this consideration, M. de Laplace
and I have hitherto been prevented from mak-

CHEMISTRY

ing the attempt. In the meantime, the place of
such an experiment may be supplied by cal-
culations, the results of which cannot be very
far from truth.

M. de Laplace and I deflagrated a conven-
ient quantity of nitre and charcoal in an ice
apparatus and found that twelve pounds of ice
were melted by the deflagration of one pound
of nitre. We shall see, in the sequel, that one
pound of nitre is composed, as below, of

potash 7 oz. 6 gros 51.84 grs. = 4515.84 grs.
dry acid 8 1 21.16 = 4700.16

The above quantity of dry acid is com-
posed of

oxygen 6 oz. 3 gros 66.34 grs. = 3738.34 grs'
azote 1 5 25.82 = 961.82

By this we find that during the above de-
flagration 2 gros l}s gr. of charcoal have suf-
fered combustion, alongst with 3738.34 grs.
or 6 oz. 3 gros 66.34 grs. of oxygen. Hence,
since 12 Ibs. of ice were melted during the com-
bustion, it follows that one pound of oxygen
burnt in the same manner would have melted
29.58320 Ibs. of ice. To which the quantity of
caloric, retained by a pound of oxygen after
combining with charcoal to form carbonic acid
gas, being added which was already ascer-
tained to be capable of melting 29.13844 Ibs.
of ice, we have for the total quantity of caloric
remaining in a pound of oxygen, when com-
bined with nitrous gas in the nitric acid
58.72164; which is the number of pounds of ice
the caloric remaining in the oxygen in that
state is capable of melting.

We have before seen that, in the state of
oxygen gas, it contained at least 66.66667;
wherefore it follows that, in combining with
azote to form nitric acid, it only loses 7.94502.
Further experiments upon this subject are
necessary to ascertain how far the results of
this calculation may agree with direct fact.
This enormous quantity of caloric retained by
oxygen in its combination into nitric acid ex-
plains the cause of the great disengagement of
caloric during the deflagrations of nitre; or,
more strictly speaking, upon all occasions of
the decomposition of nitric acid.

Combustion of wax

Having examined several cases of simple
combustion, I mean now to give a few examples
of a more complex nature. One pound of wax-
taper being allowed to burn slowly in an ice ap-
paratus melted 133 Ibs. 2 oz. 5% gros of ice.

According to my experiments in the Recueil de
V Academic for 1784, p. 606, one pound of wax-
taper consists of 13 oz. 1 gros 23 grs. of char-
coal and 2 oz. 6 gros 49 grs. of hydrogen.

By the foregoing experi-
ments, the above quantity
of charcoal ought to melt 79.39390 Ibs. of ice
The hydrogen should melt 52.37605

Total 131. 76995 Ibs.

Thus, we see the quantity of caloric disen-
gaged from a burning taper is pretty exactly
conformable to what was obtained by burning
separately a quantity of charcoal and hydrogen
equal to what enters into its composition. These
experiments with the taper were several times
repeated, so that I have reason to believe them
accurate.

Combustion of Olive Oil

We included a burning lamp, containing a
determinate quantity of olive oil, in the ordi-
nary apparatus and, when the experiment was
finished, we ascertained exactly the quantities
of oil consumed and of ice melted; the result
was that during the combustion of one pound
of olive oil, 148 Ibs. 14 oz. 1 gros of ice were
melted. By my experiments in the Recueil de
I'Acadtmie for 1784, and of which the follow-
ing chapter contains an abstract, it appears
that one pound of olive oil consists of 12 oz. 5
gros 5 grs. of charcoal and 3 oz. 2 gros 67 grs. of
hydrogen. By the foregoing experiments, that
quantity of charcoal should rneit 76.18723 Ibs.
of ice, and the quantity of hydrogen in a pound
of the oil should melt 62.15053 Ibs. The sum of
these two gives 138.33776 Ibs. of ice, which the
two constituent elements of the oil would have
melted had they separately suffered combus-
tion, whereas the oil really melted 148.88330
Ibs. which gives an excess of 10.54554 in the
result of the experiment above the calculated
result, from data furnished by former experi-
ments.

This difference, which is by no means very
considerable, may arise from errors which are
unavoidable in experiments of this nature, or
it may be owing to the composition of oil not
being as yet exactly ascertained. It proves,
however, that there is a great agreement be-
tween the results of our experiments, respect-
ing the combination of caloric and those which
regard its disengagement.

The following desiderata still remain to be
determined, viz : what quantity of caloric is re-

LAVOISIER

tained by oxygen, after combining with metals,
so as to convert them into oxides; what quan-
tity is contained by hydrogen, in its different
states of existence; and to ascertain, with more
precision than is as yet attained, how much
caloric is disengaged during the formation of
water, as there still remain considerable doubts
with respect to our present determination of
this point, which can only be removed by fur-
ther experiments. We are at present occupied
with this inquiry and when once these several
points are well ascertained, which we hope they
will soon be, we shall probably be under the
necessity of making considerable corrections
upon most of the results of the experiments
and calculations in this chapter. I did not,
however, consider this as a sufficient reason
for withholding so much as is already known
from such as may be inclined to labour upon
the same subject. It is difficult in our endeav-
ours to discover the principles of a new science,
to avoid beginning by guess-work; and it is
rarely possible to arrive at perfection from the
first setting out.

CHAPTER X

Of the Combination of Combustible Substances

with Each Other

As combustible substances in general have a
great affinity for oxygen, they ought likewise
to attract or tend to combine with each other ;
quae sunt eadem uni tertio, sunt eadem inter se;
and the axiom is found to be true. Almost all
the metals, for instance, are capable of uniting
with each other and forming what are called
alloys, 1 in common language. Most of these,
like all combinations, are susceptible of sev-
eral degrees of saturation; the greater number
of these alloys are more brittle than the pure
metals of which they are composed, especially
when the metals alloyed together are consid-
erably different in their degrees of fusibility.
To this difference in fusibility part of the phe-
nomena attendant upon alloyage are owing,
particularly the property of iron called by
workmen hotshort. This kind of iron must be
considered as an alloy, or mixture of pure iron,
which is almost infusible, with a small portion
of some other metal which fuses in a much low-
er degree of heat. So long as this alloy remains
cold, and both metals are in the solid state, the

1 This term alloy, which we have from the lan-
guage of the arts, serves exceedingly well for dis-
tinguishing all the combinations or intimate unions
of metals with each other, and is adopted in our new
nomenclature for that purpose. AUTHOB.

mixture is malleable; but, if heated to a suf-
ficient degree to liquefy the more fusible metal,
the particles of the liquid metal, which are
interposed between the particles of the metal
remaining solid, must destroy their continuity
and occasion the alloy to become brittle. The
alloys of mercury, with the other metals, have
usually been called amalgams, and we see no
inconvenience from continuing the use of that
term.

Sulphur, phosphorus, and charcoal readily
unite with metals. Combinations of sulphur
with metals are usually named pyrites. Their
combinations with phosphorus and charcoal
are either not yet named or have received new
names only of late; so that we have not scru-
pled to change them according to our prin-
ciples. The combinations of metal and sulphur
we call sulphurets, those with phosphorus phos-
phurets, and those formed with charcoal carbu-
rets. These denominations are extended to all
the combinations into which the above three
substances enter, without being previously oxy-
genated. Thus, the combination of sulphur
with potash, or fixed vegetable alkali, is called
sulphuret of potash; that which it forms with
ammonia, or volatile alkali, is termed sulphuret
of ammonia.

Hydrogen is likewise capable of combining
with many combustible substances. In the
state of gas it dissolves charcoal, sulphur, phos-
phorus, and several metals; we distinguish
these combinations by the terms, carbonated
hydrogen gas, sulphurated hydrogen gas, and
phosphorated hydrogen gas. The sulphurated
hydrogen gas was called hepatic air by former
chemists, or foetid air from sulphur, by M.
Scheele. The virtues of several mineral waters,
and the foetid smell of animal excrements,
chiefly arise from the presence of this gas. The
phosphorated hydrogen gas is remarkable for
the property, discovered by M. Gengembre,
of taking fire spontaneously upon getting into
contact with atmospheric air, or, what is bet-
ter, with oxygen gas. This gas has a strong fla-
vour, resembling that of putrid fish, and it is
very probable that the phosphorescent quality
of fish in the state of putrefaction arises from
the escape of this species of gas. When hydro-
gen and charcoal are combined together, with-
out the intervention of caloric to bring the hy-
drogen into the state of gas, they form oil,
which is either fixed or volatile according to
the proportions of hydrogen and charcoal in its
composition. The chief difference between fixed
or fat oils drawn from vegetables by expres-

CHEMISTRY

sion, and volatile or essential oils, is that the
former contains an excess of charcoal, which is
separated when the oils are heated above the
degree of boiling water; whereas the volatile
oils, containing a just proportion of these two
constituent ingredients, are not liable to be de-
composed by that heat, but, uniting with ca-
loric into the gaseous state, pass over in dis-
tillation unchanged.

In the Recueil de V Academic for 1784, p. 593,
I gave an account of my experiments upon the
composition of oil and alcohol, by the union of
hydrogen with charcoal, and of their combina-
tion with oxygen. By these experiments, it ap-
pears that fixed oils combine with oxygen dur-
ing combustion and are thereby converted
into water and carbonic acid. By means of cal-
culation applied to the products of these ex-
periments, we find that fixed oil is composed of
21 parts, by weight, of hydrogen combined
with 79 parts of charcoal. Perhaps the solid
substances of an oily nature, such as wax, con-
tain a proportion of oxygen to which they owe
their state of solidity. I am at present engaged
in a series of experiments, which I hope will
throw great light upon this subject.

It is worthy of being examined whether hy-
drogen in its concrete state, uncombined with
caloric, be susceptible of combination with sul-
phur, phosphorus, and the metals. There is
nothing that we know of which, a priori, should
render these combinations impossible ; for com-
bustible bodies being in general susceptible of
combination with each other, there is no evi-
dent reason for hydrogen being an exception
to the rule: however, no direct experiment as
yet establishes either the possibility or impos-
sibility of this union. Iron and zinc are the
most likely, of all the metals, for entering into
combination with hydrogen; but, as these have
the property of decomposing water, and as it is
very difficult to get entirely free from moisture
in chemical experiments, it is hardly possible
to determine whether the small portions of
hydrogen gas obtained in certain experiments
with these metals were previously combined
with the metal in the state of solid hydrogen,
or if they were produced by the decomposition
of a minute quantity of water. The more care
we take to prevent the presence of water in
these experiments, the less is the quantity of
hydrogen gas procured; and, when very accu-
rate precautions are employed, even that quan-
tity becomes hardly sensible.

However this inquiry may turn out respect-
ing the power of combustible bodies, as sul-

phur, phosphorus, and metals, to absorb hy-
drogen, we are certain that they only absorb a
very small portion ; and that this combination,
instead of being essential to their constitution,
can only be considered as a foreign substance
which contaminates their purity. It is the
province of the advocates for this system to
prove, by decisive experiments, the real exis-
tence of this combined hydrogen, which they
have hitherto only done by conjectures founded
upon suppositions.

CHAPTER XI

Observations upon Oxides and Acids with Sev-
eral Bases, and upon the Composition of Ani-
mal and Vegetable Substances

WE have in Chapters V and VIII examined the
products resulting from the combustion of the
four simple combustible substances, sulphur,
phosphorus, charcoal, and hydrogen: we have
shown in Chapter X that the simple combus-
tible substances are capable of combining with
each other into compound combustible sub-
stances and have observed that oils in general,
and particularly the fixed vegetable oils, belong
to this class, being composed of hydrogen and
charcoal. It remains, in this chapter, to treat
of the oxygenation of these compound com-
bustible substances and to show that there
exist acids and oxides having double and triple
bases. Nature furnishes us with numerous
examples of this kind of combination, by
means of which, chiefly, she is enabled to pro-
duce a vast variety of compounds from a very
limited number of elements or simple sub-
stances.

It was long ago well known that when mu-
riatic and nitric acids were mixed together a
compound acid was formed, having properties
quite distinct from those of either of the acids
taken separately. This acid was called aqua
regia, from its most celebrated property of dis-
solving gold, called king of metals by the alche-
mists. M. Berthollet has distinctly proved that
the peculiar properties of this acid arise from the
combined action of its two acidifiable bases;
and for this reason we have judged it necessary
to distinguish it by an appropriate name: that
of nitro-muriatic acid appears extremely ap-
plicable, from its expressing the nature of the
two substances which enter into its composition,
plicable, from its expressing the nature of
the two substances which enter into its com-
position.

This phenomenon of a double base in one

LAVOISIER

acid, which had formerly been observed only
in the nitro-muriatic acid, occurs continually
in the vegetable kingdom, in which a simple
acid, or one possessed of a single acidifiable
base, is very rarely found. Almost all the acids
procurable from this kingdom have bases com-
posed of charcoal and hydrogen, or of charcoal,
hydrogen, and phosphorus, combined with
more or less oxygen. All these bases, whether
double or triple, are likewise formed into ox-
ides, having less oxygen than is necessary to
give them the properties of acids. The acids
and oxides from the animal kingdom are still
more compound, as their bases generally con-
sist of a combination of charcoal, phosphorus,
hydrogen, and azote.

As it is but of late that I have acquired any
clear and distinct notions of these substances,
I shall not, in this place, enlarge much upon
the subject, which I mean to treat of very fully
in some Mtmoires I am preparing to lay before
the Academy. Most of my experiments are al-
ready performed ; but, to be able to give exact
reports of the resulting quantities, it is neces-
sary that they be carefully repeated and in-
creased in number: wherefore, I shall only give
a short enumeration of the vegetable and ani-
mal acids and oxides and terminate this article
by a few reflections upon the composition of
vegetable and animal bodies.

Sugar, mucus, under which term we include
the different kinds of gums, and starch, are
vegetable oxides, having hydrogen and char-
coal combined, in different proportions, as their
radicals or bases, and united with oxygen so as
to bring them to the state of oxides. From the
state of oxides they are capable of being changed
into acids by the addition of a fresh quantity
of oxygen; and, according to the degrees of
oxygenation, and the proportion of hydrogen
and charcoal, in their bases, they form the sev-
eral kinds of vegetable acids.

It would be easy to apply the principles of
our nomenclature to give names to these vege-
table acids and oxides by using the names of
the two substances which compose their bases:
they would thus become hydro-carbonous acids
and oxides. In this method we might indicate
which of their elements existed in excess, with-
out circumlocution, after the manner used by
M. Rouelle for naming vegetable extracts: he
calls these extracto-resinous when the extractive
matter prevails in their composition, and resir
no-extractive when they contain a larger pro-
portion of resinous matter. Upon that plan,
and by varying the terminations according to

the formerly established rules of our nomen-
clature, we have the following denominations:
hydro-carbonou8, hydro-carbonic; carbono-hyd-
rous, and carbono-hydric oxides. And for the
acids: hydro-carbonous, hydro carbonic, oxygen-
ated hydro-carbonic; carbono-hydrous, carbono-
hydric, and oxygenated carbono-hydric. It is
probable that the above terms would suffice
for indicating all the varieties in nature, and
that, in proportion as the vegetable acids be-
come well understood, they will naturally ar-
range themselves under these denominations.
But, though we know the elements of which
these are composed, we are as yet ignorant of
the proportions of these ingredients and are
still far from being able to class them in the
above methodical manner; wherefore, we have
determined to retain the ancient names pro-
visionally. I am somewhat further advanced in
this inquiry than at the time of publishing our
conjunct essay upon chemical nomenclature,
yet it would be improper to draw decided con-
sequences from experiments not yet sufficiently
precise. Though I acknowledge that this part
of chemistry still remains in some degree ob-
scure, I must express my expectations of its
being very soon elucidated.

I am still more forcibly necessitated to fol-
low the same plan in naming the acids which
have three or four elements combined in their
bases; of these we have a considerable number
from the animal kingdom, and some even from
vegetable substances. Azote, for instance, joined
to hydrogen and charcoal forms the base or
radical of prussic acid; we have reason to be-
lieve that the same happens with the base of
gallic acid; and almost all the animal acids
have their bases composed of azote, phosphor-
us, hydrogen, and charcoal. Were we to en-
deavour to express at once all these four com-
ponent parts of the bases, our nomenclature
would undoubtedly be methodical; it would
have the property of being clear and determin-
ate; but this assemblage of Greek and Latin
substantives and adjectives, which are not yet
universally admitted by chemists, would have
the appearance of a barbarous language, diffi-
cult both to pronounce and to be remembered.
Besides, this part of chemistry being still far
from that accuracy it must arrive to, the per-
fection of the science ought certainly to pre-
cede that of its language; and we must still,
for some time, retain the old names for the
animal oxides and acids. We have only ven-
tured to make a few slight modifications of
these names, by changing the termination into

CHEMISTRY

oua when we have reason to suppose the base
to be in excess, and into ic when we suspect the
oxygen predominates.

The following are all the vegetable acids
hitherto known:

CHAPTER XII

8. Pyro-mucous acid

9. Pyro-lignous acid

10. Gallic acid

11. Benzoic acid

12. Camphoric acid

13. Succinic acid

1. Acetous acid

2. Acetic acid

3. Oxalic acid

4. Tartarous acid

5. Pyro-tartarous acid

6. Citric acid

7. Malic acid

Though all these acids, as has been already
said, are chiefly, and almost entirely, composed
of hydrogen, charcoal, and oxygen, yet, prop-
erly speaking, they contain neither water, car-
bonic acid, nor oil but only the elements neces-
sary for forming these substances. The power
of affinity reciprocally exerted by the hydro-
gen, charcoal, and oxygen, in these acids is in a
state of equilibrium only capable of existing in
the ordinary temperature of the atmosphere;
for, when they are heated but a very little
above the temperature of boiling water, this
equilibrium is destroyed, part of the oxygen
and hydrogen unite and form water; part of
the charcoal and hydrogen combine into oil;
part of the charcoal and oxygen unite to form
carbonic acid; and, lastly, there generally re-
mains a small portion of charcoal, which, being
in excess with respect to the other ingredients,
is left free. I mean to explain this subject some-
what farther in the succeeding chapter.

The oxides of the animal kingdom are less
known than those from the vegetable kingdom,
and their number is as yet not at ail deter-
mined. The red part of the blood, lymph, and
most of the secretions, are true oxides, under
which point of view it is very important to con-
sider them. We are only acquainted with six
animal acids, several of which, it is probable,
approach very near each other in their nature,
or, at least, differ only in a scarcely sensible
degree. I do not include the phosphoric acid
amongst these, because it is found in all the
kingdoms of nature. They are:

1. Lactic acid 4. Formic acid

2. Saccho-lactic acid 5. Sebacic acid

3. Bombic acid 6. Prussic acid
The connection between the constituent ele-
ments of the animal oxides and acids is not
more permanent than in those from the vege-
table kingdom, as a small increase of tempera-
ture is sufficient to overturn it. I hope to ren-
der this subject more distinct in the following
chapter than has been done hitherto.

Of the Decomposition of Vegetable and Animal
Substances by the Action of Fire

BEFORE we can thoroughly comprehend what
takes place during the decomposition of vege-
table substances by fire, we must take into
consideration the nature of the elements which
enter into their composition, the different af-
finities which the particles of these elements
exert upon each other, and the affinity which
caloric possesses with them. The true constit-
uent elements of vegetables are hydrogen, oxy-
gen, and charcoal: these are common to all
vegetables, and no vegetable can exist without
them. Such other substances as exist in partic-
ular vegetables are only essential to the com-
position of those in which they are found and
do not belong to vegetables in general.

Of these elements, hydrogen and oxygen
have a strong tendency to unite with caloric
and be converted into gas, whilst charcoal is a
fixed element having but little affinity with
caloric. On the other hand, oxygen, which, in
the usual temperature, tends nearly equally to
unite with hydrogen and with charcoal, has a
much stronger affinity with charcoal when at
red heat 1 and then unites with it to form car-
bonic acid.

Although we are far from being able to ap-
preciate all these powers of affinity, or to ex-
press their proportional energy by numbers,
we are certain that, however variable they may
be when considered in relation to the quantity
of caloric with which they are combined, they
are all nearly in equilibrium in the usual tem-
perature of the atmosphere; hence vegetables
neither contain oil, 2 water, nor carbonic acid,
tho' they contain all the elements of these sub-
stances. The hydrogen is neither combined
with the oxygen nor with the charcoal, and re-
ciprocally; the particles of these three sub-
stances form a triple combination which remains
in equilibrium whilst undisturbed by caloric,
but a very slight increase of temperature is suf-

i Though this term, red heat, does not indicate any
absolutely determinate degree of temperature, I
shall use it sometimes to express a temperature con-
siderably above that of boiling water. AUTHOR.

> I must be understood here to speak of vegetables
reduced to a perfectly dry state; and, with respect to
oil, I do not mean that which is procured by expres-
sion either in the cold, or in a temperature not ex-
ceeding that of boiling water; I only allude to the
empyreumatic oil procured by distillation with a
naked fire, in a heat superior to the temperature of
boiling water; which is the only oil declared to be
produced by the operation of fire. What I have pub-
lished upon this subject in the Recueil de VAcadtmie
for 1786 may be consulted. AUTHOR.

LAVOISIER

ficient to overturn this structure of combination.

If the increased temperature to which the
vegetable is exposed does not exceed the heat
of boiling water, one part of the hydrogen com-
bines with the oxygen and forms water, the
rest of the hydrogen combines with a part of
the charcoal and forms volatile oil, whilst the
remainder of the charcoal, being set free from its
combination with the other elements, remains
fixed in the bottom of the distilling vessel.

When, on the contrary, we employ red heat,
no water is formed, or, at least, any that may
have been produced by the first application of
the heat is decomposed, the oxygen having a
greater affinity with the charcoal at this de-
gree of heat combines with it to form carbonic
acid, and the hydrogen being left free from
combination with the other elements unites
with caloric and escapes in the state of hydro-
gen gas. In this high temperature, either no oil
is formed, or, if any was produced during the
lower temperature at the beginning of the ex-
periment, it is decomposed by the action of
the red heat. Thus the decomposition of vege-
table matter, under a high temperature, is pro-
duced by the action of double and triple affin-
ities; while the charcoal attracts the oxygen on
purpose to form carbonic acid, the caloric at-
tracts the hydrogen and converts it into hy-
drogen gas.

The distillation of every species of vegetable
substance confirms the truth of this theory, if
we can give that name to a simple relation of
facts. When sugar is submitted to distillation,
so long as we only employ a heat but a little
below that of boiling water, it only loses its
water of crystallization, it still remains sugar
and retains all its properties; but, immediately
upon raising the heat only a little above that
degree, it becomes blackened, a part of the
charcoal separates from the combination, water
slightly acidulated passes over accompanied
by a little oil, and the charcoal which remains
in the retort is nearly a third part of the orig-
inal weight of the sugar.

The operation of affinities which take place
during the decomposition, by fire, of vegetables
which contain azote, such as the cruciferous
plants, and of those containing phosphorus, is
more complicated; but, as these substances
only enter into the composition of vegetables
in very small quantities, they only, apparent-
ly, produce slight changes upon the products
of distillation; the phosphorus seems to com-
bine with the charcoal and, acquiring fixity
from that union, remains behind in the retort,

while the azote, combining with a part of the
hydrogen, forms ammonia or volatile alkali.

Animal substances, being composed nearly
of the same elements with cruciferous plants,
give the same products in distillation, with
this difference that, as they contain a greater
quantity of hydrogen and azote, they produce
more oil and more ammonia. I shall only pro-
duce one fact as a proof of the exactness with
which this theory explains all the phenomena
which occur during the distillation of animal
substances, which is the rectification and total
decomposition of volatile animal oil, commonly
known by the name of Dippel's oil. When
these oils are procured by a first distillation in
a naked fire they are brown, from containing a
little charcoal almost in a free state; but they
become quite colourless by rectification. Even
in this state the charcoal in their composition
has so slight a connection with the other ele-
ments as to separate by mere exposure to the
air. If we put a quantity of this animal oil, well
rectified, and consequently clear, limpid, and
transparent, into a bell-glass filled with oxygen
gas over mercury, in a short time the gas is
much diminished, being absorbed by the oil,
the oxygen combining with the hydrogen of
the oil forms water which sinks to the bottom,
at the same time the charcoal which was com-
bined with the hydrogen, being set free, man-
ifests itself by rendering the oil black. Hence
the only way of preserving these oils colourless
and transparent, is by keeping them in bottles
perfectly full and accurately corked, to hinder
the contact of air, which always discolours them.

Successive rectifications of this oil furnish
another phenomenon confirming our theory.
In each distillation a small quantity of charcoal
remains in the retort, and a little water is
formed by the union of the oxygen contained
in the air of the distilling vessels with the hy-
drogen of the oil. As this takes place in each
successive distillation, if we make use of large
vessels and a considerable degree of heat, we
at last decompose the whole of the oil and
change it entirely into water and charcoal.
When we use small vessels, and especially when
we employ a slow fire or degree of heat little
above that of boiling water, the total decom-
position of these oils, by repeated distillation,
is greatly more tedious, and more difficult to
accomplish. I shall give a particular detail to
the Academy, in a separate Mtmoire, of all my
experiments upon the decomposition of oil;
but what I have related above may suffice to
give just ideas of the composition of animal

CHEMISTRY

and vegetable substances and of their decom-
position by the action of fire.

CHAPTER XIII

Of the Decomposition of Vegetable Oxides by the
Vinous Fermentation

THE manner in which wine, cider, mead, and
all the liquors formed by the spiritous fermen-
tation, are produced is well known to everyone.
The juice of grapes or of apples being expressed,
and the latter being diluted with water, they
are put into large vats which are kept in a
temperature of at least 10 (54.5) of the ther-
mometer. A rapid intestine motion, or fer-
mentation, very soon takes place; numerous
globules of gas form in the liquid and burst at
the surface; when the fermentation is at its
height, the quantity of gas disengaged is so
great as to make the liquor appear as if boiling
violently over a fire. When this gas is carefully
gathered, it is found to be carbonic acid per-
fectly pure and free from admixture with any
other species of air or gas whatever.

When the fermentation is completed, the
juice of grapes is changed from being sweet and
full of sugar into a vinous liquor which no
longer contains any sugar, and from which we
procure, by distillation, an inflammable liquor,
known in commerce under the name of spirit of
wine. As this liquor is produced by the fer-
mentation of any saccharine matter whatever
diluted with water, it must have been contrary
to the principles of our nomenclature to call it
spirit of wine rather than spirit of cider or of
fermented sugar; wherefore, we have adopted
a more general term, and the Arabic word
alcohol seems extremely proper for the purpose.

This operation is one of the most extraordi-
nary in chemistry. We must examine whence
proceed the disengaged carbonic acid and the
inflammable liquor produced and in what man-
ner a sweet vegetable oxide becomes thus con-
verted into two such opposite substances,
whereof one is combustible and the other em-
inently the contrary. To solve these two ques-
tions, it is necessary to be previously acquaint-
ed with the analysis of the fermentable sub-
stance and of the products of the fermentation.
We may lay it down as an incontestible axiom
that, in all the operations of art and nature,
nothing is created; an equal quantity of matter
exists both before and after the experiment;
the quality and quantity of the elements remain
precisely the same and nothing takes place be-
yond changes and modifications in the combina-

tion of these elements. Upon this principle the
whole art of performing chemical experiments
depends. We must always suppose an exact
equality between the elements of the body ex-
amined and those of the products of its analysis.

Hence, since from must of grapes we procure
alcohol and carbonic acid, I have an undoubted
right to suppose that must consists of carbonic
acid and alcohol. From these premises, we
have two methods of ascertaining what passes
during vinous fermentation, by determining
the nature of, and the elements which compose,
the fermentable substances, or by accurately
examining the products resulting from fermen-
tation; and it is evident that the knowledge of
either of these must lead to accurate conclu-
sions concerning the nature and composition of
the other. From these considerations, it be-
came necessary accurately to determine the
constituent elements of the fermentable sub-
stances; and, for this purpose, I did not make
use of the compound juices of fruits, the rigor-
ous analysis of which is perhaps impossible,
but made choice of sugar, which is easily ana-
lyzed and the nature of which I have already
explained. This substance is a true vegetable
oxide with two bases, composed of hydrogen
and charcoal brought to the state of an oxide
by a certain proportion of oxygen; and these
three elements are combined in such a way
that a very slight force is sufficient to destroy
the equilibrium of their connection. By a long
train of experiments, made in various ways,
and often repeated, I ascertained that the pro-
portion in which these ingredients exist in
sugar are nearly eight parts of hydrogen, 64
parts of oxygen, and 28 parts of charcoal, all
by weight, forming 100 parts of sugar.

Sugar must be mixed with about four times
its weight of water to render it susceptible of
fermentation; and even then the equilibrium
of its elements would remain undisturbed,
without the assistance of some substance to
give a commencement to the fermentation.
This is accomplished by means of a little yeast
from beer; and, when the fermentation is once
excited, it continues of itself until completed.
I shall, in another place, give an account of the
effects of yeast, and other ferments, upon fer-
mentable substances. I have usually employed
10 Ibs. of yeast, in the state of paste, for each
100 Ibs. of sugar, with as much water as is four
times the weight of the sugar. I shall give the
results of my experiments exactly as they were
obtained, preserving even the fractions pro-
duced by calculation.

LAVOISIER

TABLE I. Materials of Fermentation

Water
Sugar

Yeast in paste, 10 Ibs. composed of

Water
Dry yeast

Total

Ibs. oz. gros grs.

400

100

7 3 6 44

2 12 1 28

510

TABLE II. Constituent Elements of the Materials
of Fermentation

407 Ibs. 3 oz. 6 gros 44 grs. of water,
composed of

100 Ibs. sugar, composed of

2 Ibs. 12 oz. 1 gros 28 grs. of dry
yeast, composed of

Ibs.

oz.

gros

grs.

Hydrogen

71.40

Oxygen

346

44.60

Hydrogen

Oxygen

Charcoal

Hydrogen

9.30

Oxygen

28.76

Charcoal

Azote

2.94

Total 510

TABLE III. Recapitulation of these Elements

Ibs. oz. gros grs. Ibs. oz. gros grs.

of water

340

of water in yeast
of sugar

6
64

44.60

411

1.36

of dry yeast

28.76

of water

of water in yeast
of sugar

71.40

8.70

of dry yeast

9.30

of sugar
of yeast

59.00

Azote of yeast

2.94

Total

510

Having thus accurately determined the na-
ture and quantity of the constituent elements
of the materials submitted to fermentation, we
have next to examine the products resulting
from that process. For this purpose, I placed
the above 510 Ibs. of fermentable liquor in a
proper 1 apparatus, by means of which I could
accurately determine the quantity and quality
of gas disengaged during the fermentation, and
could even weigh every one of the products
separately, at any period of the process I j udged
proper. An hour or two after the substances
are mixed together, especially if they are kept
in a temperature of from 15 (65.75) to 18

The above apparatus is described in the Third
Part. AUTHOR.

(72.5) of the thermometer, the first marks of
fermentation commence; the liquor turns thick
and frothy, little globules of air are disengaged
which rise and burst at the surface; the quan-
tity of these globules quickly increases, and
there is a rapid and abundant production of
very pure carbonic acid, accompanied with a
scum which is the yeast separating from the
mixture. After some days, less or more accord-
ing to the degree of heat, the intestine motion
and disengagement of gas diminish; but these
do not cease entirely, nor is the fermentation
completed for a considerable time. During the
process, 35 Ibs. 5 oz. 4 gros 19 grs. of dry car-
bonic acid are disengaged, which carry alongst
with them 13 Ibs. 14 oz. 5 gros of water. There

CHEMISTRY

remains in the vessel 460 Ibs. 11 oz. 6 gros 53
grs. of vinous liquor, slightly acidulous. This
is at first muddy, but clears of itself, and de-
posits a portion of yeast. When we separately
analyse all these substances, which is effected

by very troublesome processes, we have the re-
sults as given in the following tables. This proc-
ess, with all the subordinate calculations and
analyses, will be detailed at large in the Recueil
de I' Academic.

TABLE IV. Products of Fermentation

Ibs. oz. gros grs.

35 Ibs. 5 oz. 4 gros 19 grs. of
carbonic acid, composed
of

Oxygen 25
Charcoal 9

7
14

1
2

34
57

408 Ibs. 15 oz. 5 gros 14 grs.

Oxygen 347

'59

of water, composed of

Hydrogen 61

Oxygen, combined

with hydrogen 31

Hydrogen, combined

57 Ibs. 1 1 oz. 1 gros 58 grs. of

with oxygen 5

dry alcohol, composed

Hydrogen, combined

with charcoal 4

Charcoal, combined

with hydrogen 16

2 Ibs. 8 oz. of dry acetous
acid, composed of

Hydrogen
Oxygen 1
Charcoal

11
10

4
4

4 Ibs. 1 oz. 4 gros 3 grs. of

Hydrogen

residuum of sugar,

Oxygen 2

composed of

Charcoal 1

Hydrogen

1 Ib. 6 oz. gros 5 grs. of

Oxygen

dry yeast, composed of

Charcoal

Azote

510 Ibs. Total 510

TABLE V. Recapitulation of the Products

Ibs.

oz.

gros

grs.

Water 347

Carbonic acid 25

409 Ibs. 10 oz. gros 54 grs.

Alcohol 31

of oxygen contained in

Acetous acid 1

the

Residuum of sugar 2

Yeast

Carbonic acid 9

28 Ibs. 12 oz. 5 gros 59 grs.
of charcoal contained in

thft

Alcohol 16
Acetous acid
Residuum of sugar 1

11
10
2

I/ 11"

Yeast

Water 61

Water of the alcohol 5

71 Ibs. 8 oz. 6 gros 66 grs. of
hydrogen, contained in

Combined with the
charcoal of the al-
cohol 4

the

Acetous acid

Residuum of sugar

Yeast

2 gros 37 grs. of azote in the yeast

510 Ibs. Total 510

LAVOISIER

In these results I have been exact, even to
grains; not that it is possible, in experiments
of this nature, to carry our accuracy so far, but
as the experiments were made only with a few
pounds of sugar, and as, for the sake of com-
parison, I reduced the results of the actual ex-
periments to the quintal or imaginary hundred
pounds, I thought it necessary to leave the
fractional parts precisely as produced by cal-
culation.

When we consider the results presented by
these tables with attention, it is easy to dis-
cover exactly what occurs during fermentation.
In the first place, out of the 100 Ibs. of sugar
employed, 4 /6s. 1 oz. 4 gros 3 grs. remain, with-
out having suffered decomposition; so that, in
reality, we have only operated upon 95 Ibs. 14
oz. 3 gros 69 grs. of sugar; that is to say, upon
61 Ibs. 6 oz. 45 grs. of oxygen, 7 Ibs. 10 oz. 6 gros
6 grs. of hydrogen, and 26 Ibs. 13 oz. 5 gros 19
grs. of charcoal. By comparing these quanti-
ties, we find that they are fully sufficient for
forming the whole of the alcohol, carbonic
acid and acetous acid produced by the fer-
mentation. It is not, therefore, necessary to
suppose that any water has been decomposed
during the experiment, unless it be pretended
that the oxygen and hydrogen exist in the
sugar in that state. On the contrary, I have al-
ready made it evident that hydrogen, oxygen
and charcoal, the three constituent elements of
vegetables, remain in a state of equilibrium or
mutual union with each other which subsists
so long as this union remains undisturbed by
increased temperature, or by some new com-
pound attraction; and that then only these ele-
ments combine, two and two together, to form
water and carbonic acid.

The effects of the vinous fermentation upon
sugar is thus reduced to the mere separation of
its elements into two portions; one part is oxy-
genated at the expense of the other so as to
form carbonic acid, whilst the other part, be-
ing disoxygenated in favour of the former, is
converted into the combustible substance alco-
hol; therefore, if it were possible to reunite al-
cohol and carbonic acid together, we ought to
form sugar. It is evident that the charcoal and
hydrogen in the alcohol do not exist in the
state of oil. They are combined with a portion
of oxygen, which renders them miscible with
water; wherefore these three substances, oxy-
gen, hydrogen, and charcoal, exist here like-
wise in a species of equilibrium or reciprocal
combination; and in fact, when they are made
to pass through a red hot tube of glass or por-

celain, this union or equilibrium is destroyed,
the elements become combined, two and two,
and water and carbonic acid are formed.

I had formally advanced, in my first Mem-
oires upon the formation of water, that it was
decomposed in a great number of chemical ex-
periments and particularly during the vinous
fermentation. I then supposed that water ex-
isted ready formed in sugar, though I am now
convinced that sugar only contains the ele-
ments proper for composing it. It may be read-
ily conceived that it must have cost me a good
deal to abandon my first notions, but by sev-
eral years reflection, and after a great number
of experiments- and observations upon vege-
table substances, I have fixed my ideas as
above.

I shall finish what I have to say upon vinous
fermentation by observing that it furnishes us
with the means of analysing sugar and every
vegetable fermentable matter. We may con-
sider the substances submitted to fermenta-
tion, and the products resulting from that op-
eration, as forming an algebraic equation; and,
by successively supposing each of the elements
in this equation unknown, we can calculate
their values in succession, and thus verify our
experiments by calculation, and our calculation
by experiment reciprocally. I have often suc-
cessfully employed this method for correcting
the first results of my experiments and to direct
me in the proper road for repeating them to
advantage. I have explained myself at large
upon this subject, in a Memoir e upon vinous
fermentation already presented to the Acad-
emy which will speedily be published.

CHAPTER XIV

Of the Putrefactive Fermentation

THE phenomena of putrefaction are caused,
like those of vinous fermentation, by the oper-
ation of very complicated affinities. The con-
stituent elements of the bodies submitted to
this process cease to continue in equilibrium in
the threefold combination and form themselves
anew into binary combinations, or compounds,
consisting of two elements only; but these are
entirely different from the results produced by
the vinous fermentation. Instead of one part of
the hydrogen remaining united with part of
the water and charcoal to form alcohol, as in
the vinous fermentation, the whole of the hy-
drogen is dissipated, during putrefaction, in
the form of hydrogen gas, whilst, at the same

CHEMISTRY

time, the oxygen and charcoal, uniting with
caloric, escape in the form of carbonic acid gas ;
so that, when the whole process is finished, es-
pecially if the materials have been mixed with
a sufficient quantity of water, nothing remains
but the earth of the vegetable mixed with a
small portion of charcoal and iron. Thus pu-
trefaction is nothing more than a complete
analysis of vegetable substance, during which
the whole of the constituent elements is disen-
gaged in form of gas, except the earth which
remains in the state of mould. 1

Such is the result of putrefaction when the
substances submitted to it contain only oxy-
gen, hydrogen, charcoal and a little earth. But
this case is rare, and these substances putrify
imperfectly and with difficulty, and require a
considerable time to complete their putrefac-
tion. It is otherwise with substances contain-
ing azote, which indeed exists in all animal
matters and even in a considerable number of
vegetable substances. This additional element
is remarkably favourable to putrefaction; and
for this reason animal matter is mixed with
vegetable when the putrefaction of these is
wished to be hastened. The whole art of form-
ing composts and dunghills, for the purposes of
agriculture, consists in the proper application
of this admixture.

The addition of azote to the materials of
putrefaction not only accelerates the process;
that element likewise combines with part of
the hydrogen and forms a new substance called
volatile alkali or ammonia. The results obtained
by analysing animal matters, by different proc-
esses, leave no room for doubt with regard to
the constituent elements of ammonia; when-
ever the azote has been previously separated
from these substances, no ammonia is pro-
duced; and in all cases they furnish ammonia
only in proportion to the azote they contain.
This composition of ammonia is likewise fully
proved by M. Berthollet, in the Recueil de
VAcademie for 1785, p. 316, where he gives a
variety of analytical processes by which am-
monia is decomposed and its two elements,
azote and hydrogen, procured separately.

I mentioned in Chapter X that almost all
combustible bodies were capable of combining
with each other. Hydrogen gas possesses this
quality in an eminent degree; it dissolves char-
coal, sulphur, and phosphorus, producing the
compounds named carbonated hydrogen gas,

In the Third Part will be given the description of
an apparatus proper for being used in experiments of
this kind. AUTHOR.

sulphurated hydrogen gas, and phosphorated hy-
drogen gas. The two latter of these gases have a
peculiarly disagreeable flavour; the sulphur-
ated hydrogen gas has a strong resemblance
to the smell of rotten eggs, and the phosphor-
ated smells exactly like putrid fish. Ammonia
has likewise a peculiar odour, not less pene-
trating or less disagreeable than these other
gases. From the mixture of these different fla-
vours proceeds the fetor which accompanies
the putrefaction of animal substances. Some-
times ammonia predominates, which is easily
perceived by its sharpness upon the eyes;
sometimes, as in feculent matters, the sulphur-
ated gas is most prevalent; and sometimes, as
in putrid herrings, the phosphorated hydrogen
gas is most abundant.

I long supposed that nothing could derange
or interrupt the course of putrefaction; but M.
Fourcroy and M. Thouret have observed
some peculiar phenomena in dead bodies,
buried at a certain depth and preserved to a
certain degree from contact with air, having
found the muscular flesh frequently converted
into true animal fat. This must have arisen
from the disengagement of the azote, naturally
contained in the animal substance, by some
unknown cause, leaving only the hydrogen
and charcoal remaining, which are the ele-
ments proper for producing fat or oil. This ob-
servation upon the possibility of converting
animal substances into fat may some time or
other Lead to discoveries of great importance
to society. The faeces of animals, and other ex-
crementitious matters, are chiefly composed of
charcoal and hydrogen and approach consider-
ably to the nature of oil, of which they furnish
a considerable quantity by distillation with a
naked fire; but the intolerable fetor which ac-
companies all the products of these substances
prevents our expecting that, at least for a long
time, they can be rendered useful in any other
way than as manures.

I have only given conjectural approxima-
tions in this chapter upon the composition of
animal substances, which is hitherto but im-
perfectly understood. We know that they are
composed of hydrogen, charcoal, azote, phos-
phorus, and sulphur, all of which, in a state of
quintuple combination, are brought to the state
of oxides by a larger or smaller quantity of oxy-
gen. We are, however, still unacquainted with
the proportions in which these substances are
combined, and must leave it to time to com-
plete this part of chemical analysis, as it has
already done with several others.

LAVOISIER

CHAPTER XV
Of the Acetous Fermentation

THE acetous fermentation is nothing more
than the acidification or oxygenation of wine,
produced in the open air by means of the ab-
sorption of oxygen. The resulting acid is the
acetous acid, commonly called vinegar, which
is composed of hydrogen and charcoal united
together in proportions not yet ascertained
and changed into the acid state by oxygen. As
vinegar is an acid, we might conclude from
analogy that it contains oxygen, but this is put
beyond doubt by direct experiments: in the
first place, we cannot change wine into vinegar
without the contact of air containing oxygen;
secondly, this process is accompanied by a di-
minution of the volume of the air in which it is
carried on from the absorption of its oxygen;
and, thirdly, wine may be changed into vinegar
by any other means of oxygenation.

Independent of the proofs which these facts
furnish of the acetous acid being produced by
the oxygenation of wine, an experiment made
by M. Chaptai, Professor of Chemistry at
Montpellier, gives us a distinct view of what
takes place in this process. He impregnated
water with about its own bulk of carbonic aeid
from fermenting beer and placed this water in
a cellar in vessels communicating with the air,
and in a short time the whole was converted
into acetous acid. The carbonic acid gas pro-
cured from beer vats in fermentation is not
perfectly pure but contains a small quantity of
alcohol in solution, wherefore water impreg-
nated with it contains all the materials neces-
sary for forming the acetous acid. The alcohol
furnishes hydrogen and one portion of char-
coal, the carbonic acid furnishes oxygen and
the rest of the charcoal, and the air of the at-
mosphere furnishes the rest of the oxygen nec-
essary for changing the mixture into acetous
acid. From this observation it follows that
nothing but hydrogen is wanting to convert
carbonic acid into acetous acid; or more gen-
erally that, by means of hydrogen and accord-
ing to the degree of oxygenation, carbonic acid
may be changed into all the vegetable acids;
and, on the contrary, that, by depriving any
of the vegetable acids of their hydrogen, they
may be converted into carbonic acid.

Although the principal facts relating to the
acetous acid are well known, yet numerical ex-
actitude is still wanting, till furnished by more
exact experiments than any hitherto performed ;
wherefore I shall not enlarge any farther upon

the subject. It is sufficiently shown by what
has been said that the constitution of all the
vegetable acids and oxides is exactly conform-
able to the formation of vinegar; but further
experiments are necessary to teach us the pro-
portion of the constituent elements in all these
acids and oxides. We may easily perceive, how-
ever, that this part of chemistry, like all the
rest of its divisions, makes rapid progress to-
wards perfection, and that it is already rendered
greatly more simple than was formerly believed.

CHAPTER XVI

Of the Formation of Neutral Salts and of their
Different Bases

WE have just seen that all the oxides and acids
from the animal and vegetable kingdoms are
formed by means of a small number of simple
elements, or at least of such as have not hither-
to been susceptible of decomposition, by means
of combination with oxygen; these are azote,
sulphur, phosphorus, charcoal, hydrogen, and
the muriatic radical. We may justly admire
the simplicity of the means employed by na-
ture to multiply qualities and forms, whether
by combining three or four acidifiable bases in
different proportions or by altering the dose of
oxygen employed for oxidating or acidifying
them. We shall find the means no less simple
and diversified, and as abundantly productive
of forms and qualities, in the order of bodies
we are now about to treat of.

Acidifiable substances, by combining with
oxygen and their consequent conversion into
acids, acquire great susceptibility of further
combination; they become capable of uniting
with earthy and metallic bodies, by which
means neutral salts are formed. Acids may
therefore be considered as true salifying prin-
ciples, and the substances with which they
unite to form neutral salts may be called sali-
fiable bases. The nature of the union which
these two principles form with each other is
meant as the subject of the present chapter.

This view of the acids prevents me from con-
sidering them as salts, though they are pos-
sessed of many of the principal properties of
saline bodies, as solubility in water, &c. I have
already observed that they are the result of a
first order of combination, being composed of
two simple elements, or at least of elements
which act as if they were simple, and we may
therefore rank them, to use the language of
Stahl, in the order of mixts. The neutral salts,

CHEMISTRY

on the contrary, are of a secondary order of
combination, being formed by the union of two
mixts with each other, and may therefore be
termed compounds. Hence I shall not arrange
the alkalies 1 or earths in the class of salts, to
which I allot only such as are composed of an
oxygenated substance united to a base.

I have already enlarged sufficiently upon the
formation of acids in the preceding chapter
and shall not add anything further upon that
subject; but having as yet given no account of
the salifiable bases which are capable of uniting
with them to form neutral salts, I mean in this
chapter to give an account of the nature and
origin of each of these bases. These are potash,
soda, ammonia, lime, magnesia, barytes, ar-
gill, and all the metallic bodies.

Of Potash

We have already shown that, when a vege-
table substance is submitted to the action of
fire in distilling vessels, its component elements,
oxygen, hydrogen, and charcoal, which formed
a threefold combination in a state of equilib-
rium, unite, two and two, in obedience to affin-
ities which act conformably to the degree of
heat employed. Thus, at the first application
of the fire, whenever the heat produced ex-
ceeds the temperature of boiling water, part of
the oxygen and hydrogen unite to form water;
soon after, the rest of the hydrogen, and part
of the charcoal, combine into oil; and, lastly,
when the fire is pushed to red heat, the oil and
water, which had been formed in the early part
of the process, become again decomposed, the
oxygen and charcoal unite to form carbonic
acid, a large quantity of hydrogen gas is set free,
and nothing but charcoal remains in the retort.

A great part of these phenomena occur dur-
ing the combustion of vegetables in the open
air; but, in this case, the presence of the air in-
troduces three new substances, the oxygen and
azote of the air, and caloric, of which two at
least produce considerable changes in the re-
sults of the operation. In proportion as the hy-
drogen of the vegetable, or that which results
from the decomposition of the water, is forced
out in the form of hydrogen gas by the progress
of the fire, it is set on fire immediately upon
getting in contact with the air, water is again

1 Perhaps my thus rejecting the alkalies, from the
class of salts may be considered as a capital defect in
the method I have adopted, and I am ready to admit
the charge; but this inconvenience is compensated
by so many advantages, that I could not think it of
sufficient consequence to make me alter my plan.
AUTHOB.

formed, and the greater part of the caloric of
the two gases becoming free produces flame.
When all the hydrogen gas is driven out, burnt,
and again reduced to water, the remaining
charcoal continues to burn, but without flame;
it is formed into carbonic acid, which carries off
a portion of caloric sufficient to give it the gas-
eous form; the rest of the caloric, from the oxy-
gen of the air, being set free, produces the heat
and light observed during the combustion of
charcoal. The whole vegetable is thus reduced
into water and carbonic acid, and nothing re-
mains but a small portion of gray earthy mat-
ter called ashes, being the only really fixed
principles which enter into the constitution of
vegetables.

The earth, or rather ashes, which seldom ex-
ceeds a twentieth part of the weight of the veg-
etable, contains a substance of a particular na-
ture, known under the name of fixed vegetable
alkali or potash. To obtain it, water is poured
upon the ashes, which dissolves the potash and
leaves the ashes which are insoluble; by after-
wards evaporating the water, we obtain the
potash in a white concrete form : it is very fixed
even in a very high degree of heat. I do not
mean here to describe the art of preparing pot-
ash, or the method of procuring it in a state of
purity, but have entered upon the above detail
that I might not use any word not previously
explained.

The potash obtained by this process is al-
ways less or more saturated with carbonic acid,
which is easily accounted for. As the potash
does not form, or at least is not set free, but in
proportion as the charcoal of the vegetable is
converted into carbonic acid by the addition of
oxygen, either from the air or the water, it fol-
lows that each particle of potash, at the instant
of its formation, or at least of its liberation, is
in contact with a particle of carbonic acid, and,
as there is a considerable affinity between these
two substances, they naturally combine to-
gether. Although the carbonic acid has lees af-
finity with potash than any other acid, yet it
is difficult to separate the last portions from it.
The most usual method of accomplishing this
is to dissolve the potash in water; to this solu-
tion add two or three times its weight of quick-
lime, then filtrate the liquor and evaporate it
in close vessels; the saline substance left by the
evaporation is potash almost entirely deprived
of carbonic acid. In this state it is soluble in an
equal weight of water, and even attracts the
moisture of the air with great avidity; by this
property it furnishes us with an excellent means

LAVOISIER

of rendering air or gas dry by exposing them to
its action. In this state it is soluble in alcohol,
though not when combined with carbonic acid;
and M. Berthollet employs this property as a
method of procuring potash in the state of per-
fect purity.

All vegetables yield less or more of potash in
consequence of combustion, but it is furnished
in various degrees of purity by different vege-
tables; usually, indeed, from all of them it is
mixed with different salts from which it is easi-
ly separable. We can hardly entertain a doubt
that the ashes or earth which is left by vege-
tables in combustion pre-existed in them be-
fore they were burnt, forming what may be
called the skeleton or osseous part of the veg-
etable. But it is quite otherwise with potash;
this substance has never yet been procured
from vegetables but by means of processes or
intermedia capable of furnishing oxygen and
azote, such as combustion, or by means of ni-
tric acid; so that it is not yet demonstrated
that potash may not be a produce from these
operations. I have begun a series of experi-
ments upon this object and hope soon to be
able to give an account of their results.

Of Soda

Soda, like potash, is an alkali procured by
lixiviation from the ashes of burnt plants, but
only from those which grow upon the seaside,
and especially from the herb kali, whence is de-
rived the name alkali given to this substance
by the Arabians. It has some properties in com-
mon with potash and others which are entirely
different. In general, these two substances have
peculiar characters in their saline combinations
which are proper to each and consequently dis-
tinguish them from each other ; thus soda, which,
as obtained from marine plants, is usually en-
tirely saturated with carbonic acid, does not at-
tract the humidity of the atmosphere like pot-
ash, but, on the contrary, desiccates, its crystals
effloresce and are converted into a white pow-
der having all the properties of soda, which it
really is, having only lost its water of crystal-
lization.

We are not better acquainted with the con-
stituent elements of soda than with those of
potash, being equally uncertain whether it
previously existed ready formed in the vege-
table or is a combination of elements effected
by combustion. Analogy leads us to suspect
that azote is a constituent element of all the
alkalies, as is the case with ammonia; but we
have only slight presumptions, unconfirmed

by any decisive experiments, respecting the
composition of potash and soda.

Of Ammonia

We have, however, very accurate knowledge
of the composition of ammonia, or volatile al-
kali as it is called by the old chemists. M. Ber-
thollet, in the Recueil de I'Acadtmie for 1784,
p. 316, has proved by analysis, that 1000 parts
of this substance consist of about 807 parts of
azote combined with 193 parts of hydrogen.

Ammonia is chiefly procurable from animal
substances by distillation, during which proc-
ess the azote and hydrogen necessary to its for-
mation unite in proper proportions; it is not,
however, procured pure by this process, being
mixed with oil and water and mostly saturated
with carbonic acid. To separate these sub-
stances it is first combined with an acid, the
muriatic for instance, and then disengaged
from that combination by the addition of lime
or potash. When ammonia is thus produced in
its greatest degree of purity, it can only exist
under the gaseous form, at least in the usual
temperature of the atmosphere; it has an ex-
cessively penetrating smell, is absorbed in
large quantities by water, especially if cold and
assisted by compression. Water thus saturated
with ammonia has usually been termed volatile
alkaline fluor; we shall call it either simply am-
monia, or liquid ammonia, and ammoniacal gas
when it exists in the aeriform state.

Of Lime, Magnesia, Barytes, and Argill

The composition of these four earths is total-
ly unknown, and, until by new discoveries their
constituent elements are ascertained, we are
certainly authorised to consider them as simple
bodies. Art has no share in the production of
these earths, as they are all procured ready
formed from nature; but, as they have all, es-
pecially the three first, great tendency to com-
bination, they are never found pure. Lime is
usually saturated with carbonic acid in the
state of chalk, calcareous spars, most of the
marbles, &c.; sometimes with sulphuric acid,
as in gypsum and plaster stones; at other times
with fluoric acid forming vitreous or fluor spars ;
and, lastly, it is found in the waters of the sea,
and of saline springs, combined with muriatic
acid. Of all the salifiable bases it is the most
universally spread through nature.

Magnesia is found in mineral waters, for the
most part combined with sulphuric acid; it is
likewise abundant in sea-water, united with
muriatic acid; and it exists in a great number

CHEMISTRY

of stones of different kinds.

Barytes is much less common than the three
preceding earths; it is found in the mineral
kingdom, combined with sulphuric acid, form-
ing heavy spars, and sometimes, though rarely,
united to carbonic acid.

Argill, or the base of alum, having less tend-
ency to combination than the other earths, is
often found in the state of argill, uncombined
with any acid. It is chiefly procurable from
clays, of which, properly speaking, it is the
base or chief ingredient.

Of Metallic Bodies

The metals, except gold and sometimes sil-
ver, are rarely found in the mineral kingdom in
their metallic state, being usually less or more
saturated with oxygen, or combined with sul-
phur, arsenic, sulphuric acid, muriatic acid,
carbonic acid, or phosphoric acid. Metallurgy,
or the docimastic art, teaches the means of
separating them from these foreign matters;
and for this purpose we refer to such chemical
books as treat upon these operations.

We are probably only acquainted as yet
with a part of the metallic substances existing
in nature, as all those which have a stronger
affinity to oxygen than charcoal possesses are
incapable of being reduced to the metallic
state and, consequently, being only presented
to our observation under the form of oxides,
are confounded with earths. It is extremely
probable that barytes, which we have just
now arranged with earths, is in this situation;
for in many experiments it exhibits proper-
ties nearly approaching to those of metallic
bodies. It is even possible that ail the sub-
stances we call earths may be only metallic
oxides, irreducible by any hitherto known
process.

Those metallic bodies we are at present ac-
quainted with, and which we can reduce to the
metallic or reguline state, are the following
seventeen:

1. Arsenic 7. Bismuth 13. Copper

2. Molybdenum 8. Antimony 14. Mercury

3. Tungsten 9. Zinc 15. Silver

4. Manganese 10. Iron 16. Platinum

5. Nickel 11. Tin 17. Gold

6. Cobalt 12. Lead

I only mean to consider these as salifiable
bases, without entering at all upon the consid-
eration of their properties in the arts and for
the uses of society. In these points of view each
metal would require a complete treatise, which

would lead me far beyond the bounds I have
prescribed for this work.

CHAPTER XVII

Continuation of the Observations upon Salifiabk
Bases and the Formation of Neutral Salts

IT is necessary to remark that earths and al-
kalies unite with acids to form neutral salts
without the intervention of any medium, where-
as metallic substances are incapable of forming
this combination without being previously less
or more oxygenated; strictly speaking, there-
fore, metals are not soluble in acids but only
metallic oxides. Hence, when we put a metal
into an acid for solution, it is necessary, in the
first place, that it become oxygenated, either
by attracting oxygen from the acid or from the
water; or, in other words, that a metal cannot
be dissolved in an acid unless the oxygen, either
of the acid or of the water mixed with it, has
a stronger affinity to the metal than to the hy-
drogen or the acidifiable base ; or, which amounts
to the same thing, that no metallic solution
can take place without a previous decomposi-
tion of the water or the acid in which it is made.
The explanation of the principal phenomena of
metallic solution depends entirely upon this
simple observation, which was overlooked even
by the illustrious Bergman.

The first and most striking of these is the ef-
fervescence, or, to speak less equivocally, the
disengagement of gas which takes place during
the solution; in the solutions made in nitric
acid this effervescence is produced by the dis-
engagement of nitrous gas; in solutions with
sulphuric acid it is either sulphurous acid gas
or hydrogen gas, according as the oxidation of
the metal happens to be made at the expense
of the sulphuric acid or of the water. As both
nitric acid and water are composed of elements
which, when separate, can only exist in the
gaseous form, at least in the common tempera-
ture of the atmosphere, it is evident that, when-
ever either of these is deprived of its oxygen,
the remaining element must instantly expand
and assume the state of gas; the effervescence
is occasioned by this sudden conversion from
the liquid to the gaseous state. The same de-
composition, and consequent formation of gas,
takes place when solutions of metals are made
in sulphuric acid. In general, especially by the
humid way, metals do not attract all the oxy-
gen it contains; they therefore reduce it, not
into sulphur, but into sulphurous acid, and as
this acid can only exist as gas in the usual tern-

LAVOISIER

perature it is disengaged and occasions effer-
vescence.

The second phenomenon is that when the
metals have been previously oxidated they all
dissolve in acids without effervescence. This is
easily explained; because, not having now any
occasion for combining with oxygen, they nei-
ther decompose the acid nor the water by
which, in the former case, the effervescence is
occasioned.

A third phenomenon, which requires partic-
ular consideration, is that none of the metals
produce effervescence by solution in oxygen-
ated muriatic acid. During this process the
metal, in the first place, carries off the excess of
oxygen from the oxygenated muriatic acid, by
which it becomes oxidated, and reduces the
acid to the state of ordinary muriatic acid. In
this case there is no production of gas, not that
the muriatic acid does not tend to exist in the
gaseous state in the common temperature,
which it does equally with the acids formerly
mentioned, but because this acid, which other-
wise would expand into gas, finds more water
combined with the oxygenated muriatic acid
than is necessary to retain it in the liquid form ;
hence it does not disengage like the sulphurous
acid, but remains and quietly dissolves and
combines with the metallic oxide previously
formed from its superabundant oxygen.

The fourth phenomenon is that metals are
absolutely insoluble in such acids as have their
bases joined to oxygen by a stronger affinity
than these metals are capable of exerting upon
that acidifying principle. Hence silver, mer-
cury, and lead, in their metallic states, are in-
soluble in muriatic acid, but, when previously
oxidated, they become readily soluble without
effervescence.

From these phenomena it appears that oxy-
gen is the bond of union between metals and
acids; and from this we are led to suppose that
oxygen is contained in all substances which
have a strong affinity with acids. Hence it is
very probable the four eminently salifiable
earths contain oxygen, and their capability of
uniting with acids is produced by the interme-
diation of that element. What I have formerly
noticed relative to these earths is considerably
strengthened by the above considerations, viz.
that they may very possibly be metallic oxides,
with which oxygen has a stronger affinity than
with charcoal, and consequently not reducible
by any known means.

All the acids hitherto known are enumerated
in the following table, the first column of which

contains the names of the acids according to
the new nomenclature, and in the second col-
umn are placed the bases or radicals of these
acids, with observations.

Names of
the Acids

1. Sulphurous

2. Sulphuric

3. Phosphorous

4. Phosphoric

5. Muriatic

6. Oxygenated

muriatic

7. Nitrous

8. Nitric

9. Oxygenated
nitric

10. Carbonic

11. Acetous

12. Acetic

13. Oxalic

14. Tartarous

15. Pyro-tartarous

16. Citric

17. Malic

18. Pyro-lignous

19. Pyro-mucous

20. Gallic

21. Prussic

22. Benzoic

23. Succinic

24. Camphoric

25. Lactic

26. Saccho-lactic

27. Bombic

28. Formic

29. Sebacic

30. Boracic

31. Fluoric

32. Antimonic

33. Argentic

34. Arseniac

35. Bismuthic

36. Cotmltic

37. Cupric

38. Stannic

39. Ferric

40. Munganic

41. Mercuric

42. Molybdic

43. Nickolic

44. Auric

45. Platinic

46. Plumbic

47. Tungstic

48. Zincic

Names of the Bases, with
Observations

Sulphur
Phosphorus

Muriatic radical or base,
hitherto unknown

Azote

Charcoal

The bases or radicals of all
these acids seem to be formed
by a combination of charcoal
and hydrogen; and the only
difference seems to be owing
to the different proportions in
which these elements combine
to form their bases, and to the
different doses of oxygen in
their acidification. A connect-
ed series of accurate experi-
ments is still wanted upon
this subject

Our knowledge of the bases
of these acids is hitherto im-
perfect; we only know that
they contain hydrogen and
charcoal as principal elements,
and that the prussic acid con-
tains azote

The base of these and all the
acids procured from animal
substances seems to consist of
charcoal, hydrogen, phosphor-
us, and azote

The bases of these two are
hitherto entirely unknown

Antimony

Silver

Arsenic

Bismuth

Cobalt

Copper

Tin

Iron

Manganese

Mercury

Molybdenum

Nickel

Gold

Platinum

Lead

Tungsten

Zinc

CHEMISTRY

In this list, which contains 48 acids, I have
enumerated 17 metallic acids hitherto very im-
perfectly known, but upon which M. Ber-
thollet is about to publish a very important
work. It cannot be pretended that all the acids
which exist in nature, or rather all the acidifi-
able bases, are yet discovered; but, on the
other hand, there are considerable grounds for
supposing that a more accurate investigation
than has hitherto been attempted will diminish
the number of the vegetable acids by showing
that several of these, at present considered
as distinct acids, are only modifications of
others. All that can be done in the present
state of our knowledge is to give a view of
chemistry as it really is and to establish fun-
damental principles by which such bodies
as may be discovered in future may re-
ceive names in conformity with one uniform
system.

The known salifiable bases, or substances
capable of being converted into neutral salts by
union with acids, amount to 24; viz., 3 alkalies,
4 earths, and 17 metallic substances; so that,
in the present state of chemical knowledge, the
whole possible number of neutral salts amounts
to 1152. This number is upon the supposition
that the metallic acids are capable of dissolving
other metals, which is a new branch of chem-
istry not hitherto investigated, upon which de-
pends all the metallic combinations named
vitreous. There is reason to believe that many
of these supposable saline combinations are
not capable of being formed, which must greatly
reduce the real number of neutral salts produc-
ible by nature and art. Even if we suppose the
real number to amount only to five or six hun-
dred species of possible neutral salts, it is evi-
dent that, were we to distinguish them after
the manner of the ancients, either by the names
of their first discoverers or by terms derived
from the substances from which they are pro-
cured, we should at last have such a confusion
of arbitrary designations as no memory could
possibly retain. This method might be toler-
able in the early ages of chemistry, or even till
within these twenty years, when only about
thirty species of salts were known; but, in the
present times, when the number is augmenting
daily, when every new acid gives us 24 or 48
new salts according as it is capable of one or
two degrees of oxygenation, a new method is
certainly necessary. The method we have adopt-
ed, drawn from the nomenclature of the acids,
is perfectly analogical and, following nature in
the simplicity of her operations, gives a na-

tural and easy nomenclature applicable to every
possible neutral salt.

In giving names to the different acids, we ex-
press the common property by the genericai
term add and distinguish each species by the
name of its peculiar acidiftable base. Hence the
acids formed by the oxygenation of sulphur,
phosphorus, charcoal, &c. are called sulphuric
add, phosphoric add, carbonic acid, &c. We
thought it likewise proper to indicate the dif-
ferent degrees of saturation with oxygen by
different terminations of the same specific
names. Hence we distinguish between sulphur-
ous and sulphuric, and between phosphorous
and phosphoric acids, &c.

By applying these principles to the nomen-
clature of neutral salts, we give a common term
to all the neutral salts arising from the combi-
nation of one acid and distinguish the species
by adding the name of the salifiable base. Thus,
all the neutral salts having sulphuric acid in
their composition are named sulphates; those
formed by the phosphoric acid, phosphates, &c.
The species being distinguished by the names
of the salifiable bases gives us sulphate of pot-
ash, sulphate of soda, sulphate of ammoniac, sul-
phate of lime, sulphate of iron, &c. As we are ac-
quainted with 24 salifiable bases, alkaline,
earthy, and metallic, we have consequently 24
sulphates, as many phosphates, and so on
through all the acids. Sulphur is, however, sus-
ceptible of two degrees of oxygenation, the first
of which produces sulphurous and the second,
sulphuric acid; and, as the neutral salts pro-
duced by these two acids have different prop-
erties and are in fact different salts, it becomes
necessary to distinguish these by peculiar term-
inations; we have therefore distinguished the
neutral salts formed by the acids in the first or
lesser degree of oxygenation by changing the
termination ate into ite, as sulphites, phosphites,
&c. Thus, oxygenated or acidified sulphur, in
its two degrees of oxygenation is capable of
forming 48 neutral salts, 24 of which are sul-
phites, and as many sulphates; which is like-
wise the case with all the acids capable of two
degrees of oxygenation.

It were both tiresome and unnecessary to
follow these denominations through all the va-
rieties of their possible application; it is enough
to have given the method of naming the vari-
ous salts which, when once well understood, is
easily applied to every possible combination.
The name of the combustible and acidifiable
body being once known, the names of the acid
it is capable of forming, and of all the neutral

LAVOISIfiR

combinations the acid is susceptible of entering
into, are most readily remembered. Such as re-
quire a more complete illustration of the meth-
ods in which the new nomenclature is applied
will, in the second part of this book, find tables
which contain a full enumeration of all the neu-
tral salts and, in general, all tire possible chem-
ical combinations, so far as is consistent with
the present state of our knowledge. To these I
shall subjoin short explanations, containing
the best and most simple means of procuring
the different species of acids, and some account
of the general properties of the neutral salts
they produce.

I shall not deny that, to render this work
more complete, it would have been necessary
to add particular observations upon each spe-
cies of salt, its solubility in water and alcohol,
the proportions of acid and of salifiable base in
its composition, the quantity of its water of
crystallization, the different degrees of satura-
tion it is susceptible of, and, finally, the degree
of force or affinity with which the acid adheres
to the base. This immense work has been al-

ready begun by MM. Bergman, Morveau,
Kirwan, and other celebrated chemists, but is
hitherto only in a moderate state of advance-
ment; even the principles upon which it is
founded are not perhaps sufficiently accurate.
These numerous details would have swelled
this elementary treatise to much too great a
size; besides that, to have gathered the neces-
sary materials, and to have completed all the
series of experiments requisite, must have re-
tarded the publication of this book for many
years. This is a vast field for employing the
zeal and abilities of young chemists, whom I
would advise to endeavour rather to do well
than to do much, and to ascertain, in the first
place, the composition of the acids, before en-
tering upon that of the neutral salts. Every
edifice which is intended to resist the ravages
of time should be built upon a sure foundation;
and, in the present state of chemistry, to at-
tempt discoveries by experiments, either not
perfectly exact or not sufficiently rigorous, will
serve only to interrupt its progress, instead of
contributing to its advancement.

SECOND PART

OF THE COMBINATION OF ACIDS WITH SALIFIABLE BASES,
AND OF THE FORMATION OF NEUTRAL SALTS

INTRODUCTION

IF I had strictly followed the plan I at first laid
down for the conduct of this work, I would
have confined myself, in the tables and accom-
panying observations which compose this sec-
ond part, to short definitions of the several
known acids and abridged accounts of the proc-
esses by which they are obtainable, with a mere
nomenclature or enumeration of the neutral
salts which result from the combination of
these acids with the various salifiable bases.
But I afterwards found that the addition of
similar tables of all the simple substances which
enter into the composition of the acids and
oxides, together with the various possible com-
binations of these elements, would add greatly
to the utility of this work without being any

great increase to its size. These additions, which
are all contained in the twelve first sections of
this part and the tables annexed to these, form
a kind of recapitulation of the first fifteen chap-
ters of the first part. The rest of the tables and
sections contain all the saline combinations.

It must be very apparent that, in this part
of the work, I have borrowed greatly from
what has been already published by M. de
Morveau in the first volume of the Encyclo-
pedic par ordre des Matieres. I could hardly
have discovered a better source of information,
especially when the difficulty of consulting
books in foreign languages is considered. I make
this general acknowledgment on purpose to
save the trouble of references to M. de Mor-
veau's work in the course of the following part
of mine.

TABLE of Simple Substances Belonging to All the

Kingdoms of Nature, Which May Be Considered as the

Elements of Bodies

Old Names
Light

Heat

Principle or element of heat
Fire. Igneous fluid
Matter of fire and of heat
Dephlogisticated air
Empyreal air

Vital air, or base of vital air
Phlogisticated air or gas
Mephitis, or its base
Inflammable air or gas, or the base of
inflammable air

New Names
Light

Caloric

Oxygen

Azote

Hydrogen

Oxidable and Acidifiable Simple Substances Not Metallic

New Names Old Names

Sulphur

Phosphorus The same names

Charcoal
Muriatic radical

Fluoric radical Still unknown

Boracic radical

LAVOISIER

TABLE of Simple Substances, Continued
Oxiddble and Acidifiable Simple Metallic Bodies

SECTION I

New Names
Antimony
Arsenic
Bismuth
Cobalt
Copper
Gold
Iron
Lead

Manganese
Mercury
Molybdenum
Nickel
Platinum
Silver
Tin

Tungsten
Zinc

Old Names
Antimony
Arsenic
Bismuth
Cobalt
Copper
Gold
Iron
Lead

Manganese
Mercury
Molybdenum
Nickel
Platinum
Silver
Tin

Tungsten
Zinc

Salifiable Simple Earthy Substances

New Names
Lime

Magnesia

Barytes

Argill

Silex

Old Names

Chalk, calcareous earth
Quicklime

Magnesia, base of Epsom salt
Calcined or caustic magnesia
Barytcs, or heavy earth
Clay, earth of alum
Siliceous or verifiable earth

Observations upon the Tabk of Simple Sub-
stances

The principal object of chemical experiments
is to decompose natural bodies, so as separate-
ly to examine the different substances which
enter into their composition. By consulting
chemical systems, it will be found that this sci-
ence of chemical analysis has made rapid prog-
ress in our own times. Formerly oil and salt
were considered as elements of bodies, whereas
later observation and experiment have shown
that all salts, instead of being simple, are com-
posed of an acid united to a base. The bounds
of analysis have been greatly enlarged by mod-
ern discoveries; 1 the acids are shown to be
composed of oxygen, as an acidifying principle
common to all, united in each to a particular
base. I have proved what M. Hassenfratz had
before advanced, that these radicals of the
acids are not all simple elements, many of
them being, like the oily principle, composed
of hydrogen and charcoal. Even the bases of
neutral salts have been proved by M. Ber-
th ollet to be compounds, as he has shown that
ammonia is composed of azote and hydrogen.

1 See Recueil de I'Acadtmie for 1776, p. 671; and
for 1778, p. 535. AUTHOR.

TABLE of Compound Oxidable and Acidifiable Bases

Names of the Radicals

Oxidable or acidifiable base, from
the mineral kingdom

Oxidable or acidifiable hydro-car-
bonous or carbono-hydrous radi-
cals from the vegetable kingdom. 2

Oxidable or acidifiable radicals
from the animal kingdom, which
mostly contain azote, and frequent-
ly phosphorus

Nitro-muriatic radical or

base of the acid formerly

called aqua regia

Tartarous radical or base

Malic

Citric

Pyro-lignous

Pyro-mucous

Pyro-tartarous

Oxalic

Acetous

Succinic

Benzoic

Camphoric

Gallic

Lactic

Saccholactic

Formic

Bombic

Sebacic

Lithic

Prussic

1 Note. The radicals from the vegetable kingdom are converted by a
first degree of oxygenation into vegetable oxides, suoh as sugar, starch,
and gum or mucus: those of the animal kingdom by the same means
form animal oxides, as lymph, <fcc. AUTHOR.

CHEMISTRY

Thus, as chemistry advances towards per-
fection, by dividing and subdividing, it is im-
possible to say where it is to end; and these
things we at present suppose simple may
soon be found quite otherwise. All we dare
venture to affirm of any substance is that it
must be considered as simple in the present
state of our knowledge and so far as chemical
analysis has been able to show. We may even
presume that the earths must soon cease to be
considered as simple bodies; they are the only
bodies of the salifiable class which have no
tendency to unite with oxygen; and I am
much inclined to believe that this proceeds
from their being already saturated with that
element. If so, they will fall to be considered
as compounds consisting of simple substances,
perhaps metallic, oxidated to a certain de-
gree. This is only hazarded as a conjecture;
and I trust the reader will take care not
to confound what I have related as truths,
fixed on the firm basis of observation and
experiment, with mere hypothetical conjec-
tures.

The fixed alkalies, potash, and soda, are
omitted in the foregoing table, because they
are evidently compound substances, though
we are ignorant as yet what are the elements
they are composed of.

SECTION II

Observations upon the Table of Compound
Radicals

The older chemists being unacquainted with
the composition of acids and not suspecting
them to be formed by a peculiar radical or
base for each, united to an acidifying principle
or element common to all, could not conse-
quently give any name to substances of which
they had not the most distant idea. We had
therefore to invent a new nomenclature for
this subject, though we were at the same time
sensible that this nomenclature must be sus-
ceptible of great modification when the nature
of the compound radicals shall be better
understood. 1

The compound oxidable and acidifiable rad-
icals from the vegetable and animal king-
doms, enumerated in the foregoing table, are
not reducible to systematic nomenclature,
because their exact analysis is as yet un-
known. We only know hi general, by some
experiments of my own and some made by

*See Part 1, Chapter XI, upon this subject.
AUTHOB.

M. Hassenfratz, that most of the vegetable
acids, such as the tartarous, oxalic, citric,
malic, acetous, pyrotartarous, and pyromucous,
have radicals composed of hydrogen and char-
coal, combined in such a way as to form
single bases, and that these acids only differ
from each other by the proportions in which
these two substances enter into the composi-
tion of their bases, and by the degree of oxy-
genation which these bases have received. We
know further, chiefly from the experiments of
M. Berthollet, that the radicals from the
animal kingdom, and even some of those
from vegetables, are of a more compound na-
ture, and, besides hydrogen and charcoal,
that they often contain azote, and sometimes
phosphorus; but we were not possessed of
sufficiently accurate experiments for calculat-
ing the proportions of these several substances.
We are therefore forced, in the manner of
the older chemists, still to name these acids
after the substances from which they are pro-
cured. There can be little doubt that these
names will be laid aside when our knowledge
of these substances becomes more accurate and
extensive; the terms hydro-carbonous, hydro-
carbonic, carbono-hydrous, and carbono-hydric,*
will then become substituted for those we now
employ, which will then only remain as testi-
monies of the imperfect state in which this
part of chemistry was transmitted to us by our
predecessors.

It is evident that the oils, being composed of
hydrogen and charcoal combined, are true car-
bono-hydrous or hydro-carbonous radicals ; and,
indeed, by adding oxygen, they are convertible
into vegetable oxides and acids according to
their degrees of oxygenation. We cannot, how-
ever, affirm that oils enter in their entire state
into the composition of vegetable oxides and
acids; it is possible that they previously lose a
part either of their hydrogen or charcoal, and
that the remaining ingredients no longer exist
in the proportions necessary to constitute oils.
We still require further experiments to eluci-
date these points.

Properly speaking, we are only acquainted
with one compound radical from the mineral
kingdom, the nitro-muriatic, which is formed
by the combination of azote with the muriatic
radical. The other compound mineral acids
have been much less attended to, from their
producing less striking phenomena.

1 See Part I, Chapter XI, upon the application of
these names according to the proportions of the two
ingredients. AUTHOB.

PQ
-*l
H

I : i H : -S

. o ft *5 5 tl

: : : : a : :

0? 3

: S b 1 ! !

: ?

uddxo

CHEMISTRY

SECTION III

Observations upon the Combinations of Light
and Caloric with Different Substances

I have not constructed any table of the com-
binations of light and caloric with the various
simple and compound substances, because our
conceptions of the nature of these combina-
tions are not hitherto sufficiently accurate. We
know, in general, that all bodies in nature are
imbued, surrounded, and penetrated in every
way with caloric, which fills up every interval
left between their particles; that, in certain
cases, caloric becomes fixed in bodies, so as to
constitute a part even of their solid substance,
though it more frequently acts upon them with
a repulsive force, from which, or from its ac-
cumulation in bodies to a greater or lesser de-
gree, the transformation of solids into fluids,
and of fluids to aeriform elasticity, is entirely
owing. We have employed the generic name
gas to indicate this aeriform state of bodies pro-
duced by a sufficient accumulation of caloric,
so that, when we wish to express the aeriform
state of muriatic acid, carbonic acid, hydrogen,
water, alcohol, &c. we do it by adding the word
gas to their names; thus muriatic acid gas,
carbonic acid gas, hydrogen gas, aqueous gas,
alcoholic gas, &c.

The combinations of light, and its mode of
acting upon different bodies, is still less known.
By the experiments of M. Bertholiet, it ap-
pears to have great affinity with oxygen, is sus-
ceptible of combining with it, and contributes
alongst with caloric to change it into the state
of gas. Experiments upon vegetation give rea-
son to believe that light combines with certain
parts of vegetables, and that the green of their
leaves, and the various colours of their flowers,
is chiefly owing to this combination. This much
is certain, that plants which grow in darkness
are perfectly white, languid, and unhealthy,
and that to make them recover vigour, and to
acquire their natural colours, the direct influ-
ence of light is absolutely necessary. Some-
thing similar takes place even upon animals:
mankind degenerate to a certain degree when
employed in sedentary manufactures, from liv-
ing in crowded houses or in the narrow lanes of
large cities; whereas they improve in their na-
ture and constitution in most of the country
labours which are carried on in the open air.
Organization, sensation, spontaneous motion,
and all the operations of life, only exist at the
surface of the earth, and in places exposed to
the influence of light. Without it nature itself

would be lifeless and inanimate. By means of
light, the benevolence of the Deity hath filled
the surface of the earth with organization, sen-
sation, and intelligence. The fable of Prome-
theus might perhaps be considered as giving a
hint of this philosophical truth, which had
even presented itself to the knowledge of the
ancients. I have intentionally avoided any dis-
quisitions relative to organized bodies in this
work, for which reason the phenomena of res-
piration, sanguification, and animal heat, are
not considered; but I hope, at some future time,
tp be able to elucidate these curious subjects.

SECTION IV

Observations upon the Combinations of Oxygen
with the Simple Substances

Oxygen forms almost a third of the mass of
our atmosphere and is consequently one of the
most plentiful substances in nature. All the
animals and vegetables live and grow in this
immense magazine of oxygen gas, and from it
we procure the greatest part of what we em-
ploy in experiments. So great is the reciprocal
affinity between this element and other sub-
stances that we cannot procure it disengaged
from all combination. In the atmosphere it is
united with caloric, in the state of oxygen gas,
and this again is mixed with about two thirds
of its weight of azotic gas.

Several conditions are requisite to enable a
body to become oxygenated or to permit oxy-
gen to enter into combination with it. In the
first place, it is necessary that the particles of
the body to be oxygenated shall have less re-
ciprocal attraction with each other than they
have for the oxygen, which otherwise cannot
possibly combine with them. Nature, in this
case, may be assisted by art, as we have it in
our power to diminish the attraction of the
particles of bodies almost at will by heating
them, or, in other words, by introducing caloric
into the interstices between their particles;
and, as the attraction of these particles for
each other is diminished in the inverse ratio of
their distance, it is evident that there must be
a certain point of distance of particles when
the affinity they possess with each other be-
comes less than that they have for oxygen, and
at which oxygenation must necessarily take
place if oxygen be present.

We can readily conceive that the degree of
heat at which this phenomenon begins must be
different in different bodies. Hence, on purpose
to oxygenate most bodies, especially the great-

LAVOISIER

er part of the simple substances, it is only nec-
essary to expose them to the influence of the
air of the atmosphere in a convenient degree of
temperature. With respect to lead, mercury,
and tin, this needs be but little higher than the
medium temperature of the earth; but it re-
quires a more considerable degree of heat to
oxygenate iron, copper, &c., by the dry way, or
when this operation is not assisted by moisture.
Sometimes oxygenation takes place with great
rapidity and is accompanied by great sensible
heat, light, and flame; such is the combustion
of phosphorus in atmospheric air and of iron
in oxygen gas. That of sulphur is less rapid;
and the oxygenation of lead, tin, and most of
the metals, takes place vastly slower, and con-
sequently the disengagement of caloric, and
more especially of light, is hardly perceptible.
Some substances have so strong an affinity
with oxygen, and combine with it in such low
degrees of temperature, that we cannot pro-
cure them in their unoxygenated state; such is
the muriatic acid, which has not hitherto been

decomposed by art, perhaps even not by na-
ture, and which consequently has only been
found in the state of acid. It is probable that
many other substances of the mineral kingdom
are necessarily oxygenated in the common tem-
perature of the atmosphere, and that being al-
ready saturated with oxygen prevents their
further action upon that element.

There are other means of oxygenating simple
substances besides exposure to air in a certain
degree of temperature, such as by placing them
in contact with metals combined with oxygen
and which have little affinity with that ele-
ment. The red oxide of mercury is one of the
best substances for this purpose, especially
with bodies which do not combine with that
metal. In this oxide the oxygen is united with
very little force to the metal, and can be driven
out by a degree of heat only sufficient to make
glass red hot; wherefore such bodies as are cap-
able of uniting with oxygen are readily oxy-
genated by means of being mixed with red
oxide of mercury and moderately heated. The

TABLE of the Combinations of Oxygen with the
Compound Radicals

Names of the Radicals Names of the Resulting Acids
New Names Old Names
Nitro-muriatic XT:A . .. . , A .

Unknown till lately

Ditto

Acid of lemons

Empyreumatic acid of

wood

pjmpyr. acid of sugar
i Empyr. acid of tartar
Acid of sorel

Vinegar, or acid of vinegar
Radical vinegar
Volatile salt of amber
Flowers of benzoin
Unknown till lately

I The astringent principle
of vegetables

Acid of sour whey
Unknown till lately
Acid of ants
Unknown till lately
Ditto

Urinary calculus
Colouring matter of Prus-
sian blue

Note 1 : These radicals by a first degree of oxygenation form vegetable
oxides, as sugar, starch, mucus, <fec. AUTHOR.

Note 2: These radicals by a first degree of oxygenation form the animal
oxides, as lymph, red part of the blood, animal secretions, &c. AUTHOR.

radical

iMwu-iiiunatiu aci

Tartaric
Malic
Citric

Tartarous acid
Malic acid
Citric acid

Pyro-lignous

Pyro-lignous acid

T 1

Pyro-mucous
Pyro-tartarous
Oxalic

Pyro-mucous acid
Pyro-tartarous aci
Oxalic acid

Acetic

Acetous acid
Acetic acid

Succinic
Benzoic
Camphoric

Saccinic acid
Benzotic acid
Camphoric acid

Gallic

Gallic acid

See Note 2

Lactic
Saccholactic
Formic
Bombic
Sebacic
Lithic

Lactic acid
Saccholactic acid
Formic acid
Bombic acid
Sebacic acid
Lithic acid

Prussic

Prussic acid

CHEMISTRY

same effect may be, to a certain degree, pro-
duced by means of the black oxide of mangan-
ese, the red oxide of lead, the oxides of silver,
and by most of the metallic oxides, if we only
take care to choose such as have less affinity
with oxygen than the bodies they are meant to
oxygenate. All the metallic reductions and re-
vivifications belong to this class of operations,
being nothing more than oxygenations of char-
coal by means of the several metallic oxides.
The charcoal combines with the oxygen and
with caloric and escapes in form of carbonic
acid gas, while the metal remains pure and re-
vivified, or deprived of the oxygen which be-
fore combined with it in the form of oxide.

All combustible substances may likewise be
oxygenated by means of mixing them with ni-
trate of potash or of soda, or with oxygenated
muriate of potash, and subjecting the mixture
to a certain degree of heat; the oxygen, in this
case, quits the nitrate or the muriate, and com-
bines with the combustible body. This species
of oxygenation requires to be performed with
extreme caution and only with very small quan-
tities; because, as the oxygen enters into the
composition of nitrates, and more especially of
oxygenated muriates, combined with almost as
much caloric as is necessary for converting it
into oxygen gas, this immense quantity of ca-
loric becomes suddenly free the instant of the
combination of the oxygen with the combust-
ible body and produces such violent explosions
as are perfectly irresistible.

By the humid way we can oxygenate most
combustible bodies, and convert most of the
oxides of the three kingdoms of nature into
acids. For this purpose we chiefly employ the
nitric acid, which has a very slight hold of oxy-
gen, and quits it readily to a great number of
bodies by the assistance of a gentle heat. The
oxygenated muriatic acid may be used for sev-
eral operations of this kind, but not in them all.

I give the name of binary to the combinations
of oxygen with the simple substances, because
in these only two elements are combined. When
three substances are united in one combina-
tion I call it ternary, and quaternary when the
combination consists of four substances united.

SECTION V

Observations upon the Combinations of Oxygen
with the Compound Radicals

I published a new theory of the nature and
formation of acids in the Recueil de I' Academic
for 1776, p. 671 and 1778, p. 535 in which I

concluded that the number of acids must be
greatly larger than was till then supposed.
Since that time, a new field of inquiry has been
opened to chemists; and, instead of five or six
acids which were then known, near thirty new
acids have been discovered, by which means
the number of known neutral salts have been
increased in the same proportion. The nature
of the acidifiable bases or radicals of the acids,
and the degrees of oxygenation they are sus-
ceptible of, still remain to be inquired into. I
have already shown that almost all the oxid-
able and acidifiable radicals from the mineral
kingdom are simple, and that, on the contrary,
there hardly exists any radical in the vegetable,
and more especially in the animal kingdom,
but is composed of at least two substances, hy-
drogen and charcoal, and that azote and phos-
phorus are frequently united to these, by which
we have compound radicals of two, three, and
four bases or simple elements united.

From these observations, it appears that the
vegetable and animal oxides and acids may differ
from each other in three several ways: 1st, ac-
cording to the number of simple acidifiable
elements of which their radicals are composed:
2nd, according to the proportions in which
these are combined together: and, 3rd, accord-
ing to their different degrees of oxygenation:
which circumstances are more than sufficient
to explain the great variety which nature pro-
duces in these substances. It is not at all sur-
prising, after this, that most of the vegetable
acids are convertible into each other, nothing
more being requisite than to change the pro-
portions of the hydrogen and charcoal in their
composition, and to oxygenate them in a greater
or lesser degree. This has been done by M.
Crell in some very ingenious experiments,
which have been verified and extended by M.
Hassenfratz. From these it appears that char-
coal and hydrogen by a first oxygenation pro-
duce tartarous acid, oxalic acid by a second
degree, and acetous or acetic acid by a third,
or higher oxygenation; only, that charcoal
seems to exist in a rather smaller proportion in
the acetous and acetic acids. The citric and
malic acids differ little from the preceding acids.

Ought we then to conclude that the oils are
the radicals of the vegetable and animal acids?
I have already expressed my doubts upon this
subject: 1st, although the oils appear to be
formed of nothing but hydrogen and charcoal,
we do not know if these are in the precise pro-
portion necessary for constituting the radicals
of the acids: 2nd, since oxygen enters into the

LAVOISIER

composition of these acids equally with hydro-
gen and charcoal, there is no more reason for
supposing them to be composed of oil rather
than of water or of carbonic acid. It is true
that they contain the materials necessary for
all these combinations, but then these do not
take place in the common temperature of the
atmosphere; all the three elements remain

either to a solid or liquid form. This is likewise
one of the essential constituent elements of
animal bodies, in which it is combined with
charcoal and hydrogen, and sometimes with
phosphorus; these are united together by a
certain portion of oxygen, by which they are
formed into oxides or acids according to the
degree of oxygenation. Hence the animal sub-

Simple
Substances

Caloric
Hydrogen

Oxygen

Charcoal

Phosphorus

Sulphur

Compound
radicals

Metallic

substances

Lime

Magnesia

Barytes

Argill

Potash

Soda

TABLE of the Binary Combinations of Azote with the
Simple Substances

Results of the Combinations

New Names
Azotic gas
Ammonia
Nitrous oxide
Nitrous acid
Nitric acid

Old Names

Phlogisticated air, or Mephitis
Volatile alkali

Base of Nitrous gas
Smoking nitrous acid
Pale nitrous acid
Oxygenated nitric acid Unknown

This combination is unknown ; should it ever be discovered*
it will be called, according to the principles of our nomen-
clature, Azuret of Charcoal. Charcoal dissolves in azotic
gas and forms carbonated azotic gas

Azuret of phosphorus. Still unknown
Azuret of sulphur. Still unknown. We know that
sulphur dissolves in azotic gas, forming sulphurated
azotic gas

Azote combines with charcoal and hydrogen, and some-
times with phosphorus, in the compound oxydable and
acidifiable bases, and is generally contained in the radi-
cals of the animal acids

Such combinations are unknown; if ever discovered, they
will form metallic azurets, as azuret of gold, of silver, <fec.

Entirely unknown. If over discovered, they will form
azuret of lime, azuret of magnesia, &c.

combined in a state of equilibrium which is
readily destroyed by a temperature only a
little above that of boiling water. 1

SECTION VI

Observations upon the Combinations of Azote
with the Simple Substances

Azote is one of the most abundant elements;
combined with caloric it forms azotic gas, or
mephitis, which composes nearly two thirds of
the atmosphere. This element is always in the
state of gas in the ordinary pressure and tem-
perature, and no degree of compression or of
cold has been hitherto capable of reducing it

See Part I, Chapter XII, upon this subject.

AXTTBOB*

stances may be varied, in the same way with
vegetables, in three different manners: 1st,
according to the number of elements which
enter into the composition of the base or radi-
cal; 2nd, according to the proportions of these
elements; 3rd, according to the degree of oxy-
genation.

When combined with oxygen, azote forms
the nitrous and nitric oxides and acids; when
with hydrogen, ammonia is produced. Its com-
binations with the other simple elements are
very little known; to these we give the name of
azurets , preserving the, termination in uret for
all non-oxygenated compounds. It is extremely
probable that all the alkaline substances may
hereafter be found to belong to this genus of
azurets.

CHEMISTRY

The azotic gas may be procured from atmos-
pheric air, by absorbing the oxygen gas which
is mixed with it by means of a solution of sul-
phuret of potash, or sulphuret of lime. It re-
quires twelve or fifteen days to complete this
process, during which time the surface in con-
tact must be frequently renewed by agitation
and by breaking the pellicle which forms on
the top of the solution. It may likewise be pro-
cured by dissolving animal substances in dilute
nitric acid very little heated. In this operation
the azote is disengaged in form of gas, which
we receive under bell glasses filled with water
in the pneumato-chemicai apparatus. We may
procure this gas by deflagrating nitre with
charcoal, or any other combustible substance;
when with charcoal, the azotic gas is mixed
with carbonic acid gas, which may be absorbed
by a solution of caustic alkali or by lime water,
after which the azotic gas remains pure. We
can procure it in a fourth manner from com-
binations of ammonia with metallic oxides, as
pointed out by M. cle Fourcroy: the hydrogen
of the ammonia combines with the oxygen of
the oxide, and forms water; whilst the azote
being left free escapes in form of gas.

The combinations of azote were but lately
discovered: M. Cavendish first observed it in
nitrous gas and acid, and M. Rerthollet in am-
monia and the prussic acid. As no evidence of
its decomposition has hitherto appeared, we
are fully entitled to consider azote as a simple
elementary substance.

SECTION VII

Observations upon Hydrogen and Its Combina-
tions with Simple Substances

Hydrogen, as its name expresses, is one of
the constituent elements of water, of which it
forms fifteen hundredth parts by weight, com-
bined with eighty-five hundredth parts of oxy-
gen. This substance, the properties and even
existence of which was unknown till lately, is
very plentifully distributed in nature and acts
a very considerable part in the processes of the
animal and vegetable kingdoms. As it possesses
so great affinity with caloric as only to exist in
the state of gas, it is consequently impossible
to procure it in the concrete or liquid state, in-
dependent of combination.

To procure hydrogen, or rather hydrogen
gas, we have only to subject water to the ac-
tion of a substance with which oxygen has
greater affinity than it has to hydrogen; by this
means the hydrogen is set free and, by uniting
with caloric, assumes the form of hydrogen gas.
Red hot iron is usually employed for this pur-
pose: the iron, during the process, becomes
oxidated, and is changed into a sukstance re-
sembling the iron ore from the island of Elba.
In this state of oxide it is much less attractible
by the magnet, and dissolves in acids without
effervescence.

Charcoal, in a red heat, has the same power
of decomposing water, by attracting the oxy-
gen from its combination with hydrogen. In

TABLE of the Binary Combinations of Hydrogen with
Simple Substances

Simple
Substances
Caloric
Azote
Oxygen

Sulphur
Phosphorus

Charcoal

Metallic substances,!
as iron, &c |

Resulting Compounds

New Names
Hydrogen gas
Ammonia
Water

I Hydruret of sulphur, or
sulphuret of hydrogen
Hydruret of phosphorus,
or phosphuret of hydrogen
Hydro-carbonous, or car-
bono hydrous radicals 2
Metallic hydrurets 8 , as
hydruret of iron, &c

Old Names
Inflammable air
Volatile Alkali
Water

Hitherto unknown 1

Not known till lately
Hitherto unknown

1 These combinations take place in the state of gas, and form, respective-
ly, sulphurated and phosphorated oxygen gas. AUTHOR.

This combination of hydrogen with charcoal includes the fixed and
volatile oils, and forms the radicals of a considerable part of the vegetable
and animal oxides and acids. When it takes place in the state of gas it
forms carbonated hydrogen gas. AUTHOR.

8 None of these combinations are known, and it is probable that they
cannot exist, at least in the usual temperature of the atmosphere, owing
to the great affinity of hydrogen for caloric. AUTHOR.

LAVOISIER

this process carbonic acid gas is formed and
mixes with the hydrogen gas but is easily sep-
arated by means of water or alkalies, which
absorb the carbonic acid and leave the hydro-
gen gas pure. We may likewise obtain hydro-
gen gas by dissolving iron or zinc in dilute sul-
phuric acid. These two metals decompose wa-
ter very slowly, and with great difficulty, when
alone, but do it with great ease and rapidity
when assisted by sulphuric acid; the hydrogen
unites with caloric during the process and is
disengaged in form of hydrogen gas, while the
oxygen of the water unites with the metal in
the form of oxide, which is immediately dis-
solved in the acid, forming a sulphate of iron
or of zinc.

Some very distinguished chemists consider
hydrogen as the phlogiston of Stahl; and as

that celebrated chemist admitted the existence
of phlogiston in sulphur, charcoal, metals, &c.,
they are, of course, obliged to suppose that hy-
drogen exists in all these substances, though
they cannot prove their supposition; even if
they could, it would not avail much, since this
disengagement of hydrogen is quite insufficient
to explain the phenomena of calcination and
combustion. We must always recur to the ex-
amination of this question, "Are the heat and
light which are disengaged during the different
species of combustion furnished by the burning
body or by the oxygen which combines in all
these operations? " And certainly the supposi-
tion of hydrogen being disengaged throws no
light whatever upon this question. Besides, it
belongs to those who make suppositions to
prove them; and, doubtless, a doctrine which

TABLE of the Binary Combinations of Sulphur with
Simple Substances

Simple
Substances
Caloric

Oxygen

Hydrogen

Azote

Phosphorus

Charcoal

Antimony

Silver

Arsenic

Bismuth

Cobalt

Copper

Tin

Iron

Manganese

Mercury

Molybdenum

Nickel

Gold

Platinum

Lead

Tungsten

Zinc

Potash
Soda

Ammonia

Lime
Magnesia
Barytes
Argill

Resulting Compounds
New Names Old Names

Sulphuric gas

Oxide of sulphur

Sulphurous acid

Sulphuric acid

Sulphuret of hydrogen
azote

phosphorus
charcoal
antimony
silver
arsenic
bismuth
cobalt
copper
tin
iron

manganese
mercury
molybdenum
nickel
gold

platinum
lead

tungsten
zinc

potash
soda

ammonia

lime

magnesia
barytes
argill

Soft sulphur
Sulphureous acid
Vitriolic acid

Unknown combinations

Crude antimony
Orpiment, realgar

Copper pyrites

Iron pyrites

Ethiops mineral, cinnabar

Galena

Blende

Alkaline liver of sulphur
with fixed vegetable alkali
Alkaline liver of sulphur
with fixed mineral alkali
Volatile liver of sulphur,
smoking liquor of Boyle
Calcareous li ver of sulphur
Magnesian liver of sulphur
Barytic liver of sulphur
Yet unknown

CHEMISTRY

without any supposition explains the phenom-
ena as well and as naturally as theirs does by
supposition has at least the advantage of great-
er simplicity. 1

SECTION VIII
Observations on Sulphur and its Combinations

Sulphur is a combustible substance, having
a very great tendency to combination; it is
naturally in a solid state in the ordinary tem-
perature, and requires a heat somewhat higher
than boiling water to make it liquify. Sulphur
is formed by nature in a considerable degree of
purity in the neighbourhood of volcanos; we
find it likewise, chiefly in the state of sulphuric
acid, combined with argil! in aluminous schist,
with lime in gypsum, &c. From these combi-
nations it may be procured in the state of sul-
phur, by carrying off its oxygen by means of
charcoal in a red heat; carbonic acid is formed
and escapes in the state of gas; the sulphur re-
mains combined with the clay, lime, &c. in the
state of sulphuret, which is decomposed by
acids; the acid unites with the earth into a neu-
tral salt, and the sulphur is precipitated.

TABLE of the Binary Combinations of
Phosphorus with the Simple Substances

SECTION IX

Resulting Compounds
Phosphoric gas
Oxide of phosphorus
Phosphorous acid
Phosphoric acid
Phosphuret of hydrogen
Phosphuret of azote
Phosphuret of sulphur
Phosphuret of charcoal
Phosphuret of metals 2

Phosphuret of Potash,
Soda, &c. 8

Argill

1 Those who wish to see what has been said upon
this great chemical question by MM. de Morvoau,
Berthollet, de Fourcroy, and myself may consult
our translation of M. Kir wan 's Essay upon Phlo-
giston. AUTHOR.

Of all these combinations of phosphorus with
metals, that with iron only is hitherto known, form-
ing the substance formerly called siderite; neither is
it yet ascertained whether, in this combination, the
phosphorus be oxygenated or not. AUTHOR.

1 These combinations of phosphorus with the alka-
lies and earths are not yet known; and, from the ex-
periments of M. Gengembre, they appear to be im-
possible. AUTHOB.

Simple Substances
Caloric

Oxygen

Hydrogen

Azote

Sulphur

Charcoal

Metallic substances

Potash

Soda

Ammonia

Lime

Barytes

Observations upon Phosphorus and its Combi-
nations

Phosphorus is a simple combustible sub-
stance, which was unknown to chemists till
1667, when it was discovered by Brandt, who
kept the process secret; soon after, Kunkel
found out Brandt's method of preparation and
made it public. It has been ever since known
by the name of Kunkel's phosphorus. It was
for a long time procured only from urine; and,
though Homberg gave an account of the proc-
ess in the Recueil de I'Acadtmie for 1692, all
the philosophers of Europe were supplied with
it from England. It was first made in France in
1737, before a committee of the Academy at
the Royal Garden. At present it is procured in
a more commodious and more economical man-
ner from animal bones, which are real calcar-
eous phosphates, according to the process of
MM. Gahn, Scheele, Roueile, &c. The bones
of adult animals, being calcined to whiteness,
are pounded and passed through a fine silk
sieve; pour upon the fine powder a quantity of
dilute sulphuric acid, less than is sufficient for
dissolving the whole. This acid unites with the
calcareous earth of the bones into a sulphate of
lime, and the phosphoric acid remains free in
the liquor. The liquid is decanted off, and the
residuum washed with boiling water; this wa-
ter which has been used to wash out the adher-
ing acid is joined with what was before decant-
ed off, and the whole is gradually evaporated;
the dissolved sulphate of lime crystallizes in
form of silky threads, which are removed, and
by continuing the evaporation we procure the
phosphoric acid under the appearance of a
white pellucid glass. When this is powdered
and mixed with one third its weight of char-
coal, we procure very pure phosphorus by sub-
limation. The phosphoric acid, as procured by
the above process, is never so pure as that ol>
tained by oxygenating pure phosphorus either
by combustion or by means of nitric acid;
wherefore this latter should always be em-
ployed in experiments of research.

Phosphorus is found in almost all animal
substances, and in some plants which give a
kind of animal analysis. In all these it is usu-
ally combined with charcoal, hydrogen, and
azote, forming very compound radicals, which
are, for the most part, in the state of oxides by
a first degree of union with oxygen. The dis-
covery of M. Hassenfratz, of phosphorus be-
ing contained in charcoal, gives reason to BUS-

LAVOISIER

pect that it is more common in the vegetable
kingdom than has generally been supposed. It
is certain that by proper processes it may be
procured from every individual of some of the
families of plants. As no experiment has hith-
erto given reason to suspect that phosphorus
is a compound body, I have arranged it with
the simple or elementary substances. It takes
fire at the temperature of 32 (104) of the
thermometer.

In the business of charring wood, this is done
by a less expensive process. The wood is dis-
posed in heaps and covered with earth, so as to
prevent the access of any more air than is ab-
solutely necessary for supporting the fire, which
is kept up till all the water and oil is driven off,
after which the fire is extinguished by shutting
up all the air-holes.

We may analyse charcoal either by combus-
tion in air, or rather in oxygen gas, or by means

Simple
Substances

Oxygen

Sulphur

Phosphorus

Azote

Hydrogen

Metallic sub-
stances

TABLE of Binary Combinations of Charcoal
Resulting Compounds

New Names

I Oxide of charcoal
Carbonic acid
Carburet of sulphur
Carburet of phosphorus
Carburet of azote

ICarbono-hydrous radical
Fixed and volatile oils

Carburets of metals

Old Names
Unknown
Fixed air, chalky acid

Unknown

Alkalies and earths Carburet of potash, &c.

Of these only the car-
burets of iron and zinc
are known, and were
formerly called Plum-
bago
Unknown

SECTION X

Observations upon Charcoal and its Combina-
tions with Simple Substances

As charcoal has not been hitherto decom-
posed, it must, in the present state of our
knowledge, be considered as a simple substance.
By modern experiments it appears to exist
ready formed in vegetables; and I have already
remarked that in these it is combined with hy-
drogen, sometimes with azote and phosphorus,
forming compound radicals which may be
changed into oxides or acids according to their
degree of oxygenation.

To obtain the charcoal contained in vege-
table or animal substances, we subject them
to the action of fire, at first moderate and
afterwards very strong, on purpose to drive off
the last portions of water, which adhere very
obstinately to the charcoal. For chemical pur-
poses, this is usually done in retorts of stone-
ware or porcelain, into which the wood, or
other matter, is introduced, and then placed
in a reverberatory furnace, raised gradually to
its greatest heat. The heat volatilizes, or changes
into gas, all the parts of the body susceptible of
combining with caloric into that form, and the
charcoal, being more fixed in its nature, re-
mains in the retort combined with a little earth
and some fixed salts.

of nitric acid. In either case we convert it into
carbonic acid, and sometimes a little potash
and some neutral salts remain. This analysis
has hitherto been but little attended to by
chemists ; and we are not even certain if potash
exists in charcoal before combustion or wheth-
er it be formed by means of some unknown
combination during that process.

SECTION XI

Observations upon the Muriatic, Fluoric, and Bo-
racic Radicals and their Combinations

As the combinations of these substances,
either with each other or with the other com-
bustible bodies, are entirely unknown, we have
not attempted to form any table for their no-
menclature. We only know that these radicals
are susceptible of oxygenation, and of forming
the muriatic, fluoric, and boracic acids, and
that in the acid state they enter into a number
of combinations, to be afterwards detailed.
Chemistry has hitherto been unable to disoxy-
genate any of them, so as to produce them in a
simple state. For this purpose, some substance
must be employed to which oxygen has a
stronger affinity than to their radicals, either
by means of single affinity or by double elec-
tive attraction. All that is known relative to
the origin of the radicals of these acids will be

CHEMISTRY

mentioned in the sections set apart for consider-
ing their combinations with the salifiable bases.

SECTION XII

Observations upon the Combinations of Metals
with Each Other

Before closing our account of the simple or
elementary substances, it might be supposed
necessary to give a table of alloys or combina-
tions of metals with each other; but, as such a
table would be both exceedingly voluminous
and very unsatisfactory, without going into a

series of experiments not yet attempted, I have
thought it adviseable to omit it altogether. All
that is necessary to be mentioned is that these
alloys should be named according to the metal
in largest proportion in the mixture or combi-
nation; thus the term alloy of gold and silver, or
gold alloyed with silver, indicates that gold is
the predominating metal.

Metallic alloys, like all other combinations,
have a point of saturation. It would even ap-
pear, from the experiments of M. de la Briche,
that they have two perfectly distinct degrees
of saturation.

Nitrate of barytes
potash

TABLE of the Combinations of Azote, Completely Saturated

with Oxygen, in the State of Nitric Acid, with the Salifiable

Bases, in the Order of the Affinity with the Acid

Bases Names of the Resulting Neutral Salts

New Names Old Names

Nitre, with a base of
heavy earth

Nitre, Saltpetre; Nitre
with base of potash
Quadrangular nitre;
Nitre with base of
mineral alkali
Calcareous nitre; Nitre
with calcareous base;
Mother water of nitre, or
saltpetre

Magnesian nitre; Nitre
with base of magnesia

Ammoniacal nitre

Nitrous alum; Argillace-
ous nitre; Nitre with base
of earth of alum

Nitre of zinc

Nitre of iron; Martial

nitre; Nitrated iron

Nitre of manganese
Nitre of cobalt
Nitre of nickel

Barytes
Potash

Soda

Lime

Magnesia
Ammonia

Argill

Oxide of zinc
iron

soda

lime

magnesia

ammonia

argill

iron

manganese

cobalt

nickel

manganese

cobalt

nickel

lead

tin

copper

bismuth
antimony
arsenic
mercury

silver

gold
platinum

lead

tin

copper

bismuth
antimony
arsenic
mercury

silver

gold
platinum

I Saturnine nitre; Nitre of
lead

Nitre of tin

I Nitre of copper or of
Venus

Nitre of bismuth
Nitre of antimony
Arsenical nitre
Mercurial nitre

I Nitre of silver or luna;
Lunar caustic

Nitre of gold
Nitre of platinum

LAVOISIER

TABLE of the Combinations of Azote in the State of Nitrous

Acid with the Salifiable Bases, Arranged According to

the Affinities of These Bases with the Acid

Names of the

Bases

Neutral Salts

New Names Notes

Barytes

Nitrite of barytes

Potash

potash

Soda

soda

These salts are only

Lime
Magnesia

lime f
magnesia

known of late and have re-
ceived no particular name
in the old nomenclature.

Ammonia

ammonia

Argill

argill

Oxide of zinc

zinc

As metals dissolve both

iron

in nitrous and nitric acids,

manganese manganese

metallic salts must of con-

cobalt*

cobalt

sequence be formed having

nickel

different degrees of oxygen-
ation. Those wherein the

lead

metal is least oxygenated

tin

must be called Nitrites,

when more so, Nitrates; but

copper
bismuth

the limits of this distinc-
tion are difficultly ascertain-

antimony

able. The older chemists

arsenic

were not acquainted with
any of these salts.

mercury

silver

It is extremely probable that gold, silver, and

gold

platinum only form nitrates, and cannot subsist in

platinum

the state of nitrites.

SECTION XIII

Observations upon Nitrous and Nitric Acids and
their Combinations with Salifiable Bases

The nitrous and nitric acids are procured
from a neutral salt long known in the arts un-
der the name of saltpetre. This salt is extracted
by lixiviation from the rubbish of old buildings,
from the earth of cellars, stables, or barns, and
in general of all inhabited places. In these
earths the nitric acid is usually combined with
lime and magnesia, sometimes with potash,
and rarely with argill. As all these salts, ex-
cepting the nitrate of potash, attract the
moisture of the air, and consequently would
be difficultly preserved, advantage is taken,
in the manufactures of saltpetre and the
royal refining-house, of the greater affinity
of the nitric acid to potash than these other
bases, by which means the lime, magnesia,
and argill, are precipitated, and all these
nitrates are reduced to the nitrate of potash or
saltpetre.

The nitric acid is procured from this salt by
distillation, from three parts of pure saltpetre
decomposed by one part of concentrated sul-
phuric acid, in a retort with Woulfe's appara-
tus, (Plate iv, Fig. 1) having its bottles half

rilled with water, and all its joints carefully
luted. The nitrous acid passes over in form of
red vapours surcharged with nitrous gas, or, in
other words, not saturated with oxygen. Part
of the acid condenses in the recipient in form
of a dark orange red liquid, while the rest com-
bines with the water in the bottles. During the
distillation, a large quantity of oxygen gas es-
capes, owing to the greater affinity of oxygen
to caloric in a high temperature than to nitrous
ncid, though in the usual temperature of the
atmosphere this affinity is reversed. It is from
the disengagement of oxygen that the nitric
acid of the neutral salt is in this operation con-
verted into nitrous acid. It is brought back to
the state of nitric acid by heating over a gentle
fire, which drives off the superabundant nitrous
gas, and leaves the nitric acid much diluted
with water.

Nitric acid is procurable in a more concen-
trated state, and with much less loss, by mix-
ing very dry clay with saltpetre. This mixture
is put into an earthen retort and distilled with
a strong fire. The clay combines with the pot-
ash, for which it has great affinity, and the ni-
tric acid passes over, slightly impregnated with
nitrous gas. This is easily disengaged by heat-
ing the acid gently in a retort; a small quantity

CHEMISTRY

of nitrous gas passes over into the recipient,
and very pure concentrated nitric acid remains
in the retort.

We have already seen that azote is the nitric
radical. If to 20}^ parts, by weight, of azote
43J^ parts of oxygen be added, 64 parts of ni-
trous gas are formed; and, if to this we join 36
additional parts of oxygen, 100 parts of nitric
acid result from the combination. Intermedi-
ate quantities of oxygen between these two
extremes of oxygenation produce different spe-
cies of nitrous acid, or, in other words, nitric
acid less or more impregnated with nitrous gas.
I ascertained the above proportions by means
of decomposition; and, though I cannot answer
for their absolute accuracy, they cannot be far

removed from truth. M. Cavendish, who first
showed by synthetic experiments that azote is
the base of nitric acid, gives the proportions of
azote a little larger than I have done; but, as
it is not improbable that he produced the ni-
trous acid and not the nitric, that circumstance
explains in some degree the difference in the
results of our experiments.

As in all experiments of a philosophical na-
ture the utmost possible degree of accuracy is
required, we must procure the nitric acid for
experimental purposes from nitre which has
been previously purified from ail foreign matter.
If, after distillation, any sulphuric acid is sus-
pected in the nitric acid, it is easily separated
by dropping in a little nitrate of barytes, so

TABLE of the Combinations of Sulphuric Acid with the
Salifiable Bases, in the Order of Affinity

Names of the

Resulting Compounds
New Names Old Names

Barytes

Potash

Soda
Lime

Magnesia

Ammonia
Argill

Oxide of zinc

Sulphate of barytes

potash

soda
lime

magnesia

ammonia
argill

zinc

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

mercury

silver

gold

platinum

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

mercury

silver

gold

platinum

Heavy spar; vitriol of
heavy earth

Vitriolated tartar; sal
de duobus; arcanum dup-
licatam

Glauber's salt

Selenitc, gypsum, cal-
careous vitriol

Epsom salt, sedlitz salt,
magnesian vitriol

Glauber's secret sal am-
moniac

Alum

White vitriol, goslar
vitriol, white coperas,
vitriol of zinc

Green coperas, green
vitriol, martial vitriol,
vitriol of iron

Vitriol of manganese
Vitriol of cobalt
Vitriol of nickel
Vitriol of lead
Vitriol of tin

Blue coperas,, blue vi-
triol, Roman vitriol, vi-
triol of copper

Vitriol of bismuth
Vitriol of antimony
Vitriol of arsenic
Vitriol of mercury
Vitriol of silver
Vitriol of gold
Vitriol of platinum

LAVOISIER

long as any precipitation takes place; the sul-
phuric acid, from its greater affinity, attracts
the barytes and forms with it an insoluble neu-
tral salt, which falls to the bottom. It may be
purified in the same manner from muriatic
acid, by dropping in a little nitrate of silver so
long as any precipitation of muriate of silver is
produced. When these two precipitations are
finished, distill off about seven-eighths of the
acid by a gentle heat, and what comes over is
in the most perfect degree of purity.

The nitric acid is one of the most prone to
combination and is at the same time very eas-
ily decomposed. Almost all the simple sub-
stances, with the exception of gold, silver, and
-platinum, rob it less or more of its oxygen;
some of them even decompose it altogether. It
was very anciently known, and its combina-
tions have been more studied by chemists than
those of any other acid. These combinations
were named nitres by MM. Macquer and
Beaum6; but we have changed their names to
nitrates and nitrites, according as they are
formed by nitric or by nitrous acid, and have
added the specific name of each particular base,
to distinguish the several combinations from
each other.

SECTION XIV

Observations upon Sulphuric Acid and its Com-
binations

For a long time this acid was procured by
distillation from sulphate of iron, in which sul-
phuric acid and oxide of iron are combined ac-
cording to the process described by Basil Val-
entine in the fifteenth century; but, in modern
times, it is procured more economically by the
combustion of sulphur in proper vessels. Both
to facilitate the combustion, and to assist the
oxygenation of the sulphur, a little powdered
saltpetre, nitrate of potash, is mixed with it;
the nitre is decomposed and gives out its oxy-
gen to the sulphur, which contributes to its
conversion into acid. Notwithstanding this ad-
dition, the sulphur will only continue to burn
in close vessels for a limited time; the combi-
nation ceases, because the oxygen is exhausted
and the air of the vessels reduced almost to
pure azotic gas, and because the acid itself re-
mains long in the state of vapour and hinders
the progress of combustion.

In the factories for making sulphuric acid in
the large way, the mixture of nitre and sulphur
is burnt in large close-built chambers lined
with lead, having a little water at the bottom

for facilitating the condensation of the vapours.
Afterwards, by distillation m large retorts with
a gentle heat, the water passes over, slightly
impregnated with acid, and the sulphuric acid
remains behind in a concentrated state. It is
then pellucid, without any flavour, and nearly
double the weight of an equal bulk of water.
This process would be greatly facilitated, and
the combustion much prolonged, by introduc-
ing fresh air into the chambers by means of
several pairs of bellows directed towards the
flame of the sulphur, and by allowing the ni-
trous gas to escape through long serpentine ca-
nals, in contact with water, to absorb any sul-
phuric or sulphurous acid gas it might contain.
By one experiment, M. Berthollet found
that 69 parts of sulphur in combustion united
with 31 parts of oxygen to form 100 parts of
sulphuric acid; and, by another experiment,
made in a different manner, he calculates that
100 parts of sulphuric acid consists of 72 parts
sulphur, combined with 28 parts of oxygen, all
by weight.

TABLE of the Combinations of the Sulphurous

Acid with the Salifiable Bases, in the

Order of Affinity

Names of the Bases

Names of the Neutral Salts

Barytes

Sulphite of barytes

Potash

potash

Soda

soda

Lime

lime

Magnesia

magnesia

Ammonia

ammonia

Argill

argill

Oxide of zinc

zinc

iron

manganese manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

mercury mercury

silver silver

gold gold

platinum platinum

Note. The only one of these salts known to the old
chemists was the sulphite of potash, under the name
of Stahl's sulphureous salt. So that, before our new
nomenclature, these compounds must have been
named Stahl's sulphureous salt, having base of fixed
vegetable alkali, and so of the rest.

In this table we have followed Bergman's order of
affinity of the sulphuric acid, which is the same in
regard to the earths and alkalies, but it is not certain
if the order be the same for the metallic oxides.

AUTHOB.

CHEMISTRY 9

This acid, in common with every other, can SECTION XV
only dissolve metals when they have been pre- ... . . , , . . , , ..
viously oxidated; but most of the metals are Observations upon Sulphurous Acid and its
capable of decomposing a part of the acid, so Cantonaton, mth Salifiabk Bases
as to carry off a sufficient quantity of oxygen The sulphurous acid is formed by the union
to render themselves soluble in the part of the of oxygen with sulphur by a lesser degree of
acid which remains undecomposed. This hap- oxygenation than the sulphuric acid. It is pro-
pens with silver, mercury, iron, and zinc, in curable either by burning sulphur slowly, or by
boiling concentrated sulphuric acid; they be- distilling sulphuric acid from silver, antimony,
come first oxidated by decomposing part of lead, mercury, or charcoal; by which operation
the acid, and then dissolve in the other part; a part of the oxygen quits the acid and unites
but they do not sufficiently disoxygenate the to these oxidabie bases, and the acid passes
decomposed part of the acid to reconvert it over in the sulphurous state of oxygenation.
into sulphur; it is only reduced to the state of This acid, in the common pressure and tem-
sulphurous acid, which, being volatilised by perature of the air, can only exist in form of
the heat, flies off in form of sulphurous acid gas. gas; but it appears, from the experiments of

Silver, mercury, and all the other metals ex- M. Clouet, that, in a very low temperature, it

cept iron and zinc, are insoluble in diluted sul- condenses and becomes fluid. Water absorbs a

phuric acid, because they have not sufficient great deal more of this gas than of carbonic

affinity with oxygen to draw it off from its com- acid gas, but much less than it does of muriatic

bination either with the sulphur, the sulphur- acid gas.

ous acid, or the hydrogen; but iron and zinc, That the metals cannot be dissolved in acids
being assisted by the action of the acid, de- without being previously oxidated, or by pro-
compose the water and become oxidated at its curing oxygen for that purpose from the acids
expense, without the help of heat. during solution, is a general and well estab-

TABLE of the Combinations of Phosphorous and Phosphoric
Acids, with the Salifiable Bases, in Order of Affinity

Names of the Names of the Neutral Salts formed by

Bases Phosphorous Add Phosphoric Acid

Lime Phosphites of lime 2 Phosphates of lime 3

Barytes barytes barytes

Magnesia magnesia magnesia

Potash potash potash

Soda soda soda

Ammonia ammonia ammonia

Argill argill argill

Oxides of zinc 1 zinc zinc

iron iron iron

manganese manganese manganese

cobalt cobalt cobalt

nickel nickel nickel

lead lead lead

tin tin tin

copper copper copper

bismuth bismuth bismuth

antimony antimony antimony

arsenic arsenic arsenic

mercury mercury mercury

silver silver silver

gold gold gold

platinum platinum platinum

1 The existence of metallic phosphites supposes that metals are suscep-
tible of solution in phosphoric acid at different degrees of oxygenation,
which is not yet ascertained. AUTHOR.

a All the phosphites were unknown till lately, and consequently have
not yet received names. AUTHOR.

The greater part of the phosphates were only discovered of late, and
have not yet been named. AUTHOR.

LAVOISIER

lished fact which I have perhaps repeated too
often. Hence, as sulphurous acid is already de-
prived of great part of the oxygen necessary
for forming the sulphuric acid, it is more dis-
posed to recover oxygen than to furnish it to
the greatest part of the metals; and, for this
reason, it cannot dissolve them unless previous-
ly oxidated by other means. From the same
principle it is that the metallic oxides dissolve
without effervescence, and with great facility,
in sulphurous acid. This acid, like the muri-
atic, has even the property of dissolving me-
tallic oxides surcharged with oxygen, and con-
sequently insoluble in sulphuric acid, and in
this way forms true sulphates. Hence we might
be led to conclude that there are no metallic
sulphites, were it not that the phenomena
which accompany the solution of iron, mer-

cury, and some other metals, convince us that
these metallic substances are susceptible of
two degrees of oxidation, during their solution
in acids. Hence the neutral salt in which the
metal is least oxidated must be named sulphite,
and that in which it is fully oxidated must be
called sulphate. It is yet unknown whether this
distinction is applicable to any of the metallic
sulphates, except those of iron and mercury.

SECTION XVI

Observations upon Phosphorous and Phosphoric
Acids and their Combinations with Salifiable
Bases

Under the article Phosphorus, Part II, Sec-
tion IX, we have already given a history of the
discovery of that singular substance, with some

TABLE of the Combinations of Carbonic Acid, with the
Salifiable Bases, in the Order of Affinity

Resulting Neutral Salts

Old Names

Aerated or effervescent heavy earth
Chalk, calcareous spar, aerated cal-
careous earth

Effervescing or aerated fixed vege-
table alkali, mephitis of potash
Aerated or effervescing fixed mineral
alkali, mephitic soda
Aerated, effervescing, mild, or me-
phitic magnesia

Aerated, effervescing, mild, or me-
phitic volatile alkali
Aerated or effervescing argillaceous
earth, or earth of alum
Zinc spar, mephitic or aerated zinc
Sparry iron-ore, mephitic or aerated
iron

Aerated manganese
Aerated cobalt
Aerated nickel

Sparry lead-ore, or aerated lead

Aerated tin

Aerated copper

Aerated bismuth

Aerated antimony

Aerated arsenic

Aerated mercury

Aerated silver

Aerated gold

Aerated platinum

i As these salts have only been understood of late, they have not, properly
speaking, any old names. M. Morveau, in the first volume of the Encyclopedia,
calls them Mephites; M. Bergman gives them the name of aerated; and M. de
Fourcroy, wljo calls.the carbonic acid chalky add, gives them the name of chalks.
AUTHOR.

Names of Resul
Bases 1 New Names

Barytes Carbonates

of barytes

Lime

lime

Potash

potash

Soda

soda

Magnesia

magnesia

Ammonia

ammonia

Argill

argill

Oxide of zinc

zinc

iron

manganese
cobalt

nickel

lead

tin

copper
bismuth

antimony

arsenic

mercury
silver

gold
platinum

CHEMISTRY

observations upon the mode of its existence in
vegetable and animal bodies. The best method
of obtaining this acid in a state of purity is by
burning well purified phosphorus under bell-
glasses, moistened on the inside with distilled
water; during combustion it absorbs twice and
a half its weight of oxygen; so that 100 parts of
phosphoric acid is composed of 28^ parts of
phosphorus united to 71J^ parts of oxygen.
This acid may be obtained concrete, in form of
white flakes which greedily attract the moist-
ure of the air, by burning phosphorus in a dry
glass over mercury.

To obtain phosphorous acid, which is phos-
phorus less oxygenated than in the state of
phosphoric acid, the phosphorus must be burnt
by a very slow spontaneous combustion over
a glass-funnel leading into a crystal phial; after
a few days, the phosphorus is found oxygen-
ated, and the phosphorous acid, in proportion
as it forms, has attracted moisture from the
air and dropped into the phial. The phospho-
rous acid is readily changed into phosphoric
acid by exposure for a long time to the free air;
it absorbs oxygen from the air and becomes
fully oxygenated.

As phosphorus has a sufficient affinity for
oxygen to attract it from the nitric and muri-
atic acids, we may form phosphoric acid by
means of these acids in a very simple and cheap
manner. Fill a tubulated receiver half full of
concentrated nitric acid and heat it gently,
then throw in small pieces of phosphorus
through the tube; these are dissolved with ef-
fervescence and red fumes of nitrous gas fly
off; add phosphorus so long as it will dissolve,
and then increase the fire under the retort to
drive off the last particles of nitric acid ; phos-
phoric acid, partly fluid and partly concrete,
remains in the retort.

SECTION XVII

Observations upon Carbonic Acid and its Com-
binations with Salifiable Bases

Of all the known acids, the carbonic is the
most abundant in nature ; it exists ready formed
in chalk, marble, and all the calcareous stones,
in which it is neutralized by a particular earth
called lime. To disengage it from this combi-
nation, nothing more is requisite than to add
some sulphuric acid, or any other which has a
stronger affinity for lime; a brisk effervescence
ensues, which is produced by the disengagement
of the carbonic acid which assumes the state of
gas immediately upon being set free. This gas,

incapable of being condensed into the solid or
liquid form by any degree of cold or of pressure
hitherto known, unites to about its own bulk
of water and thereby forms a very weak acid.
It may likewise be obtained in great abund-
ance from saccharine matter in fermentation
but is then contaminated by a small portion of
alcohol which it holds in solution.

As charcoal is the radical of this acid, we
may form it artificially by burning charcoal
in oxygen gas, or by combining charcoal,
and metallic oxides in proper proportions; the
oxygen of the oxide combines with the char-
coal, forming carbonic acid gas, and the metal
being left free recovers its metallic or reguline
form.

We are indebted for our first knowledge of
this acid to Dr. Black, before whose time its
property of remaining always in the state of
gas had made it to elude the researches of
chemistry.

It would be a most valuable discovery to so-
ciety if we could decompose this gas by any
cheap process, as by that means we might ob-
tain, for economical purposes, the immense
store of charcoal contained in calcareous earths,
marbles, limestones, &c. This cannot be ef-
fected by single affinity, because to decompose
the carbonic acid it requires a substance as

TABLE of the Combinations of Oxygenated

Muriatic Acid with the Salifiable Bases,

in the Order of Affinity

Names of the Bases Neutral Salts, New Names
Barytes Oxygenated muriate of barytes

Potash potash

Soda soda

Lime lime

Magnesia magnesia

Argill argill

Oxide of zinc zinc

iron iron

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

mercury

silver

gold

platinum

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

mercury

silver

gold

platinum

This order of salts, entirely unknown to the an-
cient chemists, was discovered in 1786 by M. Ber-
thollet. AUTHOR.

Names of the

Bases New Names

Barytes Muriate of barytes

Potash

Soda
Lime

Magnesia
Ammonia
Argill

Oxide of zinc
iron

manganese
cobalt
nickel

lead

potash

soda
lime

magnesia
ammonia
argill

zinc

iron

manganese

cobalt

nickel

lead

TABLE of the Combinations of Muriatic Acid with the
Salifiable Bases in the Order of Affinity

Resulting Neutral Salts

Old Names

Sea-salt, having base of
heavy earth

Febrifuge salt of Sylvius;
Muriated vegetable fixed
alkali
Sea-salt
Muriated lime
Oil of lime
Marine Epsom salt
Muriated magnesia
Sal ammoniac

Muriated alum, sea-salt with
base of earth of alum
Sea-salt of, or muriatic zinc
Salt of iron, Martial sea-salt
Sea-salt of manganese
Sea-salt of cobalt
Sea-salt of nickel
Horny-lead; plumbum
corneum

Smoking liquor of Libavius
Solid butter of tin
Sea-salt of copper
Sea-salt of bismuth
Sea-salt of antimony
Sea-salt of arsenic
Sweet sublimate of mercury,
calomel, aquila alba
Corrosive sublimate of
mercury

Horny silver, argentum

tin

1 smoking of tin
solid of tin

copper
bismuth

antimony

arsenic

mercury

silver

gold
platinum

sweet of mercury

corrosive of
mercury

silver

gold
platinum

corneum, luna cornea
Sea-salt of gold
Sea-salt of platinum

combustible as charcoal itself, so that we should
only make an exchange of one combustible
body for another not more valuable ; but it may
possibly be accomplished by double affinity,
since this process is so readily performed by
nature during vegetation from the most com-
mon materials.

SECTION XVIII

Observations upon Muriatic andOxygenatedMu-
riatic Acid and their Combinations with Sali-
fiable Bases

Muriatic acid is very abundant in the min-
eral kingdom naturally combined with differ-
ent salifiable bases, especially with soda, lime,
and magnesia. In sea-water, and the water of

several lakes, it is combined with these three
bases, and in mines of rock-salt it is chiefly
united to soda. This acid does not appear to
have been hitherto decomposed in any chem-
ical experiment; so that we have no idea what-
ever of the nature of its radical and only con-
clude from analogy with the other acids that it
contains oxygen as its acidifying principle. M.
Bertholiet suspects the radical to be of a me-
tallic nature; but, as nature appears to form
this acid daily in inhabited places by combin-
ing miasmata with aeriform fluids, this must
necessarily suppose a metallic gas to exist in
the atmosphere, which is certainly not impos-
sible but cannot be admitted without proof.

The muriatic acid has only a moderate ad-
herence to the salifiable bases and can readily

CHEMISTRY

be driven from its combination with these by
sulphuric acid. Other acids, as the nitric for
instance, may answer the same purpose; but
nitric acid being volatile would mix, during
distillation, with the muriatic. About one part
of sulphuric acid is sufficient to decompose two
parts of decrepitated sea-salt. This operation
is performed in a tubulated retort, having
WouhVs apparatus, (Plate iv, Fig. 1), adapted
to it. When ail the junctures are properly luted,
the sea-salt is put into the retort through the
tube, the sulphuric acid is poured on, and the
opening immediately closed with its ground
crystal stopper. As the muriatic acid can only
subsist in the gaseous form in the ordinary
temperature, we could not condense it without
the presence of water. Hence the use of the
water with which the bottles in Woulfe's ap-
paratus are half filled; the muriatic acid gas,
driven off from the sea-salt in the retort, com-
bines with the water and forms what the old
chemists called smoking spirit of salt, or Glau-
ber's spirit of sea-salt, which we now name
muriatic acid.

TABLE of the Combinations of Nitro- Muriatic

Acid with the Salifiable Bases in the Order

of Affinity so Far as is Known

Names of the Bases Names of the Neutral Salts
Argill Nitro-muriate of argill

Ammonia ammonia

Oxide of antimony antimony

silver silver

arsenic
Barytes

Oxide of bismuth
Lime
Oxide of cobalt

copper

tin

iron

Magnesia
Oxide of manganese

mercury

molybdenum

nickel

gold

platinum

lead
Potash ,
Soda
Oxide of tungsten

zinc

arsenic

barytes

bismuth

lime

cobalt

copper

tin

iron

magnesia

manganese

mercury

molybdenum

nickel

gold

platinum

lead

potash

soda

tungsten

zinc

Note. Most of these combinations, especially
those with the earths and alkalies, have been little
examined, and we are yet to learn whether they
form a mixed salt in which the compound radical
remains combined, or if the two acids separate to
form two distinct neutral salts. AUTHOR.

The acid obtained by the above process is
still capable of combining with a further dose
of oxygen, by being distilled from the oxides of
manganese, lead, or mercury, and the resulting
acid, which we name oxygenated muriatic acid,
can only, like the former, exist in the gaseous
form and is absorbed in a much smaller quan-
tity by water. When the impregnation of water
with this gas is pushed beyond a certain point,
the superabundant acid precipitates to the
bottom of the vessels in a concrete form. M.
Berthollet has shown that this acid is capable
of combining with a great number of the sal-
ifiable bases; the neutral salts which result
from this union are susceptible of deflagrating
with charcoal and many of the metallic sub-
stances; these deflagrations are very violent
and dangerous, owing to the great quantity of
caloric which the oxygen carries alongst with
it into the composition of oxygenated muriatic
acid.

SECTION XIX

Observations upon Nitro-Muriatic Acid and its
Combinations with Salifiable Bases

The nitro-muriatic acid, formerly called aqua
regia, is formed by a mixture of nitric and mu-
riatic acids; the radicals of these two acids
combine together and form a compound base,
from which an acid is produced, having prop-
erties peculiar to itself and distinct from those
of all other acids, especially the .property of
dissolving gold and platinum.

In dissolutions of metals in this acid, as in
all other acids, the metals are first oxidated by
attracting a part of the oxygen from the com-
pound radical. This occasions a disengagement
of a particular species of gas not hitherto de-
scribed, which may be called nitro-muriqtic gas;
it has a very disagreeable smell and is fatal to
animal life when respired; it attacks iron and
causes it to rust; it is absorbed in considerable
quantity by water, wh ich thereby acquires some
slight characters of acidity. Ihad occasion tb
make these remarks during a course of experi-
ments upon platinum, in which I dissolved a
considerable quantity of that metal iri nitro-
muriatic acid.

I at first suspected that in the mixture of ni-
tric and muriatic acids the' latter attracted a
part of the oxygen from the former and became
converted into oxygenated muriatic acid, whifch
gave it the property of dissolving gold; but
several facts remain inexplicable upon this sup*-
position. Were it sb, we must be able to diseri-

LAVOISIER '

gage nitrous gas by heating this acid, which
however does not 'sensibly happen. From these
considerations, I am led to adopt the opinion
of M. Berthollet and to consider nitro-muri-
atic acid as a single acid, with a compound
base or radical.

TABLE of the Combinations of Fluoric Acid
with the Salifiable Bases, in the Order
. of Affinity

Names of the Bases

Names of the Neutral Salts

Lime

Flu at of lime

Barytes

barytes

Magnesia

magnesia

Potash , ,

potash

Soda

soda

Ammonia

ammonia

Oxide of zinc

zinc

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic

bismuth

mercury

silver

gold

platinum

And by -the dry way,

Argill

Fluat of argill

Note. These combinations were entirely unknown
to the old chemists, and consequently have no names
in the old nomenclature. AUTHOR.

SECTION XX

Observations upon the Fluoric Acid and its
Combinations with Salifiable Bases

Fluoric exists ready formed b}' nature in the
fluoric spars, combined with calcareous earth
so a,s to form an insoluble neutral salt. To ob-
tain it disengaged froin that combination, fluor
spar, or fluat of lime,: is put into a leaden re-
tort, with a proper quantity of sulphuric acid;
a recipient likewise of lead, half full of water, is
adapted, and fire is applied to the retort. The
sulphuric acid, from its greater affinity, expels
the fluoric acid which passes over and is ab-
sorlpedvby the water in, the receiver. As fluoric
acid is naturally, in the gaseous form in the or-
dinary temperature, w,e caja receive it in a pneu-
rnato-chemical apparatus over mercury. We
are obliged, to, employ metallic vessels in this
process, beqause fluoric acid dissolves glass and

silicious earth and even renders these bodies
volatile, carrying them over with itself in dis-
tillation in the gaseous form.

We are indebted to M. Margraff for our
first acquaintance with this acid, though, as he
could never procure it free from combination
with a considerable quantity of silicious earth,
he was ignorant of its being an acid sui generis.
The Duke de Liancourt, under the name of M.
Boulanger, considerably increased our knowl-
edge of its properties; and M. Scheele seems
to have exhausted the subject. The only thing
remaining is to endeavour to discover the na-
ture of the fluoric radical, of which we cannot
form any ideas as the acid does not appear to
have been decomposed in any experiment. It is
only by means of compound affinity that ex-
periments can be made with this view with any
probability of success.

TABLE of the Combinations of Boracic Acid

with the Salifiable Bases, in the Order

of Affinity

Bases

Lime

Barytes

Magnesia

Potash

Soda

Ammonia

Oxide of zinc
iron
lead
tin

cobalt
copper
nickel
mercury

Argill

Neutral Salts
Borate of lime

barytes

magnesia

potash

soda

ammonia

zinc

iron

lead

tin

cobalt

copper

nickel

mercury

argill

Note. Most of these combinations were neither
known nor named by the old chemists. The boracic
acid was formerly called sedative salt and its com-
pounds borax, with base of fixed vegetable alkali,
<fcc. AUTHOR.

SECTION XXI

Observations upon Boracic Acid and its Com-
binations with Salifiable Bases

This is a concrete acid extracted from a salt
procured from India called borax or tincall. Al-
though borax has been very long employed in
the arts, we have as yet very imperfect knowl-
edge of its origin and of the methods by which
it is extracted and purified; there is reason to
believe it to be a native salt, found in the earth
in certain parts of the east and in the water of
some lakes. The whole trade of borax is in the

CHEMISTRY

hands of the Dutch, who have been exclusive-
ly possessed of the art of purifying it till very
lately when MM. L/Eguillier of Paris have
rivalled them in the manufacture ; but the proc-
ess still remains a secret to the world.

By chemical analysis we learn that borax is
a neutral salt with excess of base, consisting of
soda, partly saturated with a peculiar acid
long called Homberg's sedative salt, now the bo-
ratio acid. This acid is found in an uncombined
state in the waters of certain lakes. That of
Cherchiaio in Italy contains 94}^ grains in
each pint of water.

To obtain boracic acid, dissolve some borax
in boiling water, filtrate the solution, and add
sulphuric acid, or any other having greater af-
finity to soda than the boracic acid ; this latter
acid is separated and is procured in a crystal-
line form by cooling. This acid was long con-
sidered as being formed during the process by
which it is obtained and was consequently sup-
posed to differ according to the nature of the
acid employed in separating it from the soda;
but it is now universally acknowledged that it
is identically the same acid, in whatever way
procured, provided it be properly purified from
mixture of other acids by washing and by re-

TABLE of the Combinations of Arseniac Acid

with the Salifiable Bases, in the Order

of Affinity

Bases

Neutral Salts

Lime

Arseniate of lime

Barytes

barytes

Magnesia

magnesia

Potash

potash

Soda

soda

Ammonia

ammonia

Oxide of zinc

zinc

manganese

iron

lead

tin

cobalt

copper

nickel

bismuth

mercury

antimony

silver

gold

platinum

Argill

argill

Note. This order of salts was entirely unknown
to the ancient chemists. M. Macquer, in 1746, dis-
covered the combinations of arseniac acid with
potash and soda, to which he gave the name of
arsenical neutral salts. AUTHOR.

peated solution and crystallization. It is solu-
ble both in water and alcohol anfl has the prop-
erty of communicating a greefl colour to ttye
flame of that spirit. This circumstance, led to a
suspicion of its containing copper, which is not
confirmed by any decisive experiment. On the
contrary, if it contain any of that metal, it
must only be considered as an accidental mix-
ture. It combines with the saiifiable bases in
the humid way; and, though, in this manner, it
is incapable of dissolving any of the metals di-
rectly, this combination is readily effected by
compound affinity.

The table presents its combinations in the
order of affinity in the humid way; but there is
a considerable change in the order when we
operate via sicca; for, in that case, argill, though
the last in our list, must be placed immediately
after soda. r

The boracic radical is hitherto unknown; no
experiments having as yet been able to decom-
pose the acid ; we conclude, from analogy with
the other acids, that oxygen exists in its com-
position as the acidifying principle.

SECTION XXII

Observations upon Arseniac Acid and its Com-
binations with Salifiable Bases

In the Recueil de I'Acadtmie for 1746, M.
Macquer shows that when a mixture of white
oxide of arsenic and nitre are subjected to the
action of a strong fire a neutral salt is obtained,
which he calls neutral salt of arsenic. At that
time, the cause of this singular phenomenon,
in which a metal acts the part of an acid, was
quite unknown; but more modern experiments
teach that during this process the arsenic be-
comes oxygenated, by carrying off the oxygen
of the nitric acid; it is thus converted into a
real acid and combines with the potash. There
are other methods now known for oxygenating
arsenic and obtaining its acid free from com-
bination, The most simple and most effectual
of these is as follows: dissolve white oxide of
arsenic in three parts, by weight, of muriatic
acid; to this solution, in a boiling state, add
two parts of nitric acid and evaporate to dry-
ness. In this process the nitric acid is decom-
posed, its, oxygen unites with the oxide of ar-
senic and converts it into an acid, and the ni-
trous radical flies off in the state of nitrous gas;
whilst the muriatic acid is converted by the
heat into muriatic acid gas and may be col-
lected in proper vessels. The arseniac acid is

LAVOISIER

entirely fre$$ from the other acids employed
during the process by heating it in a crucible
till it begins to grow red; what remains is pure
concrete arseniac acid.

M. Scheele's process, which was repeated
with great success by M. Morveau in the lab-
oratory at Dijon, is as follows: distil muriatic
acid from the black oxide of manganese; this
converts it into oxygenated muriatic acid; by
carrying off the oxygen from the manganese;
receive this in a recipient containing white
oxide of arsenic, covered by a little distilled
water; the arsenic decomposes the oxygenated
muriatic acid by carrying off its supersatura-
tion of oxygen ; the arsenic is converted into ar-
seniac acid, and the oxygenated muriatic acid
is brought back to the state of common muri-
atic acid. The two acids are separated by dis-
tillation, with a gentle heat increased towards
the end of the operation; the muriatic acid
passes over and the arseniac acid remains be-
hind in a white concrete form.

The arseniac acid is considerably less vola-
tile than white oxide of arsenic; it often con-
tains white oxide of arsenic in solution, owing
to its not being sufficiently oxygenated; this is
prevented by continuing to add nitrous acid,
as in the former process, till no more nitrous
gas is produced. From ail these observations I
would give the following definition of arseniac
acid . It is a white concrete metallic acid, formed
by the combination of arsenic with oxygen,
fixed in a red heat, soluble in water, and ca-
pable of combining with many of the salifiable

SECTION XXIII

Observations upon Molybdic Acid and its Com*
binations with Salifiable Bases

Molybdenum is a particular metallic body,
capable of being oxygenated so far as to be-
come a true concrete acid. 1 For this purpose,
one part ore of molybdenum, which is a natural
sulphuret of that metal, is put into a retort
with five or six parts nitric acid, diluted with a
quarter of its weight of wafer, and heat is ap-
plied to the retort; the oxygen of the nitric acid
acts both upon the molybdenum and the sul-
phur, converting the one into molybdic and
the other into sulphuric acid; pour on fresh
Quantities of nitric acid so long as any red
fumes of nitrous gas escape; the molybdenum

This acid was discovered by M. J Scheele, to
whom chemistry is indebted for the discovery of
several other acids.

is then oxygenated as far as is possible and is
found at the bottom of the retort in a pulveru-
lent form, resembling chalk. It must be washed
in warm water, to separate any adhering parti-
cles of sulphuric acid; and, as it is hardly sol-
uble, we lose very little of it in this operation.
All its combinations with salifiable bases were
unknown to the ancient chemists.

TABLE of the Combinations of Tungstic Acid
with the Salifiable Bases

Bases
Lime
Barytes
Magnesia
Potash
Soda
Ammonia
Argill
Oxide of antimony,

Neutral Salts
Tungstate of lime
barytes
magnesia
potash
soda
ammonia
argill
&c. antimony, &c. 2

SECTION XXIV

Observations upon Tungstic Acid and its Com-
binations with Salifiable Bases

Tungsten is a particular metal, the ore of
which has frequently been confounded with
that of tin. The specific gravity of this ore is to
water as 6 to 1 ; in its form of crystallization it
resembles the garnet and varies in colour from
a pearl-white to yellow and reddish ; it is found
in several parts of Saxony and Bohemia. The
mineral called wolfram, which is frequent in
the mines of Cornwall, is likewise an ore of
this metal. In all these ores the metal is oxi-
dated; and, in some of them, it appears even
to be oxygenated to the state of acid, being
combined with lime into a true tungstate of
lime.

To obtain the acid free, mix one part of ore
of tungsten with four parts of carbonate of pot-
ash and melt the mixture in a crucible; then
powder and pour on twelve parts of boiling wa-
ter, add nitric acid, and the tungstic acid pre-
cipitates in a concrete form. Afterwards, to in-
sure the complete oxygenation of the metal,
add more nitric acid and evaporate to dryness,
repeating this operation so long as red fumes of
nitrous gas are produced. To procure tungstic
acid perfectly pure, the fusion of the ore with
carbonate of potash must be made in a crucible
of platinum, otherwise the earth of the com-

'All these salts were unknown to the ancient
chemists. AUTHOR.

CHEMISTRY

mon crucibles will mix with the products and
adulterate the acid.

TABLE of the Combinations of Tartarous Acid

with the Salifiable Bases, in the Order

of Affinity

Bases

Neutral Salts

Lime

Tartarite of lime

Barytes

barytes

Magnesia

magnesia

Potash

potash

Soda

soda

Ammonia

ammonia

Argill

argill

Oxide of zinc

zinc

iron

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

silver

mercury

gold

platinum

SECTION XXV

Observations upon Tartarous Add and its Com-
binations with Salifiable Bases

Tartar, or the concretion which fixes to the
inside of vessels in which the fermentation of
wine is completed, is a well known salt, com-
posed of a peculiar acid united in considerable
excess to potash. M. Scheele first pointed out
the method of obtaining this acid pure. Having
observed that it has a greater affinity to lime
than to potash, he directs us to proceed in the
following manner. Dissolve purified tartar in
boiling water and add a sufficient quantity of
lime till the acid be completely saturated. The
tartarite of lime which is formed, being almost
insoluble in cold water, falls to the bottom and
is separated from the solution of potash by de-
cantation; it is afterwards washed in cold wa-
ter and dried ; then pour on some sulphuric acid,
diluted with eight or nine parts of water, digest
for twelve hours in a gentle heat, frequently
stirring the mixture; the sulphuric acid com-
bines with the lime, and the tartarous acid is
left free. A small quantity of gas, not yet ex-
amined, is disengaged during this process. At

the end of twelve hours, having decanted off
the clear liquor, wash the sulphate of lime in
cold water, which add to the decanted liquor,
then evaporate the whole, and the tartarous
acid is obtained in a concrete form. Two pounds
of purified tartar, by means of from eight to
ten ounces of sulphuric acid, yield about elev-
en ounces of tartarous acid.

As the combustible radical exists in excess,
or as the acid from tartar is not fully saturated
with oxygen, we call it tartarous acid, and the
neutral salts formed by its combinations with
Salifiable bases tartarites. The base of the tar-
tarous acid is a carbono-hydrous or hydro-car-
bonous radical, less oxygenated than in the ox-
alic acid; and it would appear, from the exper-
iments of M. Hassenfratz, that azote enters
into the composition of the tartarous radical
even in considerable quantity. By oxygenating
the tartarous acid, it is convertible into oxalic,
malic, and acetous acids ; but it is probable the
proportions of hydrogen and charcoal in the
radical are changed during these conversions,
and that the difference between these acids
does not alone consist in the different degrees
of oxygenation.

The tartarous acid is susceptible of two de-
grees of saturation in its combinations with the
fixed alkalies; by one of these a salt is formed
with excess of acid, improperly called cream of
tartar, which in our new nomenclature is named
acidulous tartarite of potash; by a second or
equal degree of saturation a perfectly neutral
salt is formed, formerly called vegetable salt,
which we name tartarite of potash. With soda
this acid forms tartarite of soda, formerly called
sal de Seignette, or sal polychrest of RochelL

SECTION XXVI

Observations upon Malic Acid and its Combinor
tions with Salifiable Bases

The malic acid exists ready formed in the
sour juice of ripe and unripe apples, and many
other fruits, and is obtained as follows: satu-
rate the juice of apples with potash or soda and
add a proper proportion of acetite of lead dis-
solved in water; a double decomposition takes
place; the malic acid combines with the oxide
of lead and precipitates, being almost insolu-
ble, and the acetite of potash or soda remains
in the liquor. The malate of lead being separat-
ed by decantation is washed with cold water,
and some dilute sulphuric acid is added; this

LAVOISIER

unites with the lead into an insoluble sul-
phate and the malic acid remains free in the
liquor.

This acid, which is found mixed with citric
and tartarous acid in a great number of fruits,
is a kind of medium between oxalic and
acetous acids, being more oxygenated than the
former and less so than the latter. From this
circumstance, M. Hermbstadt calls it imper-
fect vinegar; but it differs likewise from ace-
tous acid, by having rather more charcoal
and less hydrogen in the composition of its
radical.

When an acid much diluted has been used in
the foregoing process, the liquor contains oxalic
as well as malic acid and probably a little tar-
tarous; these are separated by mixing lime-
water with the acids, oxalate, tartarite, and
malate of lime are produced; the two former,

TABLE of the Combinations of Citric Acid

with the Salifiable Bases, in the Order

of Affinity 1

Bases
Barytes
Lime
Magnesia
Potash
Soda
Ammonia
Oxide of zinc

manganese

iron

lead

cobalt

copper

arsenic

mercury

antimony

silver

gold

platinum

Neutral Salts
Citrate of barytes
lime

magnesia
potash
soda

ammonia
zinc

manganese
iron
lead
cobalt
copper
arsenic
mercury
antimony
silver
gold

platinum
argill

Argill

being insoluble, are precipitated, and the
malate of lime remains dissolved; from this the
pure malic acid is separated by the acetite of
lead and afterwards by sulphuric acid, as direct-
ed above.

SECTION XXVII

Observations upon Citric Acid and its Combina-
tions with Salifiable Bases

The citric acid is procured by expression
from lemons and is found in the juices of many

1 These combinations were unknown to the ancient
chemists. The order of affinity of the salifiable bases
with this acid was determined by M. Bergman and
by M. de Breney of the Dijon Academy. AUTHOR.

other fruits mixed with malic acid. To obtain
it pure and concentrated, it is first allowed to
depurate from the mucous part of the fruit by
long rest in a cool cellar, and is afterwards
concentrated by exposing it to the temperature
of 4 or 5 degrees below zero, from 21 to 23
of Fahrenheit; the water is frozen, and the

TABLE of the Combinations of Pyro-lignous

Acid with the Salifiable Bases, in the Order

of Affinity*

Bases Neutral Salts

Lime Pyro-mucite
Barytes
Potash
Soda

of lime
barytes
potash
soda

Magnesia
Ammonia

magnesia
ammonia

Oxide of zinc

zinc

manganese

iron

lead

tin

cobalt

copper
nickel

arsenic

bismuth

mercury

antimony
silver

gold
platinum

Argill

argill

acid remains liquid, reduced to about an eighth
part of its original bulk. A lower degree of
cold would occasion the acid to be engaged
amongst the ice, and render it difficultly separ-
able. This process was pointed out by M.
Georgius.

It is more easily obtained by saturating the
lemon-juice with lime, so as to form a citrate
of lime which is insoluble in water; wash this
salt and pour on a proper quantity of sulphuric
acid; this forms a sulphate of lime, which pre-
cipitates and leaves the citric acid free in the
liquor.

SECTION XXVIII

Observations upon Pyro-lignous Acid and its
Combinations with Salifiable Bases

The ancient chemists observed that most of
the woods, especially the more heavy and com-
pact ones, gave out a particular acid spirit, by
distillation, in a naked fire; but, before M.

* The above affinities were determined by MM.
de Mprveau and Elos Bourfier de Clervaux. These
combinations were entirely unknown till lately.
AUTHOR.

CHEMISTRY

Goetling, who gives an account of his experi-
ments upon this subject in Creli's Chemical
Journal for 1779, no one had ever made any
inquiry into its nature and properties. This
acid appears to be the same, whatever be the
wood it is procured from. When first distilled,
it is of a brown colour and considerably im-
pregnated with charcoal and oil; it is purified
from these by a second distillation. The pyro-
lignous radical is chiefly composed of hydrogen
and charcoal.

SECTION XXIX

Observations upon Pyro-tartarous Add and its
Combinations with Salifiable Bases

The name of Pyro-tartarous acid is given to a
dilute empyreumatic acid obtained from puri-
fied acidulous tartarite of potash by distilla-
tion in a naked fire. To obtain it, let a retort be
half filled with powdered tartar, adapt a tubu-
lated recipient, having a bent tube communi-
cating with a bell-glass in a pneumato-chemical
apparatus; by gradually raising the fire under
the retort, we obtain the pyro-tartarous acid
mixed with oil, which is separated by means of
a funnel. A vast quantity of carbonic acid gas
is disengaged during the distillation. The acid
obtained by the above process is much contam-
inated with oil, which ought to be separated
from it. Some authors advise to do this by a
second distillation; but the Dijon academicians
inform us that this is attended with great dan-

TABLE of the Combinations of Pyro-mucous

Add, with the Salifiable Bases, in the Order

of Affinity 1

Bases
Potash
Soda
Barytes
Lime
Magnesia
Ammonia
Argill
Oxide of zinc

Neutral Salts
Pyro-mucite of potash
soda
barytes
lime

magnesia
ammonia
argill
zinc

manganese

iron

lead

tin

cobalt

copper

nickel

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic arsenic

bismuth bismuth

antimony antimony

iAll these combinations were unknown to the
ancient chemists. AUTHOR.

ger from explosions which take place during
the process.

SECTION XXX

Observations upon Pyro-mucous Add and its
Combinations with Salifiable Bases

This acid is obtained by distillation in a na-
ked fire from sugar and all the saccharine bod-
ies; and, as these substances swell greatly in
the fire, it is necessary to leave seven-eighths
of the retort empty. It is of a yellow colour,
verging to red, and leaves a mark upon the
skin which will not remove but alongst with
the epidermis. It may be procured less coloured,
by means of a second distillation, and is con-
centrated by freezing, as is directed for the
citric acid. It is chiefly composed of water and
oil slightly oxygenated and is convertible into
oxalic and malic acids by farther oxygenation
with the nitric acid.

It has been pretended that a large quantity
of gas is disengaged during the distillation of
this acid, which is not the case if it be conduct-
ed slowly by means of moderate heat.

SECTION XXXI

Observations upon Oxalic Add and its Combi-
nations with Salifiable Bases

The oxalic acid is mostly prepared in Swit-
zerland and Germany from the expressed juice

TABLE of the Combinations of the Oxalic Acid,

with the Salifiable Bases, in the Order

of Affinity 2

Bases Neutral Salts

Lime Oxalate of lime

Barytes barytes

Magnesia magnesia

Potash potash

Soda soda

Ammonia ammonia

Argill argill

Oxide of zinc zinc

iron iron

manganese manganese

cobalt cobalt

nickel nickel

lead lead

copper copper

bismuth bismuth

antimony antimony

arsenic arsenic

mercury mercury

silver silver

gold gold

platinum platinum
* All unknown to the ancient chemists. AUTHOR.

LAVOISIER

of sorrel, from which it crystallizes by being
left long at rest; in this state it is partly sat-
urated with potash, forming a true acidulous
oxalate of potash, or salt with excess of acid. To
obtain it pure, it must be formed artificially by
oxygenating sugar, which seems to be the true
oxalic radical. Upon one part of sugar pour six
or eight parts of nitric acid and apply a gentle
heat; a considerable effervescence takes place,
and a great quantity of nitrous gas is disen-
gaged; the nitric acid is decomposed, and its
oxygen unites to the sugar. By allowing the
liquor to stand at rest, crystals of pure oxalic
acid are formed, which must be dried upon

blotting paper to separate any remaining por-
tions of nitric acid; and, to ensure the purity of
the acid, dissolve the crystals in distilled water
and crystallize them afresh.

From the liquor remaining after the first
crystallization of the oxalic acid we may obtain
malic acid by refrigeration. This acid is more
oxygenated than the oxalic; and, by a further
oxygenation, the sugar is convertible into ace-
tous acid, or vinegar.

The oxalic acid, combined with a small quan-
tity of soda or potash, has the property, like
the tartarous acid, of entering into a number
of combinations without suffering decomposi-

TABLE of the Combinations of Acetous Acid with the Salifiable Bases
in the Order of Affinity

Barytes

Potash

Soda

Lime

Magnesia
Ammonia

Oxide of zinc

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic

Neutral Salts
Acetite of barytes

potash

soda

lime

magnesia
ammonia

zinc

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic

bismuth Acetite of bismuth

mercury

antimony
silver

gold
platinum

Argill

mercury

antimony
silver

gold

platinum

argill

Names of the Resulting Neutral Salts
According to the Old Names

Unknown to the ancients. Discovered by
M. de Morveau, who calls it barotic acte.

Secret terra foliata tartari of Muller. Arcanum
tartari of Basil Valentin and Paracelsus.
Purgative magistery of tartar of Schroeder.
Essential salt of wine of Zwelfer. Regenerated
tartar of Tachonius. Diuretic salt of Sylvius
and Wilson.

Foliated earth with base of mineral alkali'
Mineral or crystallizable foliated earth. Min-
eral acetous salt.

Salt of chalk, coral, or crabs eyes; mentioned
by Hartman.

First mentioned by M. Wonzel.
Spiritus Minder eri. Ammoniacal acetous salt-
Known to Glauber, Schwedemberg, Respour,
Pott, de Lassone, and Wenzel, but not named.
Unknown to the ancients.
Martial vinegar. Described by Monnet, Wen-
zel, and the Duke d'Ayen.
Sugar, vinegar, and salt of lead or Saturn.
Known to Lemery, Margraff, Monnet, Wes-
lendorf, and Wenzel, but not named.
Sympathetic ink of M. Cadet.
Verdigris, crystals of verditer, verditer, dis-
tilled verdigris, crystals of Venus or of copper.
Unknown to the ancients.
Arsenico-acetous fuming liquor, liquid phos-
phorus of M. Cadet.

Sugar of bismuth of M. Geoffroy. Known to
Gellert, Pott, Weslendorf, Bergman, and de
Morveau.

Mercurial foliated earth, Keyser's famous
antivenereal remedy. Mentioned by Gebaver
in 1748; known to Helot, Margraff, Baume,
Bergman, and de Morveau.

Unknown.

Described by Margraff, Monnet, and Wenzel;

unknown to the ancients.

Little known, mentioned by SchroSder and

Juncker.

Unknown.

According to M. Wenzel, vinegar dissolves

only a very small proportion of argill.

CHEMISTRY

tion. These combinations form triple salts, or
neutral salts with double bases, which ought to
have proper names. The salt of sorrel, which is
potash having oxalic acid combined in excess,
is named acidulous oxalate of potash in our
new nomenclature.

The acid procured from sorrel has been known
to chemists for more than a century, being
mentioned by M. Duclos in the Recueil de
I' Academic for 1688, and was pretty accurately
described by Boerhaave; but M. Scheele first
showed that it contained potash and demon-
strated its identity with the acid formed by the
oxygenation of sugar.

SECTION XXXII

Observations upon Acetous Acid and its Com-
binations with Salifidble Bases

This acid is composed of charcoal and hydro-
gen united together and brought to the state of
an acid by the addition of oxygen; it is conse-
quently formed by the same elements with the
tartarous oxalic, citric, malic acids, and others,
but the elements exist in different proportions
in each of these; and it would appear that the
acetous acid is in a higher state of oxygenation
than these other acids. I have some reason to
believe that the acetous radical contains a
small portion of azote; and, as this element is
not contained in the radicals of any vegetable
acid except the tartarous, this circumstance is
one of the causes of difference. The acetous acid,
or vinegar, is produced by exposing wine to a
gentle heat, with the addition of some ferment:
this is usually the dregs, or mother, which have
separated from other vinegar during fermenta-
tion, or some similar matter. The spiritous part
of the wine, which consists of charcoal and
hydrogen, is oxygenated and converted into
vinegar. This operation can only take place
with free access of air and is always attended
by a diminution of the air employed in conse-
quence of the absorption of oxygen; wherefore,
it ought always to be carried on in vessels only
half filled with the vinous liquor submitted to
the acetous fermentation. The acid formed dur-
ing this process is very volatile, is mixed with a
large proportion of water and with many foreign
substances; and, to obtain it pure, it is distilled
in stone or glass vessels by a gentle fire. The acid
which passes over in distillation is somewhat
changed by the process, and is not exactly of the
same nature with what remains in the alembic,
but seems less oxygenated. This circumstance
has not been formerly observed by chemists.

Distillation is not sufficient for depriving
this acid of all its unnecessary water; an<dj for
this purpose, the best way is by exposing it to a
degree of cold from 4 to 6 below the freezing
point, from 19 to 23 of Fahrenheit; by this
means the aqueous part becomes frozen and
leaves the acid in a liquid state and consider-
ably concentrated. In the usual temperature of
the air, this acid can only exist in the gaseous
form and can only be retained by combination
with a large proportion of water. There are
other chemical processes for obtaining the ace-
tous acid, which consist in oxygenating the
tartarous, oxalic, or malic acids, by means of
nitric acid; but there is reason to believe the
proportions of the elements of the radical are
changed during this process. M. Hassenfratz
is at present engaged in repeating the experi-
ments by which these conversions are said to
be produced.

The combinations of acetous acid with the
various salifiable bases are very readily formed ;
but most of the resulting neutral salts are not
crystallizable, whereas those produced by the
tartarous and oxalic acids are, in general, hard-
ly soluble. Tartarite and oxalate of lime are
not soluble in any sensible degree. The malates
are a medium between the oxalates and ace-

TABLE of the Combinations of Acetic Acid with
the Salifiable Bases, in the Order of Affinity

Bases Neutral Salts
Barytes Acetate of barytes

Potash potash

Soda soda

Lime lime

Magnesia magnesia

Ammonia ammonia

Oxide of zinc zinc

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic

bismuth

manganese

iron

lead

tin

cobalt

copper

nickel

arsenic

bismuth

mercury mercury

antimony antimony

silver silver

gold gold

platinum platinum

Argill argill

Note. All these salts were unknown to the an-
cients; and even those chemists who are most vers-
ant in modern discoveries, are yet at a loss whether
the greater part of the salts produced by the oxygen-
ated aoetio radical belong properly to the class of
acetites, or to that of acetates. AUTHOR.

LAVOISIER

tites, with respect to solubility, and the malic
acid is in the middle degree of saturation be-
tween the oxalic and acetous acids. With this,
as with all the acids, the metals require to be
oxidated previous to solution.

The ancient chemists knew hardly any of
the salts formed by the combinations of ace-
tous acid with the salifiable bases, except the
acetites of potash, soda, ammonia, copper, and
lead. M. Cadet discovered the acetite of ar-
senic; 1 M. Wenzel, the Dijon academicians,
M. de Lassone, and M. Proust, made us ac-
quainted with the properties of the other ace-
tites. From the property which acetite of pot-
ash possesses, of giving out ammonia in distil-
lation, there is some reason to suppose that,
besides charcoal and hydrogen, the acetous
radical contains a small proportion of azote,
though it is not impossible but the above pro-
duction of ammonia may be occasioned by the
decomposition of the potash.

SECTION XXXIII

Observations upon Acetic Acid and its Combina-
tions with Salifiable Bases

We have given to radical vinegar the name
of acetic acid, from supposing that it consists

TABLE of the Combinations of Succinic Acid

with the Salifiable Bases, in the Order

of Affinity

Bases

Neutral Salts

Barytes Succinate
Lime

of barytes
lime

Potash
Soda

potash
soda

Ammonia

ammonia

Magnesia
Argill
Oxide of zinc

magnesia
argill
zinc

iron

manganese
cobalt

nickel

lead

tin

copper
bismuth

antimony

arsenic

mercury
silver

gold
platinum

Note. All the succinates were unknown to the
ancient chemists. AUTHOR.
i Savans Etrangers, Vol. III.

of the same radical with that of the acetous
acid but more highly saturated with oxygen.
According to this idea, acetic acid is the highest
degree of oxygenation of which the hydro-car-
bonous radical is susceptible; but, although
this circumstance be extremely probable, it re-
quires to be confirmed by further and more de-
cisive experiments, before it be adopted as an
absolute chemical truth. We procure this acid
as follows: upon three parts acetite of potash
or of copper pour one part of concentrated sul-
phuric acid, and, by distillation, a very highly
concentrated vinegar is obtained, which we call
acetic acidj formerly named radical vinegar. It
is not rigorously proved that this acid is more
highly oxygenated than the acetous acid, nor
that the difference between them may not con-
sist in a different proportion between the ele-
ments of the radical or base.

SECTION XXXIV

Observations upon Succinic Acid and its Com-
binations with Salifiable Bases

The succinic acid is drawn from amber by
sublimation in a gentle heat and rises in a con-
crete form into the neck of the subliming ves-
sel. The operation must not be pushed too far,
or by too strong a fire, otherwise the oil of the
amber rises alongst with the acid. The salt is
dried upon blotting paper and purified by re-
peated solution and crystallization.

This acid is soluble in twenty-four times its
weight of cold water and in a much smaller
quantity of hot water. It possesses the qual-
ities of an acid in a very small degree and only
affects the blue vegetable colours very slightly.
The affinities of this acid, with the salifiable
bases, are taken from M. de Morveau, who is
the first chemist that has endeavoured to as-
certain them.

SECTION XXXV

Observations upon Benzoic Acid and its Com-
binations with Salifiable Bases

This acid was known to the ancient chemists
under the name of Flowers of Benjamin, or of
Benzoin, and was procured, by sublimation,
from the gum or resin called Benzoin. The
means of procuring it, via humida, was discov-
ered by M. Geoffrey and perfected by M.
Scheele. Upon benzoin, reduced to powder,
pour strong lime-water, having rather an excess
of lime; keep the mixture continually stirring

CHEMISTRY

and, after half an hour's digestion, pour off the
liquor and use fresh portions of lime-water in
the same manner, so long as there is any ap-
pearance of neutralization. Join all the de-
canted liquors and evaporate, as far as possi-
ble, without occasioning crystallization, and,
when the liquor is cold, drop in muriatic acid till
no more precipitate is formed. By the former
part of the process a benzoate of lime is form-
ed, and by the latter the muriatic acid com-
bines with the lime, forming muriate of lime,
which remains dissolved, while the benzoic acid,
being insoluble, precipitates in a concrete state.

SECTION XXXVI

Observations upon Camphoric Acid and its Com-
binations with Salifiable Bases

Camphor is a concrete essential oil, obtained,
by sublimation from a species of laurus which
grows in China and Japan. By distilling nitric
acid eight times from camphor, M. Kosegar-
ten converted it into an acid analogous to the
oxalic; but, as it differs from that acid in some
circumstances, we have thought necessary to
give it a particular name till its nature be more
completely ascertained by farther experiment.

As camphor is a carbono-hydrous or hydro-
carbonous radical, it is easily conceived that,
by oxygenation, it should form oxalic, malic,
and several other vegetable acids. This conjec-
ture is rendered not improbable by the experi-
ments of M. Kosegarten; and the principal
phenomena exhibited in the combinations of
camphoric acid with the salifiable bases, being
very similar to those of the oxalic and malic
acids, lead me to believe that it consists of a
mixture of these two acids.

SECTION XXXVII

Observations upon Gallic Acid, and its Com-
binations with Salifiable Bases 1

The gallic acid, formerly called principle of
astringency, is obtained from gall nuts, either
by infusion or decoction with water, or by dis-
tillation with a very gentle heat. This acid has
only been attended to within these few years.
The Committee of the Dijon Academy have
followed it through all its combinations and
give the best account of it hitherto produced.

* Those combinations, which are called gallates,
were all unknown to the ancients; and the order of
their affinity is not established. AUTHOR.

Its acid properties are very weak; it reddens
the tincture of turnsole, decomposes sulphur-
ets, and unites to all the metals when they have
been previously dissolved in some other acid.
Iron, by this combination, is precipitated of a
very deep blue or violet colour. The radical of
this acid, if it deserves the name of one, is hith-
erto entirely unknown; it is contained in oak
willow, marsh iris, the strawberry, nymphea,
Peruvian bark, the flowers and bark of pome-
granate, and in many other woods and barks.

SECTION XXXVIII

Observations upon Lactic Acid and its Combina-
tions with Salifiable Bases 2

The only accurate knowledge we have of
this acid is from the works of M. Scheele. It is
contained in whey, united to a small quantity
of earth, and is obtained as follows: reduce
whey to one eighth part of its bulk by evapo-
ration and filtrate, to separate all its cheesy
matter; then add as much lime as is necessary
to combine with the acid; the lime is afterwards
disengaged by the addition of oxalic acid, which
combines with it into an insoluble neutral salt.
When the oxalate of lime has been separated by

TABLE of the Combinations of Saccho-lactic

Acid with the Salifiable Bases, in the Order

of Affinity

Neutral Salts

Lime Saccholate

of lime

Barytes
Magnesia
Potash
Soda

barytes
magnesia
potash
soda

Ammonia

ammonia

Argill
Oxide of zinc

argill
zinc

manganese

iron

lead

tin

cobalt

copper
nickel

arsenic

bismuth

mercury
antimony
silver

Note. All these were unknown to the ancient
chemists. AUTHOR.

* These combinations are called lactates; they were
all unknown to the ancient chemists and their affini-
ties have not yet been ascertained. AUTHOR.

LAVOISIER

decantation, evaporate the remaining liquor to
the consistence of honey; the lactic acid is dis-
solved by alcohol, which does not unite with
the sugar of milk and other foreign matters;
these are separated by filtration from the alco-
hol and acid ; and the alcohol being evaporated,
or distilled off, leaves the lactic acid behind.

This acid unites with all the salifiable bases,
forming salts which do not crystallize; and it
seems considerably to resemble the acetous
acid.

SECTION XXXIX

Observations upon Saccho-lactic Add and its
Combinations with Salifiable Bases

A species of sugar may be extracted, by evap-
oration, from whey, which has long been known
in pharmacy, and which has a considerable re-
semblance to that procured from sugar canes.
This saccharine matter, like ordinary sugar,
may be oxygenated by means of nitric acid.
For this purpose, several portions of nitric acid
are distilled from it; the remaining liquid is
evaporated and set to crystallize, by which
means crystals of oxalic acid are procured; at
the same time a very fine white powder precip-
itates, which is the saccho lactic acid discov-
ered by Scheele. It is susceptible of combining
with the alkalies, ammonia, the earths, and
even with the metals. Its action upon the latter
is hitherto but little known, except that, with
them, it forms difficultly soluble salts. The
order of affinity in the table is taken from
Bergman.

TABLE of Combinations of Formic Acid with
the Salifiable Bases, in the Order of Affinity

SECTION XL

Bases

Neutral Salts

Barytes

Formiate of barytes

Potash

potash

Soda

soda

Lime

lime

Magnesia

magnesia

Ammonia

ammonia

Oxide of zinc

zinc

manganese manganese

iron

lead

tin

cobalt

copper

nickel

bismuth

silver

Argill

argill

Observations upon Formic Acid and its Combi-
nations with Salifiable Bases

This acid was first obtained by distillation
from ants in the last century, by Samuel Fisher.
The subject was treated of by Margraff in 1749,
and by MM. Ardwisson and Ochrn of Leipzig
in 1777. The formic acid is drawn from a large
species of red ants, formica rufa, Lin., which
form large ant hills in woody places. It is pro-
cured either by distilling the ants with a gentle
heat in a glass retort or an alembic; or, after
having washed the ants in cold water and dried
them upon a cloth, by pouring on boiling water,
which dissolves the acid ; or the acid may be pro-
cured by gentle expression from the insects, in
which case it is stronger than in any of the form-
er ways. To obtain it pure, we must rectify, by
means of distillation, which separates it from
the uncombined oily and charry matter; and it
may be concentrated by freezing, in the man-
ner recommended for treating the acetous acid.

SECTION XLI

Observations upon Bombic Acid and its Com-
binations with Salifiable Bases 1

The juices of the silk worm seem to assume
an acid quality when that insect changes from

TABLE of the Combinations of the Sebacic Acid
with the Salifiable Bases, in the Order of Affinity

Bases

Neutral Salts

Barytes
Potash
Soda

Sebate of barytes
potash
soda

Lime

lime

Magnesia
Ammonia

magnesia
ammonia

Argill
Oxide of zinc

argill
zinc

manganese

iron

lead

tin

cobalt

copper
nickel

arsenic

bismuth

Note. All unknown to the ancient c hernia ts.-
AUTHOR.

mercury mercury

antimony antimony

silver silver

Note. All these were unknown to the ancient
chemists. AUTHOR.

1 These combinations named bombates were un-
known to the ancient chemists; and the affinities of
the salifiable bases with the bombic acid are unde-
termined . AUTHOR.

CHEMISTRY

a larva to a chrysalis. At the moment of its es-
cape from the latter to the butterfly form, it
emits a reddish liquor which reddens blue pa-
per, and which was first attentively observed
by M. Chaussier of the Dijon Academy, who
obtains the acid by infusing silk worm chrysa-
lids in alcohol, which dissolves their acid with-
out being charged with any of the gummy parts
of the insect; and, by evaporating the alcohol,
the acid remains tolerably pure. The proper-
ties and affinities of this acid are not hitherto
ascertained with any precision; and we have
reason to believe that analogous acids may be
procured from other insects. The radical of
this acid is probably, like that of the other
acids from the animal kingdom, composed of
charcoal, hydrogen, and azote, with the addi-
tion, perhaps, of phosphorus.

SECTION XLII

Observations upon Sebacic Acid and its Combi-
nations with Salijiable Bases

To obtain the sebacic acid, let some suet be
melted in a skillet over the fire, alongst with
some quicklime in fine powder, and constantly
stirred, raising the fire towards the end of the
operation, and taking care to avoid the vap-
ours, which are very offensive. By this process
the sebacic acid unites with the lime into a
sebate of lime, which is with difficulty soluble in
water; it is, however, separated from the fatty
matters with which it is mixed by solution in a
large quantity of boiling water. From this the
neutral salt is separated by evaporation; and,
to render it pure, is calcined, redissolved, and
again crystallized. After this we pour on a
proper quantity of sulphuric acid, and the se-
bacic acid passes over by distillation.

SECTION XLIII

Observations upon Lithic Acid and its Combina-
tions with Salifiable Bases 1

From the later experiments of Bergman and
Scheele, the urinary calculus appears to be a
species of salt with an earthy basis; it is slight-
ly acidulous, and requires a large quantity of
water for solution, three grains being scarcely
soluble in a thousand grains of boiling water,
and the greater part again crystallizes when
cold. To this concrete acid, which M. de Mor-
veau calls lithiasic acid, we give the name of

i All the combinations of this acid, should it final-
ly turn out to be one, were unknown to the ancient
chemists, and its affinities with the salifiable bases
have not been determined. AUTHOR.

lithic acid, the nature and properties of which
are as yet very little known. There is some ap-
pearance that it is an acidulous neutral salt, or
acid combined in excess with a salifiable base;
and I have reason to believe that it really is an
acidulous phosphate of lime; if so, it must be
excluded from the class of peculiar acids.

TABLE of the Combinations of the Prussic Acid

with the Salifiable Bases, in the Order

of Affinity

Bases
Potash
Soda

Ammonia
Lime
Barytes
Magnesia
Oxide of zinc

Neutral Salts
Prussiate of potash
soda

ammonia
lime
barytes
magnesia
zinc

iron

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

silver

mercury

gold

platinum

iron

manganese

cobalt

nickel

lead

tin

copper

bismuth

antimony

arsenic

silver

mercury

gold

platinum

Note. All these were unknown to former chem-
ists. AUTHOR.

SECTION XLIV

Observations upon the Prussic Acid and its Com-
binations with Salifiable Bases

As the experiments which have been made
hitherto upon this acid seem still to leave a con-
siderable degree of uncertainty with regard to
its nature, I shall not enlarge upon its proper-
ties, and the means of procuring it pure and
disengaged from combination. It combines with
iron, to which it communicates a blue colour,
and is equally susceptible of entering into com-
bination with most of the other metals, which
are precipitated from it by the alkalies, am-
monia, and lime, in consequence of greater af-
finity. The prussic radical, from the experi-
ments of Scheele, and especially from those of
M. Berthollet, seems composed of charcoal
and azote; hence it is an acid with a double
base. The phosphorus which has been found
combined with it appears, from the experiments
of M. Hassenfratz, to be only accidental.

86 LAVOISIER

Although this acid combines with alkalies, in the class of acids; but, as I have already ob-
earths, and metals, in the same way with other served, it is difficult to form a decided opinion
acids, it possesses only some of the properties upon the nature of this substance until the
we have been used to attribute to acids, and it subject has been farther elucidated by a great-
may consequently be improperly ranked here er number of experiments.

THIRD PART

DESCRIPTION OF THE INSTRUMENTS AND OPERATIONS
OF CHEMISTRY

INTRODUCTION

IN the two former parts of this work I designed-
ly avoided being particular in describing the
manual operations of chemistry, because I had
found from experience that, in a work appro-
priated to reasoning, minute descriptions of
processes and of plates interrupt the chain of
ideas and render the attention necessary both
difficult and tedious to the reader. On the
other hand, if I had confined myself to the sum-
mary descriptions hitherto given, beginners
could have only acquired very vague concep-
tions of practical chemistry from my work and
must have wanted both confidence and interest
in operations they could neither repeat nor
thoroughly comprehend. This want could not
have been supplied from books; for, besides that
there are not any which describe the modern
instruments and experiments sufficiently at
large, any work that could have been consulted
would have presented these things under a very
different order of arrangement and in a different
chemical language, which must greatly tend to
injure the main object of my performance.

Influenced by these motives, I determined
to reserve, for a third part of my work, a sum-
mary description of all the instruments and
manipulations relative to elementary chemis-
try. I considered it as better placed at the end,
rather than at the beginning of the book, be-
cause I must have been obliged to suppose the
reader acquainted with circumstances which a
beginner cannot know and must therefore have
read the elementary part to become acquainted
with. The whole of this third part may there-
fore be considered as resembling the explana-
tions of plates which are usually placed at the
end of academic memoirs that they may not
interrupt the connection of the text by length-
ened description. Though I have taken great
pains to render this part clear and methodical
and have not omitted any essential instrument
or apparatus, I am far from pretending by it to
set aside the necessity of attendance upon lec-

tures and laboratories for such as wish to ac-
quire accurate knowledge of the science of
chemistry. These should familiarise themselves
to the employment of apparatus, and to the
performance of experiments by actual experi-
ence. Nihil est in intellectu quod non priusfuerit
in sensu, the motto which the celebrated Rou-
elle caused to be painted in large characters in
a conspicuous part of his laboratory, is an im-
portant truth never to be lost sight of either by
teachers or students of chemistry.

Chemical operations may be naturally di-
vided into several classes, according to the pur-
poses they are intended for performing. Some
may be considered as purely mechanical, such
as the determination of the weight and bulk of
bodies, trituration, ievigation, searching, wash-
ing, filtration, <fec. Others may be considered
as real chemical operations, because they are
performed by means of chemical powers and
agents; such are solution, fusion, &c. Some of
these are intended for separating the elements
of bodies from each other, some for reuniting
these elements together; and some, as combus-
tion, produce both these effects during the
same process.

Without rigorously endeavouring to follow
the above method, I mean to give a detail of
the chemical operations in such order of ar-
rangement as seemed best calculated for con-
veying instruction. I shall be more particular
in describing the apparatus connected with
modern chemistry, because these are little
known by men who have devoted much of their
time to chemistry and even by many professors
of the science.

CHAPTER I

Of the Instruments Necessary for Determining
the Absolute and Specific Gravities of Solid
and Liquid Bodies

THE best method known for determining the
quantities of substances submitted to chemical
experiment or resulting from them, is by means

LAVOISIER

of an accurately constructed beam and scales,
with properly regulated weights, which well
known operation is called weighing. The de-
nomination and quantity of the weights used
as an unit or standard for this purpose are ex-
tremely arbitrary, and vary not only in differ-
ent kingdoms, but even in different provinces
of the same kingdom, and in different cities of
the same province. This variation is of infinite
consequence to be well understood in commerce
and in the arts; but, in chemistry, it is of no
moment what parti cular denomination of weigh t
be employed, provided the results of experi-
ments be expressed in convenient fractions of
the same denomination. For this purpose, until
all the weights used in society be reduced to
the same standard, it will be sufficient for chem-
ists in different parts to use the common pound
of their own country as the unit or standard,
and to express all its fractional parts in deci-
mals instead of the arbitrary divisions now in
use. By this means the chemists of all countries
will be thoroughly understood by each other,
as, although the absolute weights of the ingred-
ients and products cannot be known, they will
readily, and without calculation, be able to de-
termine the relative proportions of these to
each other with the utmost accuracy; so that
in this way we shall be possessed of an univer-
sal language for this part of chemistry.

With this view I have long projected to have
the pound divided into decimal fractions, and
I have of late succeeded through the assistance
of M. Fourche, balance-maker at Paris, who
has executed it for me with great accuracy and
judgment. I recommend to all who carry on ex-
periments to procure similar divisions of the
pound, which they will find both easy and sim-
ple in its application, with a very small knowl-
edge of decimal fractions. 1

As the usefulness and accuracy of chemistry
depend entirely upon the determination of the
weights of the ingredients and products both
before and after experiments, too much preci-
sion cannot be employed in this part of the sub-
ject; and, for this purpose, we must be provid-
ed with good instruments. As we are often
obliged, in chemical processes, to ascertain,
within a grain or less, the tare or weight of
large and heavy instruments, we must have
beams made with peculiar niceness by accurate

1 M. Lavoisier's very accurate directions for re-
ducing the common subdivisions of the French pound
into decimal fractions, and vice versa, given in tables
subjoined to this 3d part are not printed in this edi-
tion , TRANSLATOR.

workmen, and these must always be kept apart
from the laboratory in some place where the
vapours of acids, or other corrosive liquors,
cannot have access; otherwise the steel will
rust, and the accuracy of the balance be de-
stroyed. I have three sets, of different sizes,
made by M. Fontin with the utmost nicety,
and, excepting those made by M. Ramsden of
London, I do not think any can compare with
them for precision and sensitivity. The largest
of these is about three feet long in the beam
for large weights, up to fifteen or twenty pounds ;
the second, for weights of eighteen or twenty
ounces, is exact to a tenth part of a grain; and
the smallest, calculated only for weighing about
one gros, is sensibly affected by the five hun-
dredth part of a grain.

Besides these nicer balances, which are only
used for experiments of research, we must have
others of less value for the ordinary purposes of
the laboratory. A large iron balance, capable
of weighing forty or fifty pounds within half a
dram, one of a middle size, which may ascer-
tain eight or ten pounds, within ten or twelve
grains, and a small one, by which about a
pound may be determined, within one grain.

We must likewise be provided with weights
divided into their several fractions, both vul-
gar and decimal, with the utmost nicety, and
verified by means of repeated and accurate
trials in the nicest scales; and it requires some
experience, and to be accurately acquainted
with the different weights, to be able to use
them properly. The best way of precisely as-
certaining the weight of any particular sub-
stance is to weigh it twice, once with the deci-
mal divisions of the pound and another time
with the common subdivisions or vulgar frac-
tions, and, by comparing these, we attain the
utmost accuracy.

By the specific gravity of any substance is
understood the quotient of its absolute weight
divided by its magnitude, or, what is the same,
the weight of a determinate bulk of any body.
The weight of a determinate magnitude of wa-
ter has been generally assumed as unity for
this purpose; and we express the specific grav-
ity of gold, sulphuric acid, &c. by saying that
gold is nineteen times, and sulphuric acid twice
the weight of water, and so of other bodies.

It is the more convenient to assume water as
unity in specific gravities, that those substances
whose specific gravity we wish to determine are
most commonly weighed in water for that pur-
pose. Thus, if we wish to determine the spe-

CHEMISTRY

cific gravity of gold flattened under the ham-
mer, and supposing the piece of gold to weigh
8 02. 4 gros 2% grs. in the air, 1 it is suspended
by means of a fine metallic wire under the scale
of a hydrostatic balance so as to be entirely
immersed in water and again weighed. The
piece of gold in Mr. Brisson's experiment lost
by this means 3 gros 37 grs.; and, as it is evi-
dent that the weight lost by a body weighed in
water is precisely equal to the weight of the
water displaced, or to that of an equal volume
of water, we may conclude that, in equal mag-
nitudes, gold weighs 4893H 9 r s> and water 253
grs. which, reduced to unity, gives 1.0000 as
the specific gravity of water and 19.3617 for
that of gold. We may operate in the same man-
ner with all solid substances. We have rarely
any occasion, in chemistry, to determine the
specific gravity of solid bodies, unless when
operating upon alloys or metallic glasses; but
we have very frequent necessity to ascertain
that of fluids, as it is often the only means of
judging of their purity or degree of concen-
tration.

This object may be very fully accomplished
with the hydrostatic balance, by weighing a
solid body; such, for example, as a little ball of
rock crystal suspended by a very fine gold wire,
first in the air, and afterwards in the fluid whose
specific gravity we wish to discover. The weight
lost by the crystal, when weighed in the liquor,
is equal to that of an equal bulk of the liquid.
By repeating this operation successively in wa-
ter and different fluids, we can very readily as-
certain, by a simple and easy calculation, the
relative specific gravities of these fluids, either
with respect to each other or to water. This
method is not, however, sufficiently exact, or,
at least, is rather troublesome, from its extreme
delicacy, when used for liquids differing but
little in specific gravity from water; such, for
instance, as mineral waters, or any other water
containing very small portions of salt in solu-
tion.

In some operations of this nature, which have
not hitherto been made public, I employed an
instrument of great sensitivity for this purpose
with great advantage. It consists of a hollow
cylinder A b cf (Plate vu, Fig. 6), of brass, or
rather of silver, loaded at its bottom, bcf,
with tin, as represented swimming in a jug of
water, Imno. To the upper part of the cylin-
der is attached a stalk of silver wire, not more

i Vide Mr. Brisson's Essay upon Specific Gravity,
p. 5. AUTHOR.

than three fourths of a line diameter, sur-
mounted by a little cup d, intended for contain-
ing weights; upon the stalk a mark is made at
0, the use of which we shall presently explain.
This cylinder may be made of any size; but, to
be accurate, ought at least to displace four
pounds of water. The weight of tin with which
this instrument is loaded ought to be such as
will make it remain almost in equilibrium in
distilled water and should not require more
than half a dram, or a dram at most, to make it
sink to g.

We must first determine, with great preci-
sion, the exact weight of the instrument and
the number of additional grains requisite for
making it sink, in distilled water of a deter-
minate temperature, to the mark. We then per-
form the same experiment upon all the fluids
of which we wish to ascertain the specific grav-
ity, and, by means of calculation, reduce the
observed differences to a common standard of
cubic feet, pints or pounds, or of decimal frac-
tions, comparing them with water. This method,
joined to experiments with certain reagents,
is one of the best for determining the quality of
waters and is even capable of pointing out dif-
ferences which escape the most accurate chem-
ical analysis. I shall, at some future period,
give an account of a very extensive set of
experiments which I have made upon this
subject.

These metallic hydrometers are only to be
used for determining the specific gravities of
such waters as contain only neutral salts or al-
kaline substances; and they may be construct-
ed with different degrees of ballast for alcohol
and other spiritous liquors. When the specific
gravities of acid liquors are to be ascertained,
we must use a glass hydrometer (Plate vu, Fig.
14). This consists of a hollow cylinder of glass,
abcf, hermetically sealed at its lower end, and
drawn out at the upper into a capillary tube a,
ending in the little cup or basin d. This instru-
ment is ballasted with more or less mercury, at
the bottom of the cylinder introduced through
the tube, in proportion to the weight of the
liquor intended to be examined. We may intro-
duce a small graduated slip of paper into the
tube ad; and, though these degrees do not ex-
actly correspond to the fractions of grains in
the different liquors, they may be rendered
very useful in calculation.

What is said in this chapter may suffice,
without further enlargement, for indicating the
means of ascertaining the absolute and specific

LAVOISIER

gravities of solids and fluids, as the necessary
instruments are generally known, and may easi-
ly be procured. But, as the instruments I have
used for measuring the gases are not anywhere
described, I shall give a more detailed account
of these in the following chapter.

CHAPTER II

Of Gazometry, or the Measurement of the Weight
and Volume of Aeriform Substances

SECTION I Of the Pneumato-chemical Apparatus

THE French chemists have of late applied the
name of pneumato-chemical apparatus to the
very simple and ingenious contrivance, invent-
ed by Dr. Priestley, which is now indispensably
necessary to every laboratory. This consists of
a wooden trough, of larger or smaller dimen-
sions as is thought convenient, lined with plate-
lead or tinned copper, as represented in per-
spective, Plate v. In Fig. 1 the same trough or
cistern is supposed to have two of its sides cut
away, to show its interior construction more
distinctly. In this apparatus, we distinguish be-
tween the shelf ABCD (Figs. 1 and 0) and the
bottom or body of the cistern FGHI (Fig. 2) . The
jars or bell-glasses are filled with water in this
deep part, and, being turned with their mouths
downwards, are afterwards set upon the shelf
ABCD, as shown (Plate x, Fig. 1, F) The
upper parts of the sides of the cistern above
the level of the shelf are called the rim or
borders.

The cistern ought to be filled with water, so
as to stand at least an inch and a half deep up-
on the shelf, and it should be of such dimen-
sions as to admit of at least one foot of water in
every direction in the well. This size is suffici-
ent for ordinary occasions; but it is often con-
venient, and even necessary, to have more
room. I would therefore advise such as intend
to employ themselves usefully in chemical ex-
periments, to have this apparatus made of con-
siderable magnitude, where their place of
operating will allow. The well of my princi-
pal cistern holds four cubic feet of water,
and its shelf has a surface of fourteen square
feet; yet, in spite of this size, which I at first
thought immoderate, I am often straitened
for room.

In laboratories, where a considerable num-
ber of experiments are performed, it is neces-
sary to have several lesser cisterns, besides the
large one, which may be called the general mag-

azine; and even some portable ones, which may
be moved, when necessary, near a furnace or
wherever they may be wanted. There are like-
wise some operations which dirty the water of
the apparatus and therefore require to be car-
ried on in cisterns by themselves.

It were doubtless considerably cheaper to
use cisterns, or iron-bound tubs, of wood sim-
ply dove-tailed, instead of being lined with lead
or copper; and in my first experiments I used
them made in that way; but I soon discovered
their inconvenience. If the water be not always
kept at the same level, such of the dovetails
as are left dry shrink, and when more water is
added it escapes through the joints, and runs
out.

We employ crystal jars or bell-glasses, (Plate
v, Fig. 9, A) for containing the gases in this
apparatus; and, for transporting these, when
full of gas, from one cistern to another, or for
keeping them in reserve when the cistern is too
full, we make use of a flat dish BC, surrounded
by a standing up rim or border, with two han-
dles DE for carrying it by.

After several trials of different materials, I
have found marble the best substance for con-
structing the mercurial pneumato-chemical ap-
paratus, as it is perfectly impenetrable by mer-
cury, and is not liable, like wood, to separate at
the junctures, or to allow the mercury to es-
cape through chinks; neither does it run the
risk of breaking, like glass, stone-ware, or por-
celain. Take a block of marble BCDE (Plate v,
Figs. 8 and 4), about two feet long, 15 or 18
inches broad, and ten inches thick, and cause
it to be hollowed out as at m n (Fig. 5) about
four inches deep, as a reservoir for the mer-
cury; and, to be able more conveniently to fill
the jars, cut the gutter TV (Figs. 3, 4, and 5) at
least four inches deeper; and, as this trench
may sometimes prove troublesome, it is made
capable of being covered at pleasure by thin
boards, which slip into the grooves x y, (Fig.
5). I have two marble cisterns upon this con-
struction, of different sizes, by which I can al-
ways employ one of them as a reservoir of mer-
cury, which it preserves with more safety than
any other vessel, being neither subject to over-
turn, nor to any other accident. We operate
with mercury in this apparatus exactly as with
water in the one before described; but the bell-
glasses must be of smaller diameter and much
stronger; or we may use glass tubes, having
their mouths widened, as in Fig. 7; these are
called eudiometers by the glass-men who sell
them. One of the bell-glasses is represented,

CHEMISTRY

Fig. 5, A, standing in its place, and what is
called a jar is engraved Fig. 6.

The mercurial pneumato-chemical apparatus
is necessary in all experiments wherein the dis-
engaged gases are capable of being absorbed by
water, as is frequently the case, especially in
all combinations, excepting those of metals, in
fermentation, &c.

SECTION II Of the Gazometer

I give the name of gazometer to an instru-
ment which I invented and caused constructed,
for the purpose of a kind of bellows which
might furnish an uniform and continued stream
of oxygen gas in experiments of fusion. M.
Meusnier and I have since made very consid-
erable corrections and additions, having con-
verted it into what may be called an universal
instrument, without which it is hardly pos-
sible to perform most of the very exact experi-
ments. The name we have given the instru-
ment indicates its intention for measuring the
volume or quantity of gas submitted to it for
examination.

It consists of a strong iron beam, DE (Plate
vin, Fig. 1), three feet long, having at each end,
D and E, a segment of a circle, likewise strong-
ly constructed of iron, and very firmly joined.
Instead of being poised as in ordinary balances,
this beam rests, by means of a cylindrical axis
of polished steel F (Fig. 9), upon two large
moveable brass friction-wheels, by which the
resistance to its motion from friction is consid-
erably diminished, being converted into fric-
tion of the second order. As an additional pre-
caution, the parts of these wheels which sup-
port the axis of the beam are covered with
plates of polished rock-crystal. The whole of
this machinery is fixed to the top of the solid
column of wood BC (Fig. l).To one extremity
D of the beam, a scale P for holding weights is
suspended by a flat chain, which applies to the
curvature of the arc riDo, in a groove made for
the purpose. To the other extremity E of the
beam is applied another flat chain, ikm, so
constructed as to be incapable of lengthening
or shortening, by being less or more charged
with weight; to this chain, an iron trivet, with
three branches, ai, ci, and hi, is strongly fixed
at i, and these branches support a large invert-
ed jar A, of hammered copper, of about 18
inches diameter and 20 inches deep. The whole
of this machine is represented in perspective,
Plate vm, Fig. 1; and Plate ix, Figs. 2 and 4
give perpendicular sections, which show its in-
terior structure.

/Round the bottom of the jar, on its outside,
is fixed (Plate ix, Fig. 2) a border divided into
compartments 1, 2, 3, 4, &c., intended to re-
ceive leaden weights separately represented 1,
2, 3, Fig. 3. These are intended for increasing
the weight of the jar when a considerable pres-
sure is requisite, as will be afterwards explained,
though such necessity seldom occurs. The cy-
lindrical jar A is entirely open below, de (Plate
ix, Fig. 4)', but is closed above with a copper
lid, abc, open at bf, and capable of being shut
by the cock g. This lid, as may be seen by in-
specting the figures, is placed a few inches within
the top of the jar to prevent the jar from being
ever entirely immersed in the water and cov-
ered over. Were I to have this instrument
made over again, I should cause the lid to be
considerably more flattened, so as to be almost
level. This jar or reservoir of air is contained in
the cylindrical copper vessel LMNO (Plate
vm, Fig. 1) filled with water.

In the middle of the cylindrical vessel LMNO
(Plate ix, Fig. 4) are placed two tubes st, xy,
which are made to approach each other at their
upper extremities ty\ these are made of such a
length as to rise a little above the upper edge
LM of the vessel LMNO, and when the jar
abcde touches the bottom NO, their upper ends
enter about half an inch into the conical hol-
low b leading to the stop-cock g.

The bottom of the vessel LMNO is repre-
sented, Plate ix, Fig. 3, in the middle of which
a small hollow semispherical cap is soldered,
which may be considered as the broad end of a
funnel reversed; the two tubes st, xy (Fig. 4)
are adapted to this cap at s and x, and by this
means communicate with the tubes mm, nn,
oo, pp (Fig. 3), which are fixed horizontally up-
on the bottom of the vessel, and all of which
terminate in, and are united by, the spherical
cap sx. Three of these tubes are continued out
of the vessel, as in Plate vm, Fig. 1. The first
marked in that figure 1, 2, 3, is inserted at its
extremity 3 by means of an intermediate stop-
cock 4 to the jar V which stands upon the shelf
of a small pneumato-chemical apparatus GHIK,
the inside of which is shown Plate ix, Fig. 1.
The second tube is applied against the outside
of the vessel LMNO from 6 to 7, is continued
at 8, 9, 10, and at 11 is engaged below the jar
V. The former of these tubes is intended for
conveying gas into the machine and the latter
for conducting small quantities for trials under
jars. The gas is made either to flow into or out
of the machine, according to the degree of pres-
sure it receives; and this pressure is varied at

LAVOISIER

pleasure, by loading the scale P less or more by
means of weights. When gas is to be introduced
into the machine, the pressure is taken off, or
even rendered negative; but, when gas is to be
expelled, a pressure is made with such degree
of force as is found necessary.

The third tube 12, 13, 14, 15, is intended for
conveying air or gas to any necessary place or
apparatus for combustions, combinations, or
any other experiment in which it is required.

To explain the use of the fourth tube, I must
enter into some discussions. Suppose the vessel
LMNO (Plate vm, Fig. 1) full of water, and
the jar A partly filled with gas, and partly with
water; it is evident that the weights in the ba-
sin P may be so adjusted as to occasion an ex-
act equilibrium between the weight of the ba-
sin and of the jar, so that the external air shall
not tend to enter into the jar nor the gas to es-
cape from it; and in this case the water will
stand exactly at the same level both within
and without the jar. On the contrary, if the
weight in the basin P be diminished, the jar
will then press downwards from its own grav-
ity, and the water will stand lower within the
jar than it does without; in this case, the in-
cluded air or gas will suffer a degree of com-
pression above that experienced by the extern-
al air, exactly proportioned to the weight of a
column of water, equal to the difference of the
external and internal surfaces of the water.
From these reflections, M. Meusnier contrived
a method of determining the exact degree of
pressure to which the gas contained in the jar
is at any time exposed. For this purpose, he
employs a double glass siphon 19, 20, 21, 22,
23, firmly cemented at 19 and 23. The extrem-
ity 19 of this siphon communicates freely with
the water in the external vessel of the machine,
and the extremity 23 communicates with the
fourth tube at the bottom of the cylindrical
vessel, and consequently, by means of the per-
pendicular tube st (Plate ix, Fig. 4) with the
air contained in the jar. He likewise cements,
at 16 (Plate vm, Fig. Jf), another glass tube 16,
17, 18, which communicates at 16 with the wa-
ter in the exterior vessel LMNO, and, at its
upper end 18, is open to the external air.

By these several contrivances, it is evident
that the water must stand in the tube 16, 17,
18, at the same level with that in the cistern
LMNO; and, on the contrary, that, in the
branch 19, 20, 21, it must stand higher or lower
according as the air in the jar is subjected to a
greater or lesser pressure than the external air.
To ascertain these differences, a brass scale di-

vided into inches and lines is fixed between
these two tubes. It is readily conceived that, as
air, and all other elastic fluids must increase in
weight by compression, it is necessary to know
their degree of condensation to be enabled to
calculate their quantities and to convert the
measure of their volumes into correspondent
weights; and this object is intended to be ful-
filled by the contrivance now described.

But, to determine the specific gravity of air
or of gases, and to ascertain their weight in a
known volume, it is necessary to know their
temperature as well as the degree of pressure
under which they subsist; and this is accom-
plished by means of a small thermometer,
strongly cemented into a brass collet which
screws into the lid of the jar A. This thermom-
eter is represented separately, Plate vm, Fig.
10, and in its place 24, 25, Fig. 1 and Plate ix,
Fig. 4> The bulb is in the inside of the jar A,
and its graduated stalk rises on the outside of
the lid.

The practice of gazometry would still have
laboured under great difficulties without fur-
ther precautions than those above described.
When the jar A sinks in the water of the cistern
LMNO, it must lose a weight equal to that of
the water which it displaces; and consequently
the compression which it makes upon the con-
tained air or gas must be proportionally dimin-
ished. Hence the gas furnished, during experi-
ments from the machine, will not have the same
density towards the end that it had at the be-
ginning, as its specific gravity is continually
diminishing. This difference may, it is true, be
determined by calculation; but this would have
occasioned such mathematical investigations
as must have rendered the use of this appara-
tus both troublesome and difficult. M. Meus-
nier has remedied this inconvenience by the
following contrivance. A square rod of iron, 26,
27 (Plate vm, Fig. 1), is raised perpendicular
to the middle of the beam DE. This rod passes
through a hollow box of brass 28, which opens,
and may be filled with lead; and this box is
made to slide alongst the rod by means of a
toothed pinion playing in a rack, so as to raise
or lower the box and to fix it at such places as
is judged proper.

When the lever or beam DE stands horizon-
tal, this box gravitates to neither side; but,
when the jar A sinks into the cistern LMNO,
so as to make the beam incline to that side, it
is evident the loaded box 28, which then passes
beyond the center of suspension, must gravi-
tate to the side of the jar and augment its

CHEMISTRY

pressure upon the included air. This is increased
in proportion as the box is raised towards 27,
because the same weight exerts a greater power
in proportion to the length of the lever by
which it acts. Hence, by moving the box 28
alongst the rod 26, 27, we can augment or di-
minish the correction it is intended to make
upon the pressure of the jar; and both expe-
rience and calculation show that this may be
made to compensate very exactly for the loss
of weight in the jar at all degrees of pressure.

I have not hitherto explained the most im-
portant part of the use of this machine, which
is the manner of employing it for ascertaining
the quantities of the air or gas furnished during
experiments. To determine this with the most
rigorous precision, and likewise the quantity
supplied to the machine from experiments, we
fixed to the arc which terminates the arm of
the beam E (Plate vm, Fig. 1), the brass sector
I w, divided into degrees and half degrees, which
consequently moves in common with the beam ;
and the lowering of this end of the beam is
measured by the fixed index 29, 30, which has
a nonius giving hundredth parts of a degree at
its extremity 30.

The whole particulars of the different parts
of the above described machine are represented
in Plate vui as follow:

Fig. % is the flat chain invented by M. Vau-
canson and employed for suspending the scale
or basin P, Fig. 1; but, as this lengthens or
shortens according as it is more or less loaded,
it would not have answered for suspending the
jar A, Fig. 1.

Fig. 5 is the chain ikm, which in Fig. 1 sus-
tains the jar A. This is entirely formed of plates
of polished iron interlaced into each other and
held together by iron pins. This chain does not
lengthen in any sensible degree, by any weight
it is capable of supporting.

Fig. 6. The trivet, or three branched stirrup,
by which the jar A is hung to the balance, with
the screw by which it is fixed in an accurately
vertical position.

Fig. 3. The iron rod 26, 27, which is fixed
perpendicular to the center of the beam, with
its box 28.

Figs. 7 & 8. The friction-wheels, with the
plates of rock-crystal Z as points of contact by
which the friction of the axis of the lever of the
balance is avoided.

Fig. 4- The piece of metal which supports
the axis of the friction-wheels.

Fig. 9. The middle of the lever or beam, with
the axis upon which it moves.

Fig. 10. The thermometer for determining
the temperature of the air or gas contained in
the jar.

When this gazometer is to be used, the cis-
tern or external vessel LMNO (Plate vui, Fig.
1) is to be filled with water to a determinate
height, which should be the same in all experi-
ments. The level of the water should be taken
when the beam of the balance stands horizon-
tal; this level, when the jar is at the bottom of
the cistern, is increased by all the water which
it displaces and is diminished in proportion as
the jar rises to its highest elevation. We next
endeavour, by repeated trials, to discover at
what elevation the box 28 must be fixed to ren-
der the pressure equal in all situations of the
beam. I should have said nearly, because this
correction is not absolutely rigorous; and dif-
ferences of a quarter, or even of half a line, are
not of any consequence. This height of the box
28 is not the same for every degree of pressure,
but varies according as this is of one, two, three,
or more inches. All these should be registered
with great order and precision.

We next take a bottle which holds eight or
ten pints, the capacity of which is very accu-
rately determined by weighing the water it is
capable of containing. This bottle is turned
bottom upwards, full of water, in the cistern of
the pneumato-chemical apparatus GHIK (Fig.
1), and is set on its mouth upon the shelf of the
apparatus, instead of the glass jar V, having
the extremity 11 of the tube 7, 8, 9, 10, 11, in-
serted into its mouth. The machine is fixed at
zero of pressure, and the degree marked by the
index 30 upon the sector ml is accurately ob-
served; then, by opening the stop-cock 8, and
pressing a little upon the jar A, as much air is
forced into the bottle as fills it entirely. The de-
gree marked by the index upon the sector is
now observed, and we calculate what number
of cubic inches correspond to each degree. We
then fill a second and third bottle, and so on,
in the same manner, with the same precautions,
and even repeat the operation several times
with bottles of different sizes, till at last, by
accurate attention, we ascertain the exact gage
or capacity of the jar A, in all its parts; but it
is better to have it formed at first accurately
cylindrical, by which we avoid these calcula-
tions and estimates.

The instrument I have been describing was
constructed with great accuracy and uncom-
mon skill by M. Meignie, Jr., engineer and
physical instrument-maker. It is a most valu-
able instrument, from the great number of pur-

LAVOISIER

poses to which it is applicable; and, indeed,
there are many experiments which are almost
impossible to perform without it. It becomes
expensive, because, in many experiments, such
as the formation of water and of nitric acid, it
is absolutely necessary to employ two of the
same machines. In the present advanced state
of chemistry, very expensive and complicated
instruments are become indispensably neces-
sary for ascertaining the analysis and synthesis
of bodies with the requisite precision as to quan-
tity and proportion; it is certainly proper to
endeavour to simplify these and to render them
less costly; but this ought by no means to be
attempted at the expense of their convenience
of application, and much less of their accuracy.

SECTION III Some Other Methods of Measuring
the Volume of Gases

The gazometer described in the foregoing
section is too costly and too complicated for
being generally used in laboratories for meas-
uring the gases and is not even applicable to
every circumstance of this kind. In numerous
series of experiments, more simple and more
readily applicable methods must be employed.
For this purpose I shall describe the means I
used before I was in possession of a gazometer
and which I still use in preference to it in the
ordinary course of my experiments.

Suppose that, after an experiment, there is a
residuum of gas, neither absorbable by alkali
nor water, contained in the upper part of the
jar AEF (Plate iv, Fig. 8) standing on the shelf
of a pneuma to-chemical' apparatus, of which
we wish to ascertain the quantity. We must
first mark the height to which the mercury or
water rises in the jar with great exactness, by
means of slips of paper pasted in several parts
round the jar. If we have been operating in
mercury, we begin by displacing the mercury
from the jar by introducing water in its stead.
This is readily done by filling a bottle quite full
of water; having stopped it with your finger,
turn it up, and introduce its mouth below the
edge of the jar; then, turning down its body
again, the mercury, by its gravity, falls into
the bottle, and the water rises in the jar, and
takes the place occupied by the mercury. When
this is accomplished, pour so much water into
the cistern ABCD as will stand about an inch
over the surface of the mercury; then pass the
dish BC (Plate v, Fig. 9) under the jar, and
carry it to the water cistern (Figs. 1 and #). We
here exchange the gas into another jar, which
has been previously graduated in the manner

to be afterwards described; and we thus judge
of the quantity or volume of the gas by means
of the degrees which it occupies in the gradu-
ated jar.

There is another method of determining the
volume of gas, which may either be substituted
in place of the one above described or may be
usefully employed as a correction or proof of
that method. After the air or gas is exchanged
from the first jar, marked with slips of paper,
into the graduated jar, turn up the mouth of
the marked jar and fill it with water exactly to
the marks EF (Plate iv, Fig. 3), and by weigh-
ing the water we determine the volume of the
air or gas it contained, allowing one cubic foot,
or 1 728 cubic inches, of water for each 70 pounds,
French weight.

The manner of graduating jars for this pur-
pose is very easy, and we ought to be provided
with several of different sizes, and even several
of each size in case of accidents. Take a tall,
narrow, and strong glass jar, and, having filled
it with water in the cistern (Plate v, Fig. 1),
place it upon the shelf ABCD ; we ought always
to use the same place for this operation, that
the level of the shelf may be always exactly
similar, by which almost the only error to which
this process is liable will be avoided. Then take
a narrow mouthed phial which holds exactly 6
02. 3 gros 61 grs. of water, which corresponds to
10 cubic inches. If you have not one exactly of
this dimension, choose one a little larger, and
diminish its capacity to the size requisite by
dropping in a little melted wax and rosin. This
bottle serves the purpose of a standard for
gauging the jars. Make the air contained in
this bottle pass into the jar and mark exactly
the place to which the water has descended;
add another measure of air and again mark the
place of the water, and so on, till ail the water
be displaced. It is of great consequence that,
during the course of this operation, the bottle
and jar be kept at the same temperature with
the water in the cistern; and, for this reason,
we must avoid keeping the hands upon either
as much as possible; or, if we suspect they have
been heated, we must cool them by means of
the water in the cistern. The height of the ba-
rometer and thermometer during this experi-
ment is of no consequence.

When the marks have been thus ascertained
upon the jar for every ten cubic inches, we en-
grave a scale upon one of its sides by means of
a diamond pencil. Glass tubes are graduated
in the same manner for use in the mercurial ap-
paratus, only they must be divided into cubic

CHEMISTRY

inches, 'and tenths of a cubic inch. The bottle
used for gauging these must hold 8 02. 6 gros 25
grs. of mercury, which exactly corresponds to
a cubic inch of that metal.

The method of determining the volume of
air or gas by means of a graduated jar has the
advantage of not requiring any correction for
the difference of height between the surface of
the water within the jar and in the cistern; but
it requires corrections with respect to the height
of the barometer and thermometer. But, when
we ascertain the volume of air by weighing the
water which the jar is capable of containing,
up to the marks EF, it is necessary to make a
further correction for the difference between
the surface of the water in the cistern and the
height to which it rises within the jar. This will
be explained in the fifth section of this chapter.

SECTION IV Of the Method of Separating the
Different Gases from Each Other

As experiments often produce two, three, or
more species of gas, it is necessary to be able to
separate these from each other that we may as-
certain the quantity and species of each. Sup-
pose that under the jar A (Plate iv, Fig. 3), is
contained a quantity of different gases mixed
together and standing over mercury; we begin
by marking with slips of paper, as before direct-
ed, the height at which the mercury stands
within the glass; then introduce about a cubic
inch of water into the jar, which will swim over
the surface of the mercury. If the mixture of
gas contains any muriatic or sulphurous acid
gas, a rapid and considerable absorption will
instantly take place, from the strong tendency
these two gases have, especially the former, to
combine with or be absorbed by water. If the
water only produces a slight absorption of gas
hardly equal to its own bulk, we conclude that
the mixture neither contains muriatic acid, sul-
phuric acid, or ainmoniacal gas, but that it
contains carbonic acid gas, of which water only
absorbs about its own bulk. To ascertain this
conjecture, introduce some solution of caustic
alkali, and the carbonic acid gas will be grad-
ually absorbed in the course of a few hours; it
combines with the caustic alkali or potash, and
the remaining gas is left almost perfectly free
from any sensible residuum of carbonic acid gas.

After each experiment of this kind, we must
carefully mark the height at which the mercury
stands within the jar by slips of paper pasted
on and varnished over when dry, that they
may not be washed off when placed in the wa-
ter apparatus. It is likewise necessary to regis-

ter the difference between the surface of the
mercury in the cistern and that in the jar, and
the height of the barometer and thermometer,
at the end of each experiment.

When all the gas or gases absorbable by wa-
ter and potash are absorbed, water is admitted
into the jar to displace the mercury; and, as is
described in the preceding section, the mercury
in the cistern is to be covered by one or two
inches of water. After this, the jar is to be trans-
ported by means of the flat dish BC (Plate v,
Fig. 9) into the water apparatus; and the quan-
tity of gas remaining is to be ascertained by
changing it into a graduated jar. After this,
small trials of it are to be made by experiments
in little jars, to ascertain nearly the nature of
the gas in question. For instance, into a small
jar full of the gas (Plate v, Fig. 8) a lighted ta-
per is introduced ; if the taper is not immediately
extinguished, we conclude the gas to contain
oxygen gas; and, in proportion to the bright-
ness of the flame, we may judge if it contain
less or more oxygen gas than atmospheric air
contains. If, on the contrary, the taper be in-
stantly extinguished, we have strong reason to
presume that the residuum is chiefly composed
of azotic gas. If, upon the approach of the ta-
per, the gas takes fire and burns quietly at the
surface with a white flame, we conclude it to be
pure hydrogen gas; if this flame is blue, we
judge it consists of carbonated hydrogen gas;
and, if it takes fire with a sudden deflagration,
that it is a mixture of oxygen and hydrogen
gas. If, again, upon mixing a portion of the re-
siduum with oxygen gas, red fumes are pro-
duced, we conclude that it contains nitrous gas.

These preliminary trials give some general
knowledge of the properties of the gas and na-
ture of the mixture, but arc not sufficient to de-
termine the proportions and quantities of the
several gases of which it is composed. For this
purpose all the methods of analysis must be
employed; and, to direct these properly, it is of
great use to have a previous approximation by
the above methods. Suppose, for instance, we
know that the residuum consists of oxygen and
azotic gas mixed together; put a determinate
quantity, 100 parts, into a graduated tube of
ten or twelve lines diameter, introduce a solu-
tion of sulphuret of potash in contact with the
gas, and leave them together for some days;
the suiphuret absorbs the whole oxygen gas
and leaves the azotic gas pure.

If it is known to contain hydrogen gas, a de-
terminate quantity is introduced into Volta's
eudiometer alongst with a known proportion of

LAVOISIER

hydrogen gas; these are deflagrated together
by means of the electrical spark; fresh portions
of oxygen gas are successively added till no fur-
ther deflagration takes place and till the great-
est possible diminution is produced. By this
process water is formed, which is immediately
absorbed by the water of the apparatus; but, if
the hydrogen gas contain charcoal, carbonic
acid is formed at the same time, which is not
absorbed so quickly; the quantity of this is
readily ascertained by assisting its absorption,
by means of agitation. If the residuum con-
tains nitrous gas, by adding oxygen gas, with
which it combines into nitric acid, we can very
nearly ascertain its quantity from the diminu-
tion produced by this mixture.

I confine myself to these general examples,
which are sufficient to give an idea of this kind
of operation; a whole volume would not serve
to explain every possible case. It is necessary
to become familiar with the analysis of gases
by long experience; we must even acknowledge
that they mostly possess such powerful affini-
ties to each other that we are not always cer-
tain of having separated them completely. In
these cases, we must vary our experiments in
every possible point of view, add new agents to
the combination, and keep out others, and con-
tinue our trials till we are certain of the truth
and exactitude of our conclusions.

SECTION V Of the Necessary Corrections of the
Volume of Gases, According to the Pressure of
the Atmosphere

All elastic fluids are compressible or conden-
sable in proportion to the weight with which
they are loaded. Perhaps this law, which is
ascertained by general experience, may suffer
some irregularity when these fluids are under
a degree of condensation almost sufficient to
reduce them to the liquid state, or when either
in a state of extreme rarefaction or condensa-
tion; but we seldom approach either of these
limits with most of the gases which we submit
to our experiments. I understand this proposi-
tion of gases being compressible, in proportion
to their superincumbent weights, as follows:

A barometer, which is an instrument gener-
ally known, is, properly speaking, a species of
siphon, ABCD (Plate xn, Fig. 16), whose leg
AB is filled with mercury, whilst the leg CD is
full of air. If we suppose the branch CD indef-
initely continued till it equals the height of our
atmosphere, we can readily conceive that the
barometer is, in reality, a sort of balance, in
which a column of mercury stands in equilibri-

um with a column of air of the same weight.
But it is unnecessary to prolongate the branch
CD to such a height, as it is evident that the
barometer, being immersed in air, the column
of mercury AB will be equally in equilibrium
with a column of air of the same diameter,
though the leg CD be cut off at C, and the part
CD be taken away altogether.

The medium height of mercury in equilibri-
um with the weight of a column of air, from
the highest part of the atmosphere to the sur-
face of the earth, is about twenty-eight French
inches in the lower parts of the city of Paris;
or, in other words, the air at the surface of the
earth at Paris is usually pressed upon by a
weight equal to that of a column of mercury
twenty-eight inches in height. I must be under-
stood in this way in the several parts of this
publication when talking of the different gases,
as, for instance, when the cubic foot of oxygen
gas is said to weigh 1 oz. 4 gros, under 28 inches
pressure. The height of this column of mercury,
supported by the pressure of the air, diminish-
es in proportion as we are elevated above the
surface of the earth, or rather above the level
of the sea, because the mercury can only form
an equilibrium with the column of air which is
above it and is not in the smallest degree af-
fected by the air which is below its level.

In what ratio does the mercury in the barom-
eter descend in proportion to its elevation; or,
which is the same thing, according to what law
or ratio do the several strata of the atmosphere
decrease in density? This question, which has
exercised the ingenuity of natural philosophers
during the last century, is considerably eluci-
dated by the following experiment.

If we take the glass siphon ABCDE (Plate
xn, Fig. 17), shut at E and open at A, and in-
troduce a few drops of mercury, so as to inter-
cept the communication of air between the leg
AB and the leg BE, it is evident that the air
contained in BCDE is pressed upon, in com-
mon with the whole surrounding air, by a
weight or column of air equal to 28 inches of
mercury. But, if we pour 28 inches of mercury
into the leg AB, it is plain the air in the branch
BCDE will now be pressed upon by a weight
equal to twice 28 inches of mercury, or twice
the weight of the atmosphere; and experience
shows that, in this case, the included air, in-
stead of filling the tube from B to E, only oc-
cupies from C to E, or exactly one half of the
space it filled before. If to this first column of
mercury we add two other portions of 28 inches
each, in the branch AB, the air in the branch

CHEMISTRY

BCDE will be pressed upon by four times the
weight of the atmosphere, or four times the
weight of 28 inches of mercury, and it will then
only fill the space from D to E, or exactly one
quarter of the space it occupied at the com-
mencement of the experiment. From these ex-
periments, which may be infinitely varied, has
been deduced as a general law of nature, which
seems applicable to all permanently elastic flu-
ids, that they diminish in volume in proportion
to the weights with which they are pressed up-
on; or, in other words: "the volume of all elastic
fluids is in the inverse ratio of the weight by which
they are compressed."

The experiments which have been made for
measuring the heights of mountains by means
of the barometer confirm the truth of these de-
ductions; and, even supposing them in some
degree inaccurate, these differences are so ex-
tremely small that they may be reckoned as
nullities in chemical experiments. When this
law of the compression of elastic fluids is once
well understood, it becomes easily applicable
to the corrections necessary in pneumato-
chemical experiments upon the volume of gas
in relation to its pressure. These corrections
are of two kinds, the one relative to the vari-
ations of the barometer and the other for the
column of water or mercury contained in the
jars. I shall endeavour to explain these by
examples, beginning with the most simple
case.

Suppose that 100 cubic inches of oxygen gas
are obtained at 10 (54.5) of the thermometer,
and at 28 inches 6 lines of the barometer, it is
required to know what volume the 100 cubic
inches of gas would occupy, under the pressure
of 28 inches, 1 and what is the exact weight of
the 1 00 inches of oxygen gas? Let the unknown
volume, or the number of inches this gas would
occupy at 28 inches of the barometer, be ex-
pressed by x; and, since the volumes are in the
inverse ratio of their superincumbent weights,
we have the following statement: 100 cubic
inches is to x inversely as 28.5 inches of pres-
sure is to 28.0 inches; or directly 28:28.5::100:
2=101.786 cubic inches, at 28 inches baro-
metrical pressure; that is to say, the same gas
or air which at 28.5 inches of the barometer oc-
cupies 100 cubic inches of volume, will occupy
101.786 cubic inches when the barometer is at
28 inches. It is equally easy to calculate the

* According to the proportion of 114 to 107, given
between the French and English foot, 28 inches of
the French barometer are equal to 29.83 inches of
the English. TRANSLATOR.

weight of this gas occupying 100 cubic inches,
under 28.5 inches of barometrical pressure; for,
as it corresponds to 101.786 cubic inches at the
pressure of 28, and as, at this pressure, and at
10 (54.5) of temperature, each cubic inch of
oxygen gas weighs half a grain, it follows that
100 cubic inches, under 28.5 barometrical pres-
sure, must weigh 50.893 grains. This conclu-
sion might have been formed more directly, as,
since the volume of elastic fluids is in the in-
verse ratio of their compression, their weights
must be in the direct ratio of the same com-
pression: hence, since 100 cubic inches weigh
50 grains under the pressure of 28 inches, we
have the following statement to determine the
weight of 100 cubic inches of the same gas at
28.5 barometrical pressure; 28:50::28.5:x, the
unknown quantity, = 50.893.

The following case is more complicated. Sup-
pose the jar A (Plate xn, Fig. 18) to contain a
quantity of gas in its upper part ACD, the rest
of the jar below CD being full of mercury, and
the whole standing in the mercurial basin or
reservoir GHIK, filled with mercury up to EF,
and that the difference between the surface CD
of the mercury in the jar, and EF, that in the
cistern, is six inches, while the barometer stands
at 27.5 inches. It is evident from these data
that the air contained in ACD is pressed upon
by the weight of the atmosphere, diminished
by the weight of the column of mercury CE, or
by 27.56 = 21.5 inches of barometrical pres-
sure. This air is therefore less compressed than
the atmosphere at the mean height of the ba-
rometer, and consequently occupies more space
than it would occupy at the mean pressure,
the difference being exactly proportional to the
difference between the compressing weights.
If, then, upon measuring the space ACD, it is
found to be 120 cubic inches, it must be re-
duced to the volume which it would occupy
under the mean pressure of 28 inches. This is
done by the following statement: 120:x, the
unknown volume, : :21 .5 :28 inversely; this gives

120X21.5 noi , ,. . ,
x= ~ = 92.143 cubic inches.

In these calculations we may either reduce
the height of the mercury in the barometer,
and the difference of level in the jar and basin,
into lines or decimal fractions of the inch; but
I prefer the latter, as it is more readily calculat-
ed. As, in these operations, which frequently
recur, it is of great use to have means of abbre-
viation, I have given a table in the appendix
for reducing lines and fractions of lines into dec-
imal fractions of the inch. -

LAVOISIER

In experiments performed in the water-ap-
paratus, we must make similar corrections to
procure rigorously exact results, by taking into
account, and making allowances for the differ-
ence of height of the water within the jar above
the surface of the water in the cistern. But, as
the pressure of the atmosphere is expressed in
inches and lines of the mercurial barometer,
and as homogeneous quantities only can be
calculated together, we must reduce the ob-
served inches and lines of water into corre-
spondent heights of the mercury. I have given
a table in the appendix for this conversion,
upon the supposition that mercury is 13.5681
times heavier than water. 1

SECTION VI Of the Correction Relative to the
Degrees of the Thermometer

In ascertaining the weight of gases, besides
reducing them to a mean of barometrical pres-
sure, as directed in the preceding section, we
must likewise reduce them to a standard ther-
mometrical temperature; because, ail elastic
fluids being expanded by heat and condensed
by cold, their weight in any determinate vol-
ume is thereby liable to considerable altera-
tions. As the temperature of 10 (54.5) is a
medium between the heat of summer and the
cold of winter, being the temperature of sub-
terraneous places and that which is most easily
approached to at all seasons, I have chosen that
degree as a mean to which I reduce air or gas
in this species of calculation.

M. de Luc found that atmospheric air was
increased }^i 5 part of its bulk, by each degree of
a mercurial thermometer, divided into 81 de-
grees, between the freezing and boiling points;
this gives }{ 1 1 part for each degree of Reaumur's
thermometer, which is divided into 80 degrees
between these two points. The experiments of
M. Monge seem to make this dilatation less
for hydrogen gas, which he thinks is only di-
lated }{%Q. We have not any exact experiments
hitherto published respecting the ratio of dila-
tation of the other gases; but, from the trials
which have been made, their dilatation seems
to differ little from that of atmospheric air.
Hence I may take for granted, till further ex-
periments give us better information upon this
subject, that atmospherical air is dilated >^io
part, and hydrogen gas #90 part for each de-
gree of the thermometer; but, as there is still
great uncertainty upon this point, we ought
always to operate in a temperature as near as

i The appendix is omitted in this edition.
EDITOR.

possible to the standard of 10 (54.5); by this
means any errors in correcting the weight or
volume of gases by reducing them to the com-
mon standard, will become of little moment.

The calculation for this correction is ex-
tremely easy. Divide the observed volume
of air by 210 and multiply the quotient by
the degrees of temperature above or below
10 (54.5). This correction is negative when
the actual temperature is above the standard
and positive when below. By the use of
logarithmical tables this calculation is much
facilitated.

SECTION VII Example for Calculating the Cor-
rections Relative to the Variations of Pressure
and Temperature

CASE

In the jar A (Plate iv, Fig. 3\ standing in a
water-apparatus, is contained 353 cubic inches
of air; the surface of the water within the jar
at EF is 4J/ inches above the water in the cis-
tern, the barometer is at 27 inches 9J^ lines,
and the thermometer at 15 (65.75). Having
burnt a quantity of phosphorus in the air, by
which concrete phosphoric acid is produced,
the air after the combustion occupies 295 cubic
inches, the water within the jar stands 7 inches
above that in the cistern, the barometer is at
27 inches 9J^ lines, and the thermometer at 16
(68). It is required from these data to deter-
mine the actual volume of air before and after
combustion and the quantity absorbed during
the process.

Calculation before Combustion

The air in the jar before combustion was 353
cubic inches, but it was only under a barometri-
cal pressure of 27 inches 9J^ lines, which, reduc-
ed to decimal fractions, gives 27.79167 inches;
and from this we must deduct the difference of
4J^ inches of water, which corresponds to
0.33166 inches of the barometer; hence the real
pressure of the air in the jar is 27.46001. As the
volume of elastic fluids diminish in the inverse
ratio of the compressing weights, we have the
following statement to reduce the 353 inches
to the volume the air would occupy at 28 inches
barometrical pressure.

353 :x, the unknown volume, ::27.46001:28.

353X27.46001 AQ . M ,. . ,
Hence, x = ^o 346.192 cubic inch-
es, which is the volume the same quantity of
air would have occupied at 28 inches of the ba-
rometer.

CHEMISTRY

The 210th part of this corrected volume is
1.65, which, for the five degrees of temperature
above the standard gives 8.255 cubic inches;
and, as this correction is subtractive, the real
corrected volume of the air before combustion
is 337.942 inches.

Calculation after Combustion

By a similar calculation upon the volume of
air after combustion, we find its barometrical
pressure 27.77083-0.51593 = 27.25490. Hence,
to have the volume of air under the pressure of
28 inches, 295: z::27.77083:28 inversely; or, x

this corrected volume is 1.368, which, mul-
tiplied by 6 degrees of thermometrical dif-
ference, gives the subtractive correction for
temperature 8.208, leaving the actual cor-
rected volume of air after combustion 278.942
inches.

Result

The corrected volume before combustion 337.942
Ditto remaining after combustion ..... 278.942

Volume absorbed during combustion 59.000.

SECTION VIII Method of Determining the Abso-
lute Gravity of the Different Gases

Take a large balloon A (Plate v, Fig. 10)
capable of holding 17 or 18 pints, or about half
a cubic foot, having the brass cap bcde strongly
cemented to its neck and to which the tube and
stop-cock fg is fixed by a tight screw. This ap-
paratus is connected by the double screw, rep-
resented separately at Fig. 12 to the jar BCD,
Fig. 10, which must be some pints larger in di-
mensions than the balloon. This jar is open at
top and is furnished with the brass cap hi and
stop-cock Im. One of these stop-cocks is repre-
sented separately at Fig. 11.

We first determine the exact capacity of the
balloon by filling it with water and weighing it
both full and empty. When emptied of water,
it is dried with a cloth introduced through its
neck de, and the last remains of moisture are
removed by exhausting it once or twice in an
air-pump.

When the weight of any gas is to be ascer-
tained, this apparatus is used as follows: fix
the balloon A to the plate of an air-pump by
means of the screw of the stop-cock fg, which
is left open; the balloon is to be exhausted as
completely as possible, observing carefully the
degree of exhaustion by means of the barom-

eter attached to the air-pump. When the vacu-
um is formed, the stop-cock fg is shut and the
weight of the balloon determined with the most
scrupulous exactitude. It is then fixed to the
jar BCD, which we suppose placed in water in
the shelf of the pneumato-chemical apparatus
(Fig. 1); the jar is to be filled with the gas we
mean to weigh, and then, by opening the stop-
cocks fg and Im, the gas ascends into the bal-
loon, whilst the water of the cistern rises at the
same time into the jar. To avoid very trouble-
some corrections, it is necessary, during this
first part of the operation, to sink the jar in the
cistern till the surfaces of the water within the
jar and without exactly correspond. The stop-
cocks are again shut, and the balloon being un-
screwed from its connection with the jar, is to
be carefully weighed; the difference between
this weight and that of the exhausted balloon
is the precise weight of the air or gas contained
in the balloon. Multiply this weight by 1728,
the number of cubic inches in a cubic foot, and ,
divide the product by the number of cubic
inches contained in the balloon; the quotient is
the weight of a cubic foot of the gas or air sub-
mitted to experiment.

Exact account must be kept of the baromet-
rical height and temperature of the thermom-
eter during the above experiment; and from
these the resulting weight of a cubic foot is
easily corrected to the standard of 28 inches
and 10, as directed in the preceding section.
The small portion of air remaining in the bal-
loon after forming the vacuum must likewise
be attended to, which is easily determined by
the barometer attached to the air-pump. If
that barometer, for instance, remains at the
hundredth part of the height it stood at before
the vacuum was formed, we conclude that one
hundredth part of the air originally contained
remained in the balloon and consequently that
only g %Q of gas was introduced from the jar
into the balloon.

CHAPTER III

Description of the Calorimeter, or Apparatus for
Measuring Caloric

THE calorimeter, or apparatus for measuring
the relative quantities of heat contained in
bodies, was described by M. de Laplace and
me in the Recueil de V Academic for 1780, p.
355, and from that essay the materials of this
chapter are extracted.
If, after having cooled any body to the f reez-

100

LAVOISIER

ing point, it be exposed in an atmosphere of
25 (88.25), the body will gradually become
heated, from the surface inwards, till at last it
acquires the same temperature with the sur-
rounding air. But, if a piece of ice be placed in
the same situation, the circumstances are quite
different; it does not approach in the smallest
degree towards the temperature of the circum-
ambient air but remains constantly at zero
(32), or the temperature of melting ice, till
the last portion of ice be completely melted.

This phenomenon is readily explained, as, to
melt ice, or reduce it to water, it requires to be
combined with a certain portion of caloric; the
whole caloric attracted from the surrounding
bodies, is arrested or fixed at the surface or ex-
ternal layer of ice which it is employed to dis-
solve, and combines with it to form water; the
next quantity of caloric combines with the sec-
ond layer to dissolve it into water, and so on
successively till the whole ice be dissolved or
converted into water by combination with ca-
loric, the very last atom still remaining at its
former temperature, because the caloric has
never penetrated so far as long as any inter-
mediate ice remained to melt.

Upon these principles, if we conceive a hol-
low sphere of ice at the temperature of zero (32)
placed in an atmosphere 10 (54.5), and con-
taining a substance at any degree of tempera-
ture above freezing, it follows, 1st, that the
heat of the external atmosphere cannot pene-
trate into the internal hollow of the sphere of
ice; 2nd, that the heat of the body placed in
the hollow of the sphere cannot penetrate out-
wards beyond it, but will be stopped at the in-
ternal surface and continually employed to melt
successive layers of ice, until the temperature
of the body be reduced to zero (32) by having
all its superabundant caloric above that tem-
perature carried off by the ice. If the whole wa-
ter, formed within the sphere of ice during the
reduction of the temperature of the included
body to zero, be carefully collected, the weight
of the water will be exactly proportional to the
quantity of caloric lost by the body in passing
from its original temperature to that of melting
ice; for it is evident that a double quantity of
caloric would have melted twice the quantity
of ice; hence the quantity of ice melted is a
very exact measure of the quantity of caloric
employed to produce that effect and conse-
quently of the quantity lost by the only sub-
stance that could possibly have supplied it.

I have made this supposition of what would
take place in a hollow sphere of ice for the pur-

pose of more readily explaining the method
used in this species of experiment, which was
first conceived by M. de Laplace. It would be
difficult to procure such spheres of ice and in-
convenient to make use of them when got; but,
by means of the following apparatus, we have
remedied that defect. I acknowledge the name
of calorimeter, which I have given it, as derived
partly from Greek and partly from Latin, is in
some degree open to criticism; but, in matters
of science, a slight deviation from strict ety-
mology, for the sake of giving distinctness of
idea, is excusable; and I could not derive the
name entirely from Greek without approaching
too near to the names of known instruments
employed for other purposes.

The calorimeter is represented in Plate vi. It
is shown in perspective at Fig. 1, and its inte-
rior structure is engraved in Figs. 2 and 3; the
former being a horizontal, and the latter a per-
pendicular section. Its capacity or cavity is di-
vided into three parts, which, for better dis-
tinction, I shall name the interior, middle, and
external cavities. The interior cavity//// (Fig.
4), into which the substances submitted to ex-
periment are put, is composed of a grating or
cage of iron wire supported by several iron
bars; its opening or mouth LM is covered by
the lid HG of the same materials. The middle
cavity bbbb (Figs. 2 and 8) is intended to con-
tain the ice which surrounds the interior cav-
ity, and which is to be melted by the caloric of
the substance employed in the experiment. The
ice is supported by the grate m m at the bottom
of the cavity, under which is placed the sieve
nn. These two are represented separately in
Figs. 5 and 6.

In proportion as the ice contained in the mid-
dle cavity is melted by the caloric disengaged
from the body placed in the interior cavity,
the water runs through the grate and sieve and
falls through the conical funnel ccd (Fig. 3),
and tube xy, into the receiver F (Fig. 1). This
water may be retained or let out at pleasure,
by means of the stop-cock u. The external cav-
ity a a a a (Figs. 2 and 3), is filled with ice, to
prevent any effect upon the ice in the middle
cavity from the heat of the surrounding air,
and the water produced from it is carried off
through the pipe ST, which shuts by means of
the stop-cock r. The whole machine is covered
by the lid FF (Fig. 7), made of tin painted with
oil colour to prevent rust.

When this machine is to be employed, the
middle cavity 6666 (Figs. 2 and 3), the lid
GH (Fig. 4) of the interior cavity, the exter-

CHEMISTRY

101

nal cavity aaaa (Figs. 2 and 3), and the gen-
eral lid FF (Fig. 7), are all filled with pounded
ice, well rammed so that no void spaces remain,
and the ice of the middle cavity is allowed to
drain. The machine is then opened, and the
substance submitted to experiment being placed
in the interior cavity, it is instantly closed.
After waiting till the included body is com-
pletely cooled to the freezing point, and the
whole melted ice has drained from the middle
cavity, the water collected in the vessel F (Fig.
1) is accurately weighed. The weight of the wa-
ter produced during the experiment is an exact
measure of the caloric disengaged during the
cooling of the included body, as this substance
is evidently in a similar situation with the one
formerly mentioned as included in a hollow
sphere of ice; the whole caloric disengaged is
stopped by the ice in the middle cavity, and
that ice is preserved from being affected by
any other heat by means of the ice contained
in the general lid (Fig. 7) and in the external
cavity. Experiments of this kind last from fif-
teen to twenty hours; they are sometimes ac-
celerated by covering up the substance in the
interior cavity with well drained ice, which
hastens its cooling.

The substances to be operated upon are
placed in the thin iron bucket (Fig. 8), the cov-
er of which has an opening fitted with a cork,
into which a small thermometer is fixed. When
we use acids, or other fluids capable of injuring
the metal of the instruments, they are con-
tained in the matrass (Fig. 10), which has a
similar thermometer in a cork fitted to its
mouth, and which stands in the interior cav-
ity upon the small cylindrical support RS (Fig.
10).

It is absolutely requisite that there be no
communication between the external and mid-
dle cavities of the calorimeter, otherwise the
ice melted by the influence of the surrounding
air, in the external cavity, would mix with the
water produced from the ice of the middle cav-
ity, which would no longer be a measure of the
caloric lost by the substance submitted to ex-
periment.

When the temperature of the atmosphere is
only a few degrees above the freezing point, its
heat can hardly reach the middle cavity, being
arrested by the ice of the cover ( Fig. 7) and of
the external cavity; but, if the temperature of
the air be under the degree of freezing, it might
cool the ice contained in the middle cavity by
causing the ice in the external cavity to fall, in
the first place, below zero (32). It is therefore

essential that this experiment be carried on in
a temperature somewhat above freezing : hence,
in time of frost, the calorimeter must be kept
in an apartment carefully heated. It is likewise
necessary that the ice employed be not under
zero (32) ; for which purpose it must be pound-
ed and spread out thin for some time in a place
of a higher temperature.

The ice of the interior cavity always retains
a certain quantity of water adhering to its sur-
face, which may be supposed to belong to the
result of the experiment; but as, at the begin-
ning of each experiment, the ice is already sat-
urated with as much water as it can contain, if
any of the water produced by the caloric should
remain attached to the ice, it is evident that
very nearly an equal quantity of what adhered
to it before the experiment must have run down
into the vessel F in its stead; for the inner sur-
face of the ice in the middle cavity is very little
changed during the experiment.

By any contrivance that could be devised,
we could not prevent the access of the external
air into the interior cavity when the atmos-
phere was 9 or 10 (52 or 54) above zero. The
air confined in the cavity, being in that case
specifically heavier than the external air, es-
capes downwards through the pipe xy (Fig. $),
and is replaced by the warmer external air,
which, giving out its caloric to the ice, becomes
heavier and sinks in its turn ; thus a current of
air is formed through the machine, which is the
more rapid in proportion as the external air ex-
ceeds the internal in temperature. This current
of warm air must melt a part of the ice and in-
jure the accuracy of the experiment. We may,
in a great degree, guard against this source of
error by keeping the stop-cock u continually
shut; but it is better to operate only when the
temperature of the external air does not exceed
3, or at most 4 (39 to 41); for we have ob-
served that, in this case, the melting of the in-
terior ice by the atmospheric air is perfectly
insensible; so that we may answer for the ac-
curacy of our experiments upon the specific
heat of bodies to a fortieth part.

We have had constructed two of the above-
described machines; one, which is intended for
such experiments as do not require the interior
air to be renewed, is precisely formed according
to the description here given; the other, which
answers for experiments upon combustion, res-
piration, &c. in which fresh quantities of air
are indispensably necessary, differs from the
former in having two small tubes in the two
lids, by which a current of atmospheric air

102

LAVOISIER

may be blown into the interior cavity of the
machine.

It is extremely easy, with this apparatus, to
determine the phenomena which occur in op-
erations where caloric is either disengaged or
absorbed. If we wish, for instance, to ascertain
the quantity of caloric which is disengaged from
a solid body in cooling a certain number of de-
grees, let its temperature be raised to 80 (212) ;
it is then placed in the interior cavity ////
(Figs. 2 and 8) of the calorimeter, and allowed
to remain till we are certain that its tempera-
ture is reduced to zero (32); the water pro-
duced by melting the ice during its cooling is col-
lected and carefully weighed; and this weight,
divided by the volume of the body submitted
to experiment, multiplied into the degrees of
temperature which it had above zero at the
commencement of the experiment, gives the
proportion of what the English philosophers
call specific heat.

Fluids are contained in proper vessels, whose
specific heat has been previously ascertained,
and operated upon in the machine in the same
manner as directed for solids, taking care to de-
duct, from the quantity of water melted during
the experiment, the proportion which belongs
to the containing vessel.

If the quantity of caloric disengaged during
the combination of different substances is to be
determined, these substances are to be pre-
viously reduced to the freezing degree by keep-
ing them a sufficient time surrounded with
pounded ice; the mixture is then to be made in
the inner cavity of the calorimeter, in a proper
vessel likewise reduced to zero (32) ; and they
are kept inclosed till the temperature of the
combination has returned to the same degree.
The quantity of water produced is a measure of
the caloric disengaged during the combination.

To determine the quantity of caloric disen-
gaged during combustion and during animal
respiration, the combustible bodies are burnt,
or the animals are made to breathe in the in-
terior cavity, and the water produced is care-
fully collected. Guinea pigs, which resist the
effects of cold extremely well, are well adapted
for this experiment. As the continual renewal
of air is absolutely necessary in such experi-
ments, we blow fresh air into the interior cav-
ity of the calorimeter by means of a pipe des-
tined for that purpose and allow it to escape
through another pipe of the same kind; and
that the heat of this air may not produce errors
in the results of the experiments, the tube
which conveys it into the machine is made to

pass through pounded ice, that it may be re-
duced to zero (32) before it arrives at the cal-
orimeter. The air which escapes must likewise
be made to pass through a tube surrounded
with ice, included in the interior cavity of the
machine, and the water which is produced must
make a part of what is collected, because the
caloric disengaged from this air is part of the
product of the experiment.

It is somewhat more difficult to determine
the specific caloric contained in the different
gases, on account of their small degree of den-
sity; for, if they are only placed in the calorim-
eter in vessels like other fluids, the quantity of
ice melted is so small that the result of the ex-
periment becomes at best very uncertain. For
this species of experiment we have contrived to
make the air pass through two metallic worms,
or spiral tubes; one of these, through which the
air passes and becomes heated in its way to
the calorimeter, is contained in a vessel full of
boiling water, and the other, through which
the air circulates within the calorimeter to dis-
engage its caloric, is placed in the interior cav-
ity, ////, of that machine. By means of a small
thermometer placed at one end of the second
worm, the temperature of the air, as it enters
the calorimeter, is determined, and its temper-
ature in getting out of the interior cavity is
found by another thermometer placed at the
other end of the worm. By this contrivance we
are enabled to ascertain the quantity of ice
melted by determinate quantities of air or gas,
while losing a certain number of degrees of tem-
perature, and, consequently, to determine their
several degrees of specific caloric. The same
apparatus, with some particular precautions,
may be employed to ascertain the quantity of
caloric disengaged by the condensation of the
vapours of different liquids.

The various experiments which may be made
with the calorimeter do not afford absolute con-
clusions, but only give us the measure of rela-
tive quantities; we have therefore to fix a unit,
or standard point, from whence to form a scale
of the several results. The quantity of caloric
necessary to melt a pound of ice has been chos-
en as this unit; and, as it requires a pound of
water of the temperature of 60 (167) to melt
a pound of ice, the quantity of caloric expressed
by our unit or standard point is what raises a
pound of water from zero (32) to 60 (167).
When this unit is once determined, we have
only to express the quantities of caloric disen-
gaged from different bodies by cooling a cer-
tain number of degrees in analogous values.

CHEMISTRY

103

The following is an easy mode of calculation
for this purpose, applied to one of our earliest
experiments.

We took 7 Ib. 11 oz. 2 gros 36 grs. of plate-
iron, cut into narrow slips and rolled up, or ex-
pressing the quantity in decimals, 7.7070319.
These, being heated in a bath of boiling water
to about 78 (207.5), were quickly introduced
into the interior cavity of the calorimeter. At
the end of eleven hours, when the whole quan-
tity of water melted from the ice had thorough-
ly drained off, we found that 1.109795 pounds
of ice were melted. Hence, the caloric disen-
gaged from the iron by cooling 78 (175.5) hav-
ing melted 1.109795 pounds of ice, how much
would have been melted by cooling 60 (135)?
This question gives the following statement in
direct proportion, 78:1. 109795 ::60::z =0.8569.
Dividing this quantity by the weight of the
whole iron employed, viz. 7.7070319, the quo-
tient 0.1 10770 is the quantity of ice which would
have been melted by one pound of iron whilst
cooling through 60 (135) of temperature.

Fluid substances, such as sulphuric and ni-
tric acids, &c., are contained in a matrass (Plate
vi, Fig. 9) having a thermometer adapted to
the cork, with its bulb immersed in the liquid.
The matrass is placed in a bath of boiling wa-
ter, and when, from the thermometer, we judge
the liquid is raised to a proper temperature, the
matrass is placed in the calorimeter. The cal-
culation of the products, to determine the spe-
cific caloric of these fluids, is made as above di-
rected, taking care to deduct from the water
obtained the quantity which would have been
produced by the matrass alone, which must be
ascertained by a previous experiment. The table
of the results obtained by these experiments is
omitted, because not yet sufficiently complete,
different circumstances having occasioned the
series to be interrupted; it is not, however, lost
sight of; and we are less or more employed up-
on the subject every winter.

CHAPTER IV
Of Mechanical Operations for Division of Bodies

SECTION I Of Trituration, Levigation, and Pul-
verization

THESE are, properly speaking, only prelimi-
nary mechanical operations for dividing and
separating the particles of bodies and reducing
them into very fine powder. These operations
can never reduce substances into their primary,
or elementary and ultimate particles; they do

not even destroy the aggregation of bodies; for
every particle, after the most accurate tritura-
tion, forms a small whole, resembling the orig-
inal mass from which it was divided. The real
chemical operations, on the contrary, such as
solution, destroy the aggregation of bodies and
separate their constituent and integrant par-
ticles from each other.

Brittle substances are reduced to powder by
means of pestles and mortars. These are of
brass or iron (Plate i, Fig. 1 ) ; of marble or gran-
ite (Fig. 2} ; of lignum vitae (Fig. 3) ; of glass
(Fig. 4) ; of agate (Fig. 5) ; or of porcelain^i^.
6). The pestles for each of these are represented
in the plate, immediately below the mortars to
which they respectively belong, and are made
of hammered iron or brass, of wood, glass, por-
celain, marble, granite, or agate, according to
the nature of the substances they are intended
to triturate. In every laboratory, it is requisite
to have an assortment of these utensils, of var-
ious sizes and kinds. Those of porcelain and
glass can only be used for rubbing substances
to powder, by a dexterous use of the pestle
round the sides of the mortar, as it would be
easily broken by reiterated blows of the pestle.

The bottom of mortars ought to be in the
form of a hollow sphere, and their sides should
have such a degree of inclination as to make
the substances they contain fall back to the
bottom when the pestle is lifted, but not so per-
pendicular as to collect them too much togeth-
er, otherwise too large a quantity would get be-
low the pestle and prevent its operation. For
this reason, likewise, too large a quantity of
the substance to be powdered ought not to be
put into the mortar at one time; and we must
from time to time get rid of the particles al-
ready reduced to powder, by means of sieves
to be afterwards described.

The most usual method of levigation is by
means of a flat table ABCD (Plate 1, Fig. 7) of
porphyry or other stone of similar hardness,
upon which the substance to be reduced to pow-
der is spread and is then bruised and rubbed by
a muller M of the same hard materials, the
bottom of which is made a small portion of a
large sphere; and, as the muller tends continu-
ally to drive the substances towards the sides
of the table, a thin flexible knife or spatula of
iron, horn, wood, or ivory, is used for bringing
them back to the middle of the stone.

In large works, this operation is performed
by means of large rollers of hard stone, which
turn upon each other, either horizontally, in
the way of corn-mills, or by one vertical roller

104

LAVOISIER

turning upon a flat stone. In the above opera-
tions, it is often requisite to moisten the sub-
stances a little, to prevent the fine powder from
flying off.

There are many bodies which cannot be re-
duced to powder by any of the foregoing meth-
ods; such are fibrous substances, as woods;
such as are tough and elastic, as the horns of
animals, elastic gum, &c., and the malleable
metals which flatten under the pestle, instead
of being reduced to powder. For reducing the
woods to powder, rasps (Plate 1, Fig. 8) are
employed ; files of a finer kind are used for horn,
and still finer (Plate 1 , Figs. 9 and 1 0) for metals.

Some of the metals, though not brittle enough
to powder under the pestle, are too soft to be
filed, as they clog the file and prevent its oper-
ation. Zinc is one of these, but it may be pow-
dered when hot in a heated iron mortar, or it
may be rendered brittle, by alloying it with a
small quantity of mercury. One or other of
these methods is used by fire-work makers for
producing a blue flame by means of zinc. Met-
als may be reduced into grains, by pouring them
when melted into water, which serves very well
when they are not wanted in fine powder.

Fruits, potatoes, &c., of a pulpy and fibrous
nature may be reduced to pulp by means of the
grater (Plate 1, Fig. 11).

The choice of the different substances of
which these instruments are made is a matter
of importance; brass or copper are unfit for
operations upon substances to be used as food
or in pharmacy; and marble or metallic instru-
ments must not be used for acid substances;
hence mortars of very hard wood, and those of
porcelain, granite, or glass, are of great utility
in many operations.

SECTION II Of Sifting and Washing Powdered
Substances

None of the mechanical operations employed
for reducing bodies to powder is capable of pro-
ducing it of an equal degree of fineness through-
out; the powder obtained by the longest and
most accurate trituration being still an assem-
blage of particles of various sizes. The coarser
of these are removed, so as only to leave the
finer and more homogeneous particles by means
of sieves (Plate i, Figs. 12, 13, 14, 15) of differ-
ent finenesses, adapted to the particular pur-
poses they are intended for; all the powdered
matter which is larger than the interstices of
the sieve remains behind and is again submit-
ted to the pestle, while the finer pass through.
The sieve (Fig. 12) is made of hair-cloth, or of

silk gauze; and the one represented in Fig. 18
is of parchment pierced with round holes of a
proper size; this latter is employed in the man-
ufacture of gun-powder. When very subtile or
valuable materials are to be sifted, which are
easily dispersed, or when the finer parts of the
powder may be hurtful, a compound sieve (Fig.
15) is made use of, which consists of the sieve
ABCD, with a lid EF, and receiver GH; these
three parts are represented as joined together
for use (Fig. 14).

There is a method of procuring powders of
an uniform fineness, considerably more accur-
ate than the sieve; but it can only be used with
such substances as are not acted upon by wa-
ter. The powdered substance is mixed and agi-
tated with water, or other convenient fluid;
the liquor is allowed to settle for a few mo-
ments, and is then decanted off; the coarsest
powder remains at the bottom of the vessel,
and the finer passes over with the liquid. By
repeated decantations in this manner, various
sediments are obtained of different degrees of
fineness; the last sediment, or that which re-
mains longest suspended in the liquor, being
the finest. This process may likewise be used
with advantage for separating substances of
different degrees of specific gravity, though of
the same fineness; this last is chiefly employed
in mining, for separating the heavier metallic
ores from the lighter earthy matters with which
they are mixed.

In chemical laboratories, pans and jugs of
glass or earthen ware are employed for this op-
eration; sometimes, for decanting the liquor
without disturbing the sediment, the glass si-
phon ABCHI (Plate n, Fig. 11) is used, which
may be supported by means of the perforated
board DE, at the proper depth in the vessel
FG, to draw off all the liquor required into the
receiver LM. The principles and application of
this useful instrument are so well known as to
need no explanation.

SECTION III Of Filtration

A filtre is a species of very fine sieve, which
is permeable to the particles of fluids, but
through which the particles of the finest pow-
dered solids are incapable of passing; hence its
use in separating fine powders from suspension
in fluids. In pharmacy, very close and fine
woollen cloths are chiefly used for this opera-
tion; these are commonly formed in a conical
shape (Plate n, Fig. 2), which has the advant-
age of uniting all the liquor which drains through
into a point A, where it may be readily collect-

CHEMISTRY

105

ed in a narrow mouthed vessel. In large phar-
maceutical laboratories, this filtring bag is
stretched upon a wooden stand (Plate n, Fig . 1 ) .

For the purposes of chemistry, as it is requi-
site to have the filtres perfectly clean, unsized
paper is substituted instead of cloth or flannel;
through this substance, no solid body, however
finely it be powdered, can penetrate, and fluids
percolate through it with the greatest readiness.
As paper breaks easily when wet, various meth-
ods of supporting it are^ used according to cir-
cumstances. When a large quantity of fluid is
to be filtrated, the paper is supported by the
frame of wood (Plate n, Fig. 8) ABCD, having
a piece of coarse cloth stretched over it by
means of iron hooks. This cloth must be well
cleaned each time it is used, or even new cloth
must be employed, if there is reason to suspect
its being impregnated with anything which can
injure the subsequent operations. In ordinary
operations, where moderate quantities of fluid
are to be filtrated, different kinds of glass fun-
nels are used for supporting the paper, as rep-
resented Plate n, Figs. 5, 6, and 7. When sev-
eral filtrations must be carried on at once, the
board or shelf AB, Fig. 9, supported upon stands
C and D, and pierced with round holes, is very
convenient for containing the funnels.

Some liquors are so thick and clammy as
not to be able to penetrate through paper with-
out some previous preparation, such as clari-
fication by means of white of eggs, which being
mixed with the liquor, coagulates when brought
to boil and, entangling the greater part of the
impurities of the liquor, rises with them to the
surface in the state of scum. Spiritous liquors
may be clarified in the same manner by means
of isinglass dissolved in water, which coagu-
lates by the action of the alcohol without the
assistance of heat.

As most of the acids are produced by distil-
lation, and are consequently clear, we have
rarely any occasion to filtrate them; but if, at
any time, concentrated acids require this oper-
ation, it is impossible to employ paper, which
would be corroded and destroyed by the acid.
For this purpose, pounded glass, or rather
quartz or rock-crystal, broken in pieces and
grossly powdered, answers very well; a few of
the larger pieces are put in the neck of the fun-
nel; these are covered with the smaller pieces,
the finer powder is placed over all, and the acid
is poured on top. For the ordinary purposes of
society, river-water is frequently filtrated by
means of clean washed sand, to separate its im-
purities.

SECTION IV Of Decantation

This operation is often substituted instead
of filtration for separating solid particles which
are diffused through liquors. These are allowed
to settle in conical vessels, ABODE (Plate n,
Fig. 10), the diffused matters gradually sub-
side, and the clear fluid is gently poured off. If
the sediment be extremely light, and apt to
mix again with the fluid by the slightest mo-
tion, the siphon (Fig. 11) is used, instead of de-
cantation, for drawing off the clear fluid.

In experiments where the weight of the pre-
cipitate must be rigorously ascertained, decan-
tation is preferable to filtration, providing the
precipitate be several times washed in a con-
siderable proportion of water. The weight of
the precipitate may indeed be ascertained, by
carefully weighing the filtre before and after
the operation; but, when the quantity of pre-
cipitate is small, the different proportions of
moisture retained by the paper, in a greater or
lesser degree of exsiccation, may prove a ma-
terial source of error which ought carefully to
be guarded against.

CHAPTER V

Of Chemical Means for Separating the Particles
of Bodies from Each Other Without Decompo-
sition, and for Uniting Them Again

I HAVE already shown that there are two meth-
ods of dividing the particles of bodies, the me-
chanical and chemical. The former only sepa-
rates a solid mass into a great number of small-
er masses; and for these purposes various spe-
cies of forces are employed, according to cir-
cumstances, such as the strength of man or of
animals, the weight of water applied through
the means of hydraulic engines, the expansive
power of steam, the force of the wind, &c. By
all these mechanical powers, we can never re-
duce substances into powder beyond a certain
degree of fineness; and the smallest particle
produced in this way, though it seems very mi-
nute to our organs, is still in fact a mountain
when compared with the ultimate elementary
particles of the pulverized substance.

The chemical agents, on the contrary, divide
bodies into their primitive particles. If, for in-
stance, a neutral salt be acted upon by these, it
is divided as far as is possible without ceasing
to be a neutral salt. In this chapter, I mean to
give examples of this kind of division of bodies,
to which I shall add some account of the rela-
tive operations.

106

LAVOISIER

SECTION I Of the Solution of Salts

In chemical language, the terms of solution
and dissolution have long been confounded and
have very improperly been indiscriminately em-
ployed for expressing both the division of the
particles of a salt in a fluid, such as water, and
the division of a metal in an acid. A few reflec-
tions upon the effects of these two operations
will suffice to show that they ought not to be
confounded together. In the solution of salts,
the saline particles are only separated from each
other, whilst neither the salt nor the water are
at all decomposed; we are able to recover both
the one and the other in the same quantity as
before the operation. The same thing takes
place in the solution of resins in alcohol. Dur-
ing metallic dissolutions, on the contrary, a de-
composition, either of the acid or of the water
which dilutes it, always takes place; the metal
combines with oxygen and is changed into an
oxide, and a gaseous substance is disengaged;
so that in reality none of the substances employ-
ed remain, after the operation, in the same
state they were in before. This article is entire-
ly confined to the consideration of solution.

To understand properly what takes place
during the solution of salts, it is necessary to
know that, in most of these operations, two
distinct effects are complicated together, viz.,
solution by water, and solution by caloric ; and,
as the explanation of most of the phenomena
of solution depends upon the distinction of
these two circumstances, I shall enlarge a little
upon their nature.

Nitrate of potash, usually called nitre or salt-
petre, contains very little water of crystalliza-
tion, perhaps even none at all ; yet this salt lique-
fies in a degree of heat very little superior to
that of boiling water. This liquefaction cannot
therefore be produced by means of the water of
crystallization, but in consequence of the salt
being very fusible in its nature, and from its
passing from the solid to the liquid state of ag-
gregation when but a little raised above the
temperature of boiling water. All salts are in
this manner susceptible of being liquefied by
caloric, but in higher or lower degrees of tem-
perature. Some of these, as the acetites of pot-
ash and soda, liquefy with a very moderate
heat, whilst others, as sulphate of potash, lime,
&c., require the strongest fires we are capable
of producing. This liquefaction of salts by ca-
loric produces exactly the same phenomena
with the melting of ice; it is accomplished in
each salt by a determinate degree of heat,

which remains invariably the same during the
whole time of the liquefaction. Caloric is em-
ployed and becomes fixed during the melting
of the salt, and is, on the contrary, disengaged
when the salt coagulates. These are general
phenomena which universally occur during the
passage of every species of substance from the
solid to the fluid state of aggregation, and from
fluid to solid.

These phenomena arising from solution by
caloric are always less or more conjoined with
those which take place during solutions in wa-
ter. We cannot pour water upon a salt, on pur-
pose to dissolve it, without employing a com-
pound solvent, both water and caloric; hence
we may distinguish several different cases of
solution, according to the nature and mode of
existence of each salt. If for instance, a salt be
with difficulty soluble in water, and readily so
by caloric, it evidently follows that this salt
will be with difficulty soluble in cold water,
and considerably in hot water; such is nitrate
of potash, and more especially oxygenated mu-
riate of potash. If another salt be little soluble
both in water and caloric, the difference of its
solubility in cold and warm water will be very
inconsiderable; sulphate of lime is of this kind.
From these considerations, it follows that there
is a necessary relation between the following
circumstances; the solubility of a salt in cold
water, its solubility in boiling water, and the
degree of temperature at which the same salt
liquefies by caloric, unassisted by water; and
that the difference of solubility in hot and cold
water is so much greater in proportion to its
ready solution in caloric, or in proportion to its
susceptibility of liquefying in a low degree of
temperature.

The above is a general view of solution; but,
for want of particular facts and sufficiently ex-
act experiments, it is still nothing more than
an approximation towards a particular theory.
The means of completing this part of chemical
science is extremely simple; we have only to as-
certain how much of each salt is dissolved by a
certain quantity of water at different degrees
of temperature; and as, by the experiments
published by M. de Laplace and me, the quan-
tity of caloric contained in a pound of water at
each degree of the thermometer is accurately
known, it will be very easy to determine, by
simple experiments, the proportion of water
and caloric required for solution by each salt,
what quantity of caloric is absorbed by each at
the moment of liquefaction, and how much is
disengaged at the moment of crystallization.

CHEMISTRY

107

Hence the reason why salts are more rapidly
soluble in hot than in cold water is perfectly
evident. In all solutions of salts caloric is em-
ployed; when that is furnished intermediately
from the surrounding bodies, it can only arrive
slowly to the salt; whereas this is greatly accel-
erated when the requisite caloric exists ready
combined with the water of solution.

In general, the specific gravity of water is
augmented by holding salts in solution; but
there are some exceptions to the rule. Some
time hence, the quantities of radical, of oxygen,
and of base, which constitute each neutral salt,
the quantity of water and caloric necessary for
solution, the increased specific gravity com-
municated to water, and the figure of the ele-
mentary particles of the crystals, will all be ac-
curately known. From these all the circum-
stances and phenomena of crystallization will
be explained, and by these means this part of
chemistry will be completed. M. Seguin has
formed the plan of a thorough investigation of
this kind, which he is extremely capable of
executing.

The solution of salts in water requires no
particular apparatus ; small glass phials of dif-
ferent sizes (Plate n, Figs. 16 and 17), pans of
earthern ware A (Figs. 1 and #), long-necked
matrasses (Fig. 14), and pans or basins of cop-
per or of silver (Figs. 13 and 15) answer very
well for these operations.

SECTION II Of Lixiviation

This is an operation used in chemistry and
manufactures for separating substances which
are soluble in water from such as are insoluble.
The large vat or tub (Plate n, Fig. 12), having
a hole D near its bottom containing a wooden
spiget and faucet or metallic stop-cock DE, is
generally used for this purpose. A thin stratum
of straw is placed at the bottom of the tub;
over this, the substance to be lixiviated is laid
and covered by a cloth, then hot or cold water,
according to the degree of solubility of the sa-
line matter, is poured on. When the water is
supposed to have dissolved all the saline parts,
it is let off by the stop-cock; and, as some of
the water charged with salt necessarily adheres
to the straw and insoluble matters, several fresh
quantities of water are poured on. The straw
serves to secure a proper passage for the water,
and may be compared to the straws or glass rods
used in filtrating to keep the paper from touching
the sides of the funnel. The cloth which is laid
over the matters under lixiviation prevents the
water from making a hollow in these substances

where it is poured on, through which it might
escape without acting upon the whole mass.

This operation is less or more imitated in
chemical experiments; but as in these, espe-
cially with analytical views, greater exactness is
required, particular precautions must be em-
ployed, so as not to leave any saline or soluble
part in the residuum. More water must be em-
ployed than in ordinary lixiviations, and the
substances ought to be previously stirred up in
the water before the clear liquor is drawn off,
otherwise the whole mass might not be equally
lixiviated, and some parts might even escape
altogether from the action of the water. We
must likewise employ fresh portions of water
in considerable quantity, until it comes off en-
tirely free from salt, which we may ascertain
by means of the hydrometer formerly described.

In experiments with small quantities, this
operation is conveniently performed in jugs or
matrasses of glass, and by filtrating the liquor
through paper in a glass funnel. When the sub-
stance is in larger quantity, it may be lixivi-
ated in a kettle of boiling water, and filtrated
through paper supported by cloth in the wood-
en frame (Plate n, Figs. 3 and 4) ; and in opera-
tions in the large way, the tub already men-
tioned must be used.

SECTION III Of Evaporation

This operation is used for separating two
substances from each other, of which one at
least must be fluid, and whose degrees of vola-
tility are considerably different. By this means
we obtain a salt, which has been dissolved in
water, in its concrete form ; the water, by heat-
ing, becomes combined with caloric, which ren-
ders it volatile, while the particles of the salt
being brought nearer to each other, and within
the sphere of their mutual attraction, unite
into the solid state.

As it was long thought that the air had great
influence upon the quantity of fluid evaporated,
it will be proper to point out the errors which
this opinion has produced. There certainly is a
constant slow evaporation from fluids exposed
to the free air; and, though this species of evap-
oration may be considered in some degree as a
solution in air, yet caloric has considerable in-
fluence in producing it, as is evident from the
refrigeration which always accompanies this
process; hence we may consider this gradual
evaporation as a compound solution made part-
ly in air and partly in caloric. But the evapora-
tion which takes place from a fluid kept con-
tinually boiling, is quite different in its nature,

108

LAVOISIER

and in it the evaporation produced by the ac-
tion of the air is exceedingly inconsiderable in
comparison with that which is occasioned by
caloric. This latter species may be termed va-
porization rather than evaporation. This proc-
ess is not accelerated in proportion to the ex-
tent of evaporating surface, but in proportion
to the quantities of caloric which combine with
the fluid. Too free a current of cold air is often
hurtful to this process, as it tends to carry off
caloric from the water and consequently re-
tards its conversion into vapour. Hence there
is no inconvenience produced by covering, in a
certain degree, the vessels in which liquids are
evaporated by continual boiling, provided the
covering body be of such a nature as does not
strongly draw off the caloric, or, to use an ex-
pression of Dr. Franklin's, provided it be a bad
conductor of heat. In this case, the vapours es-
cape through such opening as is left, and at least
as much is evaporated, frequently more than
when free access is allowed to the external air.

As during evaporation the fluid carried off
by caloric is entirely lost, being sacrificed for
the sake of the fixed substances with which it
was combined, this process is only employed
where the fluid is of small value, as water, for
instance. But, when the fluid is of more conse-
quence, we have recourse to distillation, in
which process we preserve both the fixed sub-
stance and the volatile fluid. The vessels em-
ployed for evaporation are basins or pans of
copper, silver, or lead (Plate n, Figs. 13 and 15),
or capsules of glass, porcelain, or stone ware
(Plate n, A, Figs. 1 and 2\ Plate in, Figs. 5 and
4) . The best utensils for this purpose are made
of the bottoms of glass retorts and matrasses,
as their equal thinness renders them more fit
than any other kind of glass vessel for bearing
a brisk fire and sudden alterations of heat and
cold without breaking.

As the method of cutting these glass vessels
is nowhere described in books, I shall here give
a description of it, that they may be made by
chemists for themselves out of spoiled retorts,
matrasses, and recipients, at a much cheaper
rate than any which can be procured from glass
manufacturers. The instrument (Plate in, Fig.
5), consisting of an iron ring AC, fixed to the
rod AB, having a wooden handle D, is employed
as follows: Make the ring red hot in the fire,
and put it upon the matrass G (Fig. 6), which
is to be cut; when the glass is sufficiently heat-
ed, throw on a little cold water, and it will gen-
erally break exactly at the circular line heated
by the ring.

Small flasks or phials of thin glass are exceed-
ing good vessels for evaporating small quantities
of fluid ; they are very cheap, and stand the fire
remarkably. One or more of these may be
placed upon a second grate above the furnace
(Plate in, Fig. #), where they will only experi-
ence a gentle heat. By this means a great num-
ber of experiments may be carried on at one
time. A glass retort, placed in a sand-bath, and
covered with a dome of baked earth (Plate in,
Fig. 1), answers pretty well for evaporations;
but in this way it is always considerably slow-
er, and is even liable to accidents; as the sand
heats unequally, and the glass cannot dilate in
the same unequal manner, the retort is very
liable to break. Sometimes the sand serves ex-
actly the office of the iron ring formerly men-
tioned ; for, if a single drop of vapour, condensed
into liquid, happens to fall upon the heated
part of the vessel, it breaks circularly at that
place. When a very intense fire is necessary,
earthen crucibles may be used ; but we gener-
ally use the word evaporation to express what
is produced by the temperature of boiling wa-
ter or not much higher.

SECTION IV Of Crystallization

In this process the integrant parts of a solid
body, separated from each other by the inter-
vention of a fluid, are made to exert the mutual
attraction of aggregation, so as to coalesce and
reproduce a solid mass. When the particles of
a body are only separated by caloric, and the
substance is thereby retained in the liquid state,
all that is necessary for making it crystallize is
to remove a part of the caloric which is lodged
between its particles, or, in other words, to cool
it. If this refrigeration be slow, and the body be
at the same time left at rest, its particles as-
sume a regular arrangement, and crystalliza-
tion, properly so called, takes place; but, if the
refrigeration is made rapidly, or if the liquor
be agitated at the moment of its passage to the
concrete state, the crystallization is irregular
and confused.

The same phenomena occur with watery so-
lutions, or rather in those made partly in water
and partly by caloric. So long as there remains
a sufficiency of water and caloric to keep the
particles of the body asunder beyond the sphere
of their mutual attraction, the salt remains in
the fluid state; but, whenever either caloric or
water is not present in sufficient quantity, and
the attraction of the particles for each other
becomes superior to the power which keeps
them asunder, the salt recovers its concrete

CHEMISTRY

109

form, and the crystals produced are the more
regular in proportion as the evaporation has
been slower and more tranquilly performed.

All the phenomena we formerly mentioned
as taking place during the solution of salts, oc-
cur in a contrary sense during their crystalliza-
tion. Caloric is disengaged at the instant of
their assuming the solid state, which furnishes
an additional proof of salt being held in solu-
tion by the compound action of water and ca-
loric. Hence, to cause salts to crystallize which
readily liquefy by means of caloric, it is not
sufficient to carry off the water which held
them in solution, but the caloric united to them
must likewise be removed. Nitrate of potash,
oxygenated muriate of potash, alum, sulphate
of soda, &c., are examples of this circumstance,
as, to make these salts crystallize, refrigeration
must be added to evaporation. Such salts, on
the contrary, as require little caloric for being
kept in solution, and which, from that circum-
stance, are nearly equally soluble in cold and
warm water, are crystallizable by simply car-
rying off the water which holds them in solu-
tion, and even recover their solid state in boil-
ing water; such are sulphate of lime, muriate
of potash and of soda, and several others.

The art of refining saltpetre depends upon
these properties of salts, and upon their differ-
ent degrees of solubility in hot and cold water.
This salt, as produced in the manufactories by
the first operation, is composed of many differ-
ent salts; some are deliquescent and not sus-
ceptible of being crystallized, such as the nitrate
and muriate of lime; others are almost equally
soluble in hot and cold water, as the muriates
of potash and of soda ; and, lastly, the saltpetre,
or nitrate of potash, is greatly more soluble in
hot than it is in cold water. The operation is
begun by pouring upon this mixture of salts as
much water as will hold even the least soluble,
the muriates of soda and of potash, in solution ;
so long as it is hot, this quantity readily dis-
solves all the saltpetre, but, upon cooling, the
greater part of this salt crystallizes, leaving
about a sixth part remaining dissolved, and
mixed with the nitrate of lime and the two mu-
riates. The nitre obtained by this process is
still somewhat impregnated with other salts,
because it has been crystallized from water in
which these abound. It is completely purified
from these by a second solution in a small quan-
tity of boiling water, and second crystallization.
The water remaining after these crystallizations
of nitre is still loaded with a mixture of salt-
petre, and other salts; by further evaporation,

crude saltpetre, or rough-petre, as the work-
men call it, is procured from it, and this is pur-
ified by two fresh solutions and crystallizations.

The deliquescent earthy salts which do not
contain the nitric acid are rejected in this man-
ufacture; but those which consist of that acid
neutralized by an earthy base are dissolved in
water, the earth is precipitated by means of
potash, and allowed to subside; the clear liquor
is then decanted, evaporated, and allowed to
crystallize. The above management for refin-
ing saltpetre may serve as a general rule for
separating salts from each other which happen
to be mixed together. The nature of each must
be considered, the proportion in which each
dissolves in given quantities of water, and the
different solubility of each in hot and cold wa-
ter. If to these we add the property which some
salts possess, of being soluble in alcohol, or in a
mixture of alcohol and water, we have many
resources for separating salts from each other
by means of crystallization, though it must be
allowed that it is extremely difficult to render
this separation perfectly complete.

The vessels used for crystallization are pans
of earthen ware A (Plate n, Figs. 1 and 2) and
large flat dishes (Plato in, Fig. 7). When a sa-
line solution is to be exposed to a slow evapora-
tion in the heat of the atmosphere, with free
access of air, vessels of some depth (Plate in,
Fig. 3) must be employed, that there may be a
considerable body of liquid; by this means the
crystals produced are of considerable size, and
remarkably regular in their figure.

Every species of salt crystallizes in a peculiar
form, and even each salt varies in the form of
its crystals according to circumstances, which
take place during crystallization. We must not
from thence conclude that the saline particles
of each species are indeterminate in their fig-
ures. The primitive particles of all bodies, es-
pecially of salts, are perfectly constant in their
specific forms; but the crystals which form in
our experiments are composed of congeries of
minute particles, which, though perfectly equal
in size and shape, may assume very dissimilar
arrangements and consequently produce a vast
variety of regular forms, which have not the
smallest apparent resemblance to each other
nor to the original crystal. This subject has
been very ably treated by the Abbe* Hatiy, in
several Mimoires presented to the Academy
and in his work upon the structure of crystals.
It is only necessary to extend generally to the
class of salts the principles he has particularly
applied to some crystallized stones.

110

LAVOISIER

SECTION V Of Simple Distillation

As distillation has two distinct objects to ac-
complish, it is divisible into simple and com-
pound; and, in this section, I mean to confine
myself entirely to the former. When two bodies,
of which one is more volatile than the other, or
has more affinity to caloric, are submitted to
distillation, our intention is to separate them
from each other. The more volatile substance
assumes the form of gas, and is afterwards con-
densed by refrigeration in proper vessels. In
this case distillation, like evaporation, becomes
a species of mechanical operation, which sep-
arates two substances from each other without
decomposing or altering the nature of either.
In evaporation, our only object is to preserve
the fixed body, without paying any regard to
the volatile matter; whereas, in distillation,
our principal attention is generally paid to the
volatile substance, unless when we intend to
preserve both the one and the other. Hence,
simple distillation is nothing more than evap-
oration produced in close vessels.

The most simple distilling vessel is a species
of bottle or matrass A (Plate in, Fig. 8), which
has been bent from its original form BC to BD,
and which is then called a retort ; when used, it
is placed either in a reverberatory furnace
(Plate xin, Fig. 2} or in a sand bath under a
dome of baked earth (Plate in, Fig. 1). To re-
ceive and condense the products, we adapt a
recipient E (Plate in, Fig. 9), which is luted to
the retort. Sometimes, more especially in phar-
maceutical operations, the glass or stone ware
cucurbit, A, with its capital B (Plate in, Fig.
12) or the glass alembic and capital (Fig. 18)
of one piece, is employed. This latter is man-
aged by means of a tubulated opening T, fitted
with a ground stopper of crystal; the capital,
both of the cucurbit and alembic, has a furrow
or trench, rr, intended for conveying the con-
densed liquor into the beak RS by which it
runs out. As, in almost all distillations, expan-
sive vapours are produced, which might burst
the vessels employed, we are under the neces-
sity of having a small hole T (Fig. 9) in the
balloon or recipient, through which these may
find vent; hence, in this way of distilling, all
the products which are permanently aeriform
are entirely lost, and even such as with diffi-
culty lose that state have not sufficient space to
condense in the balloon. This apparatus is not,
therefore, proper for experiments of investiga-
tion, and can only be admitted in the ordinary
operations of the laboratory or in pharmacy.

In the article appropriated for compound dis-
tillation, I shall explain the various methods
which have been contrived for preserving the
whole products from bodies in this process.

As glass or earthen vessels are very brittle,
and do not readily bear sudden alterations of
heat and cold, every well regulated laboratory
ought to have one or more alembics of metal
for distilling water, spiritous liquors, essential
oils, &c. This apparatus consists of a cucurbit
and capital of tinned copper or brass (Plate in,
Figs. 15 and 16), which, when judged proper,
may be placed in the water bath D (Fig. 17).
In distillations, especially of spiritous liquors,
the capital must be furnished with a refrigera-
tory, SS (Fig. 16), kept continually filled with
cold water; when the water becomes heated, it
is let off by the stop-cock, R, and renewed with
a fresh supply of cold water. As the fluid dis-
tilled is converted into gas by means of caloric
furnished by the fire of the furnace, it is evi-
dent that it could not condense, and, conse-
quently, that no distillation, properly speak-
ing, could take place, unless it is made to de-
posit in the capital all the caloric it received in
the cucurbit; with this view, the sides of the
capital must always be preserved at a lower
temperature than is necessary for keeping the
distilling substance in the state of gas, and the
water in the refrigeratory is intended for this
purpose. Water is converted into gas by the
temperature of 80 (212), alcohol by 67
(182.75), ether by 32 (104) : hence these sub-
stances cannot be distilled, or, rather,they will
fly off in the state of gas, unless the tempera-
ture of the refrigeratory be kept under these
respective degrees.

In the distillation of spiritous and other ex-
pansive liquors the above described refrigera-
tory is not sufficient for condensing all the
vapours which arise; in this case, therefore, in-
stead of receiving the distilled liquor immed-
iately from the beak, TU, of the capital into a
recipient, a worm is interposed between them.
This instrument is represented Plate in, Fig.
18, contained in a worm tub of tinned copper;
it consists of a metallic tube bent into a con-
siderable number of spiral revolutions. The
vessel which contains the worm is kept full of
cold water, which is renewed as it grows warm.
This contrivance is employed in all distilleries
of spirits, without the intervention of a capital
and refrigeratory, properly so called. The one
represented in the plate is furnished with two
worms, one of them being particularly appropri-
ated to distillations of odoriferous substances.

CHEMISTRY

111

In some simple distillations it is necessary
to interpose an adopter between the retort
and receiver, as shown (Plate in, Fig. 11). This
may serve two different purposes, either to
separate two products of different degrees of
volatility, or to remove the receiver to a
greater distance from the furnace, that it may
be less heated. But these, and several other
more complicated instruments of ancient con-
trivance, are far from producing the accuracy
requisite in modern chemistry, as will be
readily perceived when I come to treat of
compound distillation.

SECTION VI Of Sublimation

This term is applied to the distillation of sub-
stances which condense in a concrete or solid
form, such as the sublimation of sulphur, and
of muriate of ammonia, or sal ammonia. These
operations may be conveniently performed in
the ordinary distilling vessels already described ,
though, in the sublimation of sulphur, a species
of vessels, named alludels, have been usually
employed. These are vessels of stone or porce-
lain ware, which adjust to each other over a
cucurbit containing the sulphur to be sublimed.
One of the best subliming vessels, for substances
which are not very volatile, is a flask, or phial
of glass, sunk about two thirds into a sand
bath; but in this way we are apt to lose a part
of the products. When these are wished to be
entirely preserved, we must have recourse to
the pneumato-chemical distilling apparatus,
to be described in the following chapter.

CHAPTER VI

Of Pneumato-chemical Distillations, Metallic
Dissolutions, and Some Other Operations
Which Require Very Complicated Instruments

SECTION I Of Compound and Pneumato-chemi-
cal Distillations

IN the preceding chapter, I have only treated
of distillation as a simple operation, by which
two substances, differing in degrees of volatil-
ity, may be separated from each other; but dis-
tillation often actually decomposes the sub-
stances submitted to its action and becomes
one of the most complicated operations in
chemistry. In every distillation, the substance
distilled must be brought to the state of gas in
the cucurbit or retort, by combination with ca-
loric. In simple distillation, this caloric is given

out in the refrigeratory or in the worm, and
the substance again recovers its liquid or solid
form, but the substances submitted to com-
pound distillation are absolutely decompound-
ed; one part, as for instance the charcoal they
contain, remains fixed in the retort, and all the
rest of the elements are reduced to gases of dif-
ferent kinds. Some of these are susceptible of
being condensed and of recovering their solid
or liquid forms, whilst others are permanently
aeriform; one part of these are absorbable by
water, some by the alkalies, and others are not
susceptible of being absorbed at all. An ordi-
nary distilling apparatus, such as has been de-
scribed in the preceding chapter, is quite insuf-
ficient for retaining or for separating these di-
versified products, and we are obliged to have
recourse, for this purpose, to methods of a more
complicated nature.

The apparatus I am about to describe is cal-
culated for the most complicated distillations,
and may be simplified according to circum-
stances. It consists of a tubulated glass retort
A (Plate iv, Fig. 1), having its beak fitted to a
tubulated balloon or recipient BC; to the up-
per orifice D of the balloon a bent tube DE/gr
is adjusted, which, at its other extremity g, is
plunged into the liquor contained in the bottle
L, with three necks xxx. Three other similar
bottles are connected with this first one, by
means of three similar bent tubes disposed in
the same manner; and the farthest neck of the
last bottle is connected with a jar in a pneu-
mato-chemical apparatus, by means of a bent
tube. A determinate weight of distilled water
is usually put into the first bottle, and the other
three have each a solution of caustic potash in
water. The weight of all these bottles, and of
the water and alkaline solution they contain,
must be accurately ascertained. Every thing
being thus disposed, the junctures between the
retort and recipient, and of the tube D of the
latter, must be luted with fat lute, covered
over with slips of linen, spread with lime and
white of egg; all the other junctures are to be
secured by a lute made of wax and rosin melted
together.

When all these dispositions are completed,
and when, by means of heat applied to the re-
tort A, the substance it contains becomes de-
composed, it is evident that the least volatile
products must condense or sublime in the beak
or neck of the retort itself, where most of the
concrete substances will fix themselves. The
more volatile substances, as the lighter oils,
ammonia, and several others, will condense in

112

LAVOISIER

the recipient GC, whilst the gases, which are
not susceptible of condensation by cold, will
pass on by the tubes, and boil up through the
liquors in the several bottles. Such as are
absorbable by water will remain in the first
bottle, and those which caustic alkali can
absorb will remain in the others; whilst such
gases as are not susceptible of absorption,
either by water or alkalies, will escape by the
tube RM, at the end of which they may be
received into jars in a pneumato-chemical ap-
paratus. The charcoal and fixed earth, &c.
which form the substance or residuum, once
called caput mortuum, remain behind in the
retort.

In this manner of operating, we have always
a very material proof of the accuracy of the
analysis, as the whole weights of the products
taken together, after the process is finished,
must be exactly equal to the weight of the orig-
inal substance submitted to distillation. Hence,
for instance, if we have operated upon eight
ounces of starch or gum arabic, the weight of
the charry residuum in the retort, together with
that of all the products gathered in its neck
and the balloon, and of ail the gas received into
the jars by the tube RM added to the addition-
al weight acquired by the bottles, must, when
taken together, be exactly eight ounces. If the
product be less or more, it proceeds from error,
and the experiment must be repeated until a
satisfactory result be procured, which ought
not to differ more than six or eight grains in the
pound from the weight of the substance sub-
mitted to experiment.

In experiments of this kind, I for a long time
met with an almost insurmountable difficulty,
which must at last have obliged me to desist al-
together but for a very simple method of avoid-
ing it, pointed out to me by M. Hassenfratz.
The smallest diminution in the heat of the fur-
nace, and many other circumstances insepar-
able from this kind of experiments, cause fre-
quent reabsorptions of gas; the water in the
cistern of the pneumato-chemical apparatus
rushes into the last bottle through the tube
RM, the same circumstance happens from one
bottle into another, and the fluid is often forced
even into the recipient C. This accident is pre-
vented by using bottles having three necks, as
represented in the plate, into one of which, in
each bottle, a capillary glass-tube St y st, st, st,
is adapted, so as to have its lower extremity t
immersed in the liquor. If any absorption takes
place, either in the retort or in any of the bot-
tles, a sufficient quantity of external air enters,

by means of these tubes, to fill up the void;
and we get rid of the inconvenience at the price
of having a small mixture of common air with
the products of the experiment, which is there-
by prevented from failing altogether. Though
these tubes admit the external air, they cannot
permit any of the gaseous substances to escape,
as they are always shut below by the water of
the bottles.

It is evident that, in the course of experi-
ments with this apparatus, the liquor of the bot-
tles must rise in these tubes in proportion to the
pressure sustained by the gas or air contained
in the bottles; and this pressure is determined
by the height and gravity of the column of
fluid contained in all the subsequent bottles.
If we suppose that each bottle contains three
inches of fluid, and that there are three inches
of water in the cistern of the connected ap-
paratus above the orifice of the tube RM,
and allowing the gravity of the fluids to be
only equal to that of water, it follows that the
air in the first bottle must sustain a pressure
equal to twelve inches of water; the water must
therefore rise twelve inches in the tube S, con-
nected with the first bottle, nine inches in that
belonging to the second, six inches in the third,
and three in the last; wherefore these tubes
must be made somewhat more than twelve,
nine, six and three inches long respectively, al-
lowance being made for oscillatory motions,
which often take place in the liquids. It is some-
times necessary to introduce a similar tube be-
tween the retort and recipient; and, as the
tube is not immersed in fluid at its lower ex-
tremity until some has collected in the prog-
ress of the distillation, its upper end must be
shut at first with a little lute, so as to be opened
according to necessity or after there is suffici-
ent liquid in the recipient to secure its lower
extremity.

This apparatus cannot be used in very accu-
rate experiments, when the substances intend-
ed to be operated upon have a very rapid ac-
tion upon each other or when one of them can
only be introduced in small successive portions,
as in such as produce violent effervescence when
mixed together. In such cases, we employ a
tubulated retort A (Plate vu, Fig. 1), into
which one of the substances is introduced, pre-
ferring always the solid body, if any such is to
be treated ; we then lute to the opening of the
retort a bent tube BCD A, terminating at its
upper extremity B in a funnel, and at its other
end A in a capillary opening. The fluid material
of the experiment is poured into the retort by

CHEMISTRY

113

means of this funnel, which must be made of
such a length, from B to C, that the column of
liquid introduced may counterbalance the re-
sistance produced by the liquors contained in
all the bottles (Plate iv, Fig. 1).

Those who havejiot been accustomed to use
the above described distilling apparatus may
perhaps be startled at the great number of
openings which require luting, and the time
necessary for making all the previous prepara-
tions in experiments of this kind. It is very
true that, if we take into account all the neces-
sary weighings of materials and products, both
before and after the experiments, these pre-
paratory and succeeding steps require much
more time and attention than the experiment
itself. But, when the experiment succeeds prop-
erly, we are well rewarded for all the time and
trouble bestowed, as by one process carried on
in this accurate manner much more just and
extensive knowledge is acquired of the nature
of the vegetable or animal substance thus sub-
mitted to investigation than by many weeks
assiduous labour in the ordinary method of
proceeding.

When in want of bottles with three orifices,
those with two may be used; it is even possible
to introduce all the three tubes at one opening,
so as to employ ordinary wide-mouthed bot-
tles, provided the opening be sufficiently large.
In this case we must carefully fit the bottles
with corks very accurately cut and boiled in a
mixture of oil, wax, and turpentine. These
corks are pierced with the necessary holes for
receiving the tubes by means of a round file,
as in Plate iv, Fig. 8.

SECTION II Of Metallic Dissolutions

I have already pointed out the difference be-
tween solution of salts in water and metallic
dissolutions. The former requires no particular
vessels, whereas the latter requires very com-
plicated vessels of late invention, that we may
not lose any of the products of the experiment,
and may thereby procure truly conclusive re-
sults of the phenomena which occur. The met-
als, in general, dissolve in acids with efferves-
cence, which is only a motion excited in the
solvent by the disengagement of a great num-
ber of bubbles of air or aeriform fluid, which
proceed from the surface of the metal and break
at the surface of the liquid.

M. Cavendish and Dr. Priestley were the
first inventors of a proper apparatus for col-
lecting these elastic fluids. That of Dr. Priest-
ley is extremely simple and consists of a bottle

A (Plate vn, Fig. #), with its cork B, through
which passes the bent glass tube BC, which is
engaged under a jar filled with water in the
pneumato-chemical apparatus, or simply in a
basin full of water. The metal is first intro-
duced into the bottle, the acid is then poured
over it, and the bottle is instantly closed with
its cork and tube, as represented in the plate. But
this apparatus has its inconveniences. When
the acid is much concentrated, or the metal
much divided, the effervescence begins before
we have time to cork the bottle properly, and
some gas escapes, by which we are prevented
from ascertaining the quantity disengaged with
rigorous exactness. In the next place, when we
are obliged to employ heat, or when heat is
produced by the process, a part of the acid dis-
tills and mixes with the water of the pneumato-
chemical apparatus, by which means we are
deceived in our calculation of the quantity of
acid decomposed. Besides these, the water in
the cistern of the apparatus absorbs all the gas
produced which is susceptible of absorption
and renders it impossible to collect these with-
out loss.

To remedy these inconveniences, I at first
used a bottle with two necks (Plate vn, Fig. 8),
into one of which the glass funnel BC is luted
so as to prevent any air escaping; a glass rod
DE is fitted with emery to the funnel, so as to
serve the purpose of a stopper. When it is used,
the matter to be dissolved is first introduced
into the bottle, and the acid is then permitted
to pass in as slowly as we please, by raising the
glass rod gently as often as is necessary until
saturation is produced.

Another method has been since employed,
which serves the same purpose, and is prefer-
able to the last described in some instances.
This consists in adapting to one of the mouths
of the bottle A (Plate vii, Fig. 4), a bent tube
DEFG, having a capillary opening at D, and
ending in a funnel at G. This tube is securely
luted to the mouth C of the bottle. When any
liquid is poured into the funnel, it falls down to
F; and, if a sufficient quantity be added, it
passes by the curvature E and falls slowly into
the bottle, so long as fresh liquor is supplied at
the funnel. The liquor can never be forced out
of the tube, and no gas can escape through it,
because the weight of the liquid serves the pur-
pose of an accurate cork.

To prevent any distillation of acid, espe-
cially in dissolutions accompanied with heat,
this tube is adapted to the retort A (Plate vii,
Fig. 1\ and a small tubulated recipient, M, is

114

LAVOISIER

applied, in which any liquor which may distill
is condensed. On purpose to separate any gas
that is absorbable by water, we add the double
necked bottle L, half filled with a solution of
caustic potash; the alkali absorbs any carbonic
acid gas, and usually only one or two other gases
pass into the jar of the connected pneuma to-
chemical apparatus through the tube NO. In
the first chapter of this third part we have di-
rected how these are to be separated and ex-
amined. If one bottle of alkaline solution be
not thought sufficient, two, three, or more,
may be added.

SECTION III Apparatus Necessary in Experi-
ments upon Vinous and Putrefactive Fermen-
tations

For these operations a peculiar apparatus,
especially intended for this kind of experiment,
is requisite. The one I am about to describe is
finally adopted as the best calculated for the
purpose, after numerous corrections and im-
provements. It consists of a large matrass, A
(Plate x, Fig. 1), holding about twelve pints,
with a cap of brass a 6, strongly cemented to
its mouth, and into which is screwed a bent
tube c d, furnished with a stop-cock e. To this
tube is joined the glass recipient B, having
three openings, one of which communicates
with the bottle C placed below it. To the pos-
terior opening of this recipient is fitted a glass
tube ghij cemented at g and i to collets of
brass, and intended to contain a very deliques-
cent concrete neutral salt, such as nitrate or
muriate of lime, acetite of potash, &c. This
tube communicates with two bottles D and E,
filled to x and y with a solution of caustic
potash.

All the parts of this machine are joined to-
gether by accurate screws, and the touching
parts have greased leather interposed, to pre-
vent any passage of air. Each piece is likewise
furnished with two stop-cocks, by which its
two extremities may be closed, so that we can
weigh each separately at any period of the op-
eration.

The fermentable matter, such as sugar, with
a proper quantity of yeast and diluted with
water, is put into the matrass. Sometimes, when
the fermentation is too rapid, a considerable
quantity of froth is produced, which not only
fills the neck of the matrass, but passes into
the recipient, and from thence runs down into
the bottle C. On purpose to collect this scum
and must, and to prevent it from reaching the
tube filled with deliquescent salts, the recipient

and connected bottle are made of considerable
capacity.

In the vinous fermentation, only carbonic
acid gas is disengaged, carrying with it a small
proportion of water in solution. A great part of
this water is deposited in passing through the
tube ghi, which is filled with a deliquescent
salt in gross powder, and the quantity is ascer-
tained by the augmentation of the weight of
the salt. The carbonic acid gas bubbles up
through the alkaline solution in the bottle D,
to which it is conveyed by the tube klm. Any
small portion which may not be absorbed by
this first bottle is secured by the solution in the
second bottle E, so that nothing, in general,
passes into the jar F, except the common air
contained in the vessels at the commencement
of the experiment.

The same apparatus answers extremely well
for experiments upon the putrefactive fermen-
tation; but, in this case, a considerable quan-
tity of hydrogen gas is disengaged through the
tube qrstUj by which it is conveyed into the
jar F; and, as this disengagement is very rapid,
especially in summer, the j ar must be frequently
changed. These putrefactive fermentations re-
quire constant attendance from the above cir-
cumstance, whereas the vinous fermentation
hardly needs any. By means of this apparatus
we can ascertain, with great precision, the
weights of the substances submitted to fermen-
tation, and of the liquid and aeriform products
which are disengaged. What has been already
said in Part I, Chapter XIII, upon the products
of the vinous fermentation, may be consulted.

SECTION IV Apparatus for the Decomposition
of Water

Having already given an account, in the first
part of this work, of the experiments relative
to the decomposition of water, I shall avoid
any unnecessary repetitions and only give a
few summary observations upon the subject in
this section. The principal substances which
have the power of decomposing water are iron
and charcoal; for which purpose, they require
to be made red hot, otherwise the water is only
reduced into vapours and condenses afterwards
by refrigeration without sustaining the small-
est alteration. In a red heat, on the contrary,
iron or charcoal carry off the oxygen from its
union with hydrogen; in the first case, black
oxide of iron is produced, and the hydrogen is
disengaged pure in form of gas; in the other
case, carbonic acid gas is formed, which disen-
gages, mixed with the hydrogen gas; and this

CHEMISTRY

116

latter is commonly carbonated, or holds char-
coal in solution.

A musket barrel, without its breach pin, an-
swers exceedingly well for the decomposition
of water by means of iron, and one should be
chosen of considerable length and pretty strong.
When too short, so as to run the risk of heating
the lute too much, a tube of copper is to be
strongly soldered to one end . The barrel is placed
in a long furnace CDfiF (Plate vn, Fig. 11),
so as to have a few degrees of inclination from
E to F; a glass retort, A, is luted to the upper
extremity E, which contains water and is placed
upon the furnace WXX. The lower extremity
F is luted to a worm SS, which is connected
with the tubulated bottle H, in which any wa-
ter distilled without decomposition, during the
operation, collects, and the disengaged gas is
carried by the tube KK to jars in a pneuma to-
chemical apparatus. Instead of the retort, a fun-
nel may be employed, having its lower part
shut by a stop-cock, through which the water
is allowed to drop gradually into the gun-bar-
rel. Immediately upon getting into contact with
the heated part of the iron, the water is con-
verted into steam, and the experiment pro-
ceeds in the same manner as if it were furnished
in vapours from the retort.

In the experiment made by M. Meusnier
and me before a committee of the Academy, we
used every precaution to obtain the greatest
possible precision in the result of our experi-
ment, having even exhausted all the vessels
employed before we began, so that the hydro-
gen gas obtained might be free from any mix-
ture of azotic gas. The results of that experi-
ment will hereafter be given at large in a par-
ticular M6moire.

In numerous experiments, we are obliged to
use tubes of glass, porcelain, or copper, instead
of gun-barrels; but glass has the disadvantage
of being easily melted and flattened, if the heat
be in the smallest degree raised too high; and
porcelain is mostly full of small minute pores,
through which the gas escapes, especially when
compressed by a column of water. For these
reasons I procured a tube of brass, which M.
de la Briche got cast and bored out of the solid
for me at Strasburg, under his own inspection.
This tube is extremely convenient for decom-
posing alcohol, which resolves into charcoal,
carbonic acid gas, and hydrogen gas; it may
likewise be used with the same advantage
for decomposing water by means of charcoal,
and in a great number of experiments of this
nature.

CHAPTER VII

Of the Composition and Use of Lutes

THE necessity of properly securing the junc-
tures of chemical vessels to prevent the escape
of any of the products of experiments must be
sufficiently apparent ; for this purpose lutes are
employed, which ought to be of such a nature
as to be equally impenetrable to the most sub-
tile substances, as glass itself through which
only caloric can escape.

This first object of lutes is very well accom-
plished by bees wax, melted with about an
eighth part of turpentine. This lute is very eas-
ily managed, sticks very closely to glass, and is
very difficult to penetrate ; it may be rendered
more consistent, and less or more hard or pli-
able, by adding different kinds of resinous mat-
ters. Though this species of lute answers ex-
tremely well for retaining gases and vapours,
there are many chemical experiments which
produce considerable heat, by which this lute
becomes liquefied, and consequently the expan-
sive vapours must very readily force through
and escape.

For such cases, the following fat lute is the
best hitherto discovered, though not without
its disadvantages, which shall be pointed out.
Take very pure and dry unbaked clay reduced
to a very fine powder; put this into a brass mor-
tar and beat it for several hours with a heavy
iron pestle, dropping in slowly some boiled lin-
seed oil; this is oil which has been oxygenated,
and has acquired a drying quality by being
boiled with litharge. This lute is more tena-
cious, and applies better, if amber varnish be
used instead of the above oil. To make this
varnish, melt some yellow amber in an iron
ladle, by which operation it loses a part of its
succinic acid and essential oil, and mix it with
linseed oil. Though the lute prepared with this
varnish is better than that made with boiled
oil, yet, as its additional expense is hardly
compensated by its superior quality, it is sel-
dom used.

The above fat lute is capable of sustaining a
very violent degree of heat, is impenetrable by
acids and spiritous liquors, and adheres exceed-
ingly well to metals, stone ware, or glass, pro-
viding they have been previously rendered per-
fectly dry. But if, unfortunately, any of the
liquor in the course of an experiment gets
through, either between the glass and the lute
or between the layers of the lute itself, so as to
moisten the part, it is extremely difficult to
close the opening. This is the chief inconveni-

116

LAVOISIER

ence which attends the use of fat lute and per-
haps the only one it is subject to. As it is apt to
soften by heat, we must surround all the junc-
tures with slips of wet bladder applied over the
luting and fixed on by pack-thread tied round
both above and below the joint; the bladder,
and consequently the lute below, must be far-
ther secured by a number of turns of pack-
thread all over it. By these precautions, we are
free from every danger of accident; and the
junctures secured in this manner may be con-
sidered, in experiments, as hermetically sealed.

It frequently happens that the figure of the
junctures prevents the application of ligatures,
which is the case with the three-necked bottles
formerly described; and it even requires great
address to apply the twine without shaking the
apparatus: so that, where a number of junc-
tures require luting, we are apt to displace sev-
eral while securing one. In these cases, we may
substitute slips of linen, spread with white of
egg and lime mixed together, instead of the wet
bladder. These are applied while still moist,
and very speedily dry and acquire consider-
able hardness. Strong glue dissolved in water
may answer instead of white of egg. These fil-
lets are usefully applied likewise over junctures
luted together with wax and rosin.

Before applying a lute, all the junctures of
the vessels must be accurately and firmly fitted
to each other, so as not to admit of being moved .
If the beak of a retort is to be luted to the neck
of a recipient, they ought to fit pretty accurate-
ly; otherwise we must fix them, by introducing
short pieces of soft wood or of cork. If the dis-
proportion between the two be very consider-
able, we must employ a cork which fits the
neck of the recipient, having a circular hole of
proper dimensions to admit the beak of the re-
tort. The same precaution is necessary in adapt-
ing bent tubes to the necks of bottles in the ap-
paratus represented Plate iv, Fig. 1 , and others
of a similar nature. Each mouth of each bottle
must be fitted with a cork, having a hole made
with a round file of a proper size for containing
the tube. And, when one mouth is intended to
admit two or more tubes, which frequently
happens when we have not a sufficient num-
ber of bottles with two or three necks, we must
use a cork with two or three holes (Plate iv,
Fig. 8).

When the whole apparatus is thus solidly
joined, so that no part can play upon another,
we begin to lute. The lute is softened by knead-
ing and rolling it between the fingers, with the
assistance of heat if necessary. It is rolled into

little cylindrical pieces and applied to the junc-
tures, taking great care to make it apply close
and adhere firmly in every part; a second roll
is applied over the first, so as to pass it on each
side, and so on till each juncture be sufficiently
covered; after this, the slips of bladder, or of
linen, as above directed, must be carefully ap-
plied over all. Though this operation may ap-
pear extremely simple, yet it requires peculiar
delicacy and management; great care must be
taken not to disturb one juncture whilst luting
another, and more especially when applying
the fillets and ligatures.

Before beginning any experiment, the close-
ness of the luting ought always to be previous-
ly tried, either by slightly heating the retort A
(Plate iv, Fig. l)j or by blowing in a little air
by some of the perpendicular tubes S s s s; the
alteration of pressure causes a change in the
level of the liquid in these tubes. If the appa-
ratus be accurately luted, this alteration of
level will be permanent; whereas, if there be
the smallest opening in any of the junctures,
the liquid will very soon recover its former lev-
el. It must always be remembered that the
whole success of experiments in modern chem-
istry depends upon the exactness of this oper-
ation, which therefore requires the utmost pa-
tience and most attentive accuracy.

It would be of infinite service to enable chem-
ists, especially those who are engaged in pneu-
matic processes, to dispense with the use of
lutes, or at least to diminish the number neces-
sary in complicated instruments. I once thought
of having my apparatus constructed so as to
unite in all its parts by fitting with emery, in
the way of bottles with crystal stoppers; but
the execution of this plan was extremely diffi-
cult. I have since thought it preferable to sub-
stitute columns of a few lines of mercury in
place of lutes, and have got an apparatus con-
structed upon this principle, which appears
capable of very convenient application in a
great number of circumstances.

It consists of a double necked bottle A (Plate
xn, Fig. 12} ; the interior neck be communi-
cates with the inside of the bottle, and the ex-
terior neck or rim de leaves an interval between
the two necks, forming a deep gutter intended
to contain the mercury. The cap or lid of glass
B enters this gutter and is properly fitted to it,
having notches in its lower edge for the passage
of the tubes which convey the gas. These tubes,
instead of entering directly into the bottles as
in the ordinary apparatus, have a double bend
for making them enter the gutter, as repre-

CHEMISTRY

117

sented in Fig. 18, and for making them fit the
notches of the cap B ; they rise again from the
gutter to enter the inside of the bottle over the
border of the inner mouth. When the tubes are
disposed in their proper places and the cap
firmly fitted on, the gutter is filled with mer-
cury, by which means the bottle is completely
excluded from any communication, excepting
through the tubes. This apparatus may be very
convenient in many operations in which the
substances employed have no action upon
mercury. Plate xn, Fig. 14, represents an ap-
paratus upon this principle properly fitted
together.

M. Seguin, to whose active and intelligent
assistance I have been very frequently much
indebted, has bespoken for me, at the glass-
houses, some retorts hermetically united to
their recipients, by which luting will be alto-
gether unnecessary.

CHAPTER VIII

Of Operations upon Combustion and Deflagra-
tion

SECTION I Of Combustion in General

COMBUSTION, according to what has been al-
ready said in the first part of this work, is the
decomposition of oxygen gas produced by a
combustible body. The oxygen which forms
the base of this gas is absorbed by and enters
into combination with the burning body, while
the caloric and light are set free. Every com-
bustion, therefore, necessarily supposes oxy-
genation; whereas, on the contrary, every oxy-
genation does not necessarily imply concomi-
tant combustion; because combustion, prop-
erly so called, cannot take place without dis-
engagement of caloric and light. Before com-
bustion can take place, it is necessary that the
base of oxygen gas should have greater affinity
to the combustible body than it has to caloric;
and this elective attraction, to use Bergman's
expression, can only take place at a certain de-
gree of temperature, which is different for each
combustible substance; hence the necessity of
giving a first motion or beginning to every com-
bustion by the approach of a heated body.
This necessity of heating any body we mean to
burn depends upon certain considerations,
which have not hitherto been attended to by any
natural philosopher, for which reason I shall
enlarge a little upon the subject in this place.
Nature is at present in a state of equilibrium,
which cannot have been attained until all the

spontaneous combustions or oxygenations pos-
sible in the ordinary degrees of temperature
had taken place. Hence, no new combustions
or oxygenations can happen without destroy-
ing this equilibrium and raising the combust-
ible substances to a superior degree of temper-
ature. To illustrate this abstract view of the
matter by example: let us suppose the usual
temperature of the earth a little changed, and
that it is raised only to the degree of boiling
water; it is evident that, in this case, phos-
phorus, which is combustible in a considerably
lower degree of temperature, would no longer
exist in nature in its pure and simple state but
would always be procured in its acid or oxy-
genated state, and its radical would become one
of the substances unknown to chemistry. By
gradually increasing the temperature of the
earth the same circumstance would successive-
ly happen to all the bodies capable of combus-
tion; and, at last, every possible combustion
having taken place, there would no longer ex-
ist any combustible body whatever, as every
substance susceptible of that operation would
be oxygenated and consequently incombust-
ible.

There cannot therefore exist, so far as relates
to us, any combustible body, except such as
are incombustible in the ordinary temperatures
of the earth; or, which is the same thing in
other words, that it is essential to the nature of
every combustible body not to possess the
property of combustion, unless heated, or raised
to the degree of temperature at which its com-
bustion naturally takes place. When this de-
gree is once produced, combustion commences,
and the caloric which is disengaged by the de-
composition of the oxygen gas keeps up the
temperature necessary for continuing combus-
tion. When this is not the case, that is, when
the disengaged caloric is insufficient for keep-
ing up the necessary temperature, the combus-
tion ceases. This circumstance is expressed in
common language by saying that a body burns
ill or with difficulty.

Although combustion possesses some circum-
stances in common with distillation, especially
with the compound kind of that operation, they
differ in a very material point. In distillation
there is a separation of one part of the elements
of the substance from each other, and a com-
bination of these in a new order, occasioned by
the affinities which take place in the increased
temperature produced during distillation. This
likewise happens in combustion, but with this
farther circumstance, that a new element, not

118

.LAVOISIER

originally in the body, is brought into action;
oxygen is added to the substance submitted to
the operation, and caloric is disengaged.

The necessity of employing oxygen in the
state of gas in all experiments with combustion,
and the rigorous determination of the quanti-
ties employed, render this kind of operations
peculiarly troublesome. As almost all the prod-
ucts of combustion are disengaged in the state
of gas, it is still more difficult to retain them
than even those furnished during compound
distillation; hence this precaution was entirely
neglected by the ancient chemists; and this set
of experiments exclusively belong to modern
chemistry.

Having thus pointed out, in a general way,
the objects to be had in view in experiments
upon combustion, I proceed, in the following
sections of this chapter, to describe the differ-
ent instruments I have used with this view.
The following arrangement is formed, not upon
the nature of the combustible bodies, but upon
that of the instruments necessary for combus-
tion.

SECTION II Of the Combustion of Phosphorus

In these combustions we begin by filling a
jar, capable at least of holding six pints, with
oxygen gas in the water apparatus (Plate v,
Fig. 1); when it is perfectly full, so that the gas
begins to flow out below, the jar, A, is carried
to the mercury apparatus (Plate iv, Fig. 3).
We then dry the surface of the mercury, both
within and without the jar, by means of blot-
ting-paper, taking care to keep the paper for
some time entirely immersed in the mercury
before it is introduced under the jar, lest we let
in any common air, which sticks very obsti-
nately to the surface of the paper. The body to
be submitted to combustion, being first very
accurately weighed in nice scales, is placed in
a small flat shallow dish, D, of iron or porce-
lain; this is covered by the larger cup P, which
serves the office of a diving bell, and the whole
is passed through the mercury into the jar,
after which the larger cup is retired. The diffi-
culty of passing the materials of combustion in
this manner through the mercury may be avoid-
ed by raising one of the sides of the jar, A, for
a moment, and slipping in the little cup, D,
with the combustible body as quickly as pos-
sible. In this manner of operating, a small quan-
tity of common air gets into the jar, but it is so
v&y inconsiderable as not to injure either the
progress or accuracy of the experiment in' any
sensible degree.

When the cup, D, is introduced under the
jar, we suck out a part of the oxygen gas, so as
to raise the mercury to EF, as formerly direct-
ed, Part I, Chapter V; otherwise, when the
combustible body is set on fire, the gas becom-
ing dilated would be in part forced out, and we
should no longer be able to make any accurate
calculation of the quantities before and after
the experiment. A very convenient mode of
drawing out the air is by means of an air-pump
syringe adapted to the siphon, GHI, by which
the mercury may be raised to any degree under
twenty-eight inches. Very inflammable bodies,
as phosphorus, are set on fire by means of the
crooked iron wire MN (Plate iv, Fig. 16) made
red hot and passed quickly through the mer-
cury. Such as are less easily set on fire have a
small portion of tinder, upon which a minute
particle of phosphorus is fixed, laid upon them
before using the red hot iron.

In the first moment of combustion the air,
being heated, rarifies, and the mercury de-
scends; but when, as in combustions of phos-
phorus and iron, no elastic fluid is formed, ab-
sorption becomes presently very sensible, and
the mercury rises high into the jar. Great at-
tention must be used not to burn too large a
quantity of any substance in a given quantity
of gas, otherwise, towards the end of the exper-
iment the cup would approach so near the top
of the jar as to endanger breaking it by the
great heat produced and the sudden refrigera-
tion from the cold mercury. For the methods
of measuring the volume of the gases, and for
correcting the measures according to the height
of the barometer and thermometer, &c., see
Chapter II, Sections V and VI of this part.

The above process answers very well for
burning all the concrete substances, and even
for the fixed oils. These last are burnt in lamps
under the jar and are readily set on fire by
means of tinder, phosphorus, and hot iron. But
it is dangerous for substances susceptible of
evaporating in a moderate heat, such as ether,
alcohol, and the essential oils; these substances
dissolve in considerable quantity in oxygen gas ;
and, when set on fire, a dangerous and sudden
explosion takes place, which carries up the jar
to a great height, and dashes it in a thousand
pieces. From two such explosions some of the
members of the Academy and myself escaped
very narrowly. Besides, though this manner of
operating is sufficient for determining pretty
accurately the quantity of oxygen gas absorbed
and of carbonic acid produced, as water is like-
wise formed in all experiments upon vegetable

CHEMISTRY

119

and animal matters which contain an excess of
hydrogen, this apparatus can neither collect it
nor determine its quantity. The experiment
with phosphorus is even incomplete in this way,
as it is impossible to demonstrate that the
weight of the phosphoric acid produced is equal
to the sum of the weights of the phosphorus
burnt and oxygen gas absorbed during the
process. I have been, therefore, obliged to vary
the instruments according to circumstances,
and to employ several of different kinds, which
I shall describe in their order, beginning with
that used for burning phosphorus.

Take a large balloon A (Plate iv, Fig. 4) of
crystal or white glass, with an opening, EF,
about two inches and a half or three inches di-
ameter, to which a cap of brass is accurately
fitted with emery, and which has two holes for
the passage of the tubes xxx,yyy. Before shut-
ting the balloon with its cover, place within it
the stand, BC, supporting the cup of porcelain
D, which contains the phosphorus. Then lute
on the cap with fat lute and allow it to dry for
some days and weigh the whole accurately;
after this exhaust the balloon by means of an
air-pump connected with the tube xxx, and
fill it with oxygen gas by the tube y y y, from
the gazometer (Plate vm, Fig. 1) described
Chapter II, Section II, of this part. The phos-
phorus is then set on fire by means of a burn-
ing-glass and is allowed to burn till the cloud
of concrete phosphoric acid stops the combus-
tion, oxygen gas being continually supplied
from the gazometer. When the apparatus has
cooled, it is weighed and unluted; the tare of
the instrument being allowed, the weight is that
of the phosphoric acid contained. It is proper,
for greater accuracy, to examine the air or gas
contained in the balloon after combustion, as
it may happen to be somewhat heavier or lighter
than common air; and this difference of weight
must be taken into account in the calculations
upon the results of the experiment.

SECTION III Of the Combustion of Charcoal

The apparatus I have employed for this proc-
ess consists of a small conical furnace of ham-
mered copper, represented in perspective, Plate
xn, Fig. 9, and internally displayed Fig. ll.lt
is divided into the furnace, ABC, where the
charcoal is burnt, the grate, de, and the ash-
hole, F; the tube, GH, in the middle of the
dome of the furnace serves to introduce the
charcoal, and as a chimney for carrying off the
air which has served for combustion. Through
the tube, Imn, which communicates with the

gazometer, the hydrogen gas, or air, intended
for supporting the combustion, is conveyed in-
to the ash-hole, F, whence it is forced, by the
application of pressure to the gazometer, to
pass through the grate, de, and to blow upon
the burning charcoal placed immediately above.

Oxygen gas, which forms 2 % o of atmospheric
air, is changed into carbonic acid gas during
combustion with charcoal, whilst the azotic
gas of the air is not altered at all. Hence, after
the combustion of charcoal in atmospheric air,
a mixture of carbonic acid gas and azotic gas
must remain; to allow this mixture to pass off,
the tube, o p, is adapted to the chimney, GH,
by means of a screw at G, and conveys the gas
into bottles half filled with solution of caustic
potash. The carbonic acid gas is absorbed by
the alkali, and the azotic gas is conveyed into
a second gazometer where its quantity is as-
certained.

The weight of the furnace, ABC, is first ac-
curately determined; then introduce the tube
RS, of known weight, by the chimney, GH, till
its lower end S rests upon the grate, de, which
it occupies entirely; in the next place, fill the
furnace with charcoal and weigh the whole
again, to know the exact quantity of charcoal
submitted to experiment. The furnace is now
put in its place, the tube, linn, is screwed to
that which communicates with the gazometer,
and the tube, o p, to that which communicates
with the bottles of alkaline solution. Every-
thing being in readiness, the stop-cock of the
gazometer is opened, a small piece of burning
charcoal is thrown into the tube, RS, which is
instantly withdrawn, and the tube, op, is
screwed to the chimney, GH. The little piece
of charcoal falls upon the grate, and in this
manner gets below the whole charcoal, and is
kept on fire by the stream of air from the ga-
zometer. To be certain that the combustion is
begun, and goes on properly, the tube, qrs, is
fixed to the furnace, having a piece of glass ce-
mented to its upper extremity, s, through which
we can see if the charcoal be on fire.

I neglected to observe above that the fur-
nace and its appendages are plunged in water
in the cistern TVXY (Plate xn, Fig. 11), to
which ice may be added to moderate the heat,
if necessary; though the heat is by no means
very considerable, as there is no air but what
comes from the gazometer, and no more of the
charcoal burns at one time than what is immed-
iately over the grate.

As one piece of charcoal is consumed another
falls down into its place, in consequence of the

120

LAVOISIER

declivity of the sides of the furnace; this gets
into the stream of air from the grate, de, and
is burnt; and so on, successively, till the whole
charcoal is consumed. The air which has served
the purpose of the combustion passes through
the mass of charcoal and is forced by the pres-
sure of the gazometer to escape through the
tube, op, and to pass through the bottles of
alkaline solution.

This experiment furnishes all the necessary
data for a complete analysis of atmospheric air
and of charcoal. We know the weight of char-
coal consumed; the gazometer gives us the
measure of the air employed ; the quantity and
quality of gas remaining after combustion may
be determined as it is received, either in an-
other gazometer, or in jars, in a pneumato-
chemical apparatus; the weight of ashes re-
maining in the ash-hole is readily ascertained ;
and, finally, the additional weight acquired
by the bottles of alkaline solution gives the
exact quantity of carbonic acid formed dur-
ing the process. By this experiment we may
likewise determine, with sufficient accuracy,
the proportions in which charcoal and oxy-
gen enter into the composition of carbonic
acid.

In a future M6moire I shall give an account
to the Academy of a series of experiments I
have undertaken with instrument upon all the
vegetable and animal charcoals. By some very
slight alterations, this machine may be made
to answer for observing the principal phenom-
ena of respiration.

SECTION IV Of the Combustion of Oils

Oils are more compound in their nature than
charcoal, being formed by the combination of
at least two elements, charcoal and hydrogen;
of course, after their combustion in common
air, water, carbonic acid gas, and azotic gas
remain. Hence the apparatus employed for
their combustion requires to be adapted
for collecting these three products, and is con-
sequently more complicated than the charcoal
furnace.

The apparatus I employ for this purpose is
composed of a large jar or pitcher A (Plate xn,
Fig. 4), surrounded at its upper edge by a rim
of iron properly cemented at DE and receding
from the jar at BC so as to leave a furrow or
gutter xx between it and the outside of the jar
somewhat more than two inches deep. The cover
or lid of the jar (Fig. 5) is likewise surrounded
by an iron rim/0, which adjusts into the gut-
ter xx (Fig. 4) which, being filled with mercury,

has the effect of closing the jar hermetically in
an instant, without using any lute; and, as the
gutter will hold about two inches of mercury,
the air in the jar may be made to sustain the
pressure of more than two feet of water, with-
out danger of its escaping.

The lid has four holes, Thik, for the pas-
sage of an equal number of tubes. The opening
T is furnished with a leather box, through which
passes the rod (Fig. 8) intended for raising and
lowering the wick of the lamp, as will be after-
wards directed. The three other holes are in-
tended for the passage of three several tubes,
one of which conveys the oil to the lamp, a sec-
ond conveys air for keeping up the combustion,
and the third carries off the air, after it has
served for combustion. The lamp in which the
oil is burnt is represented Fig. 2; a is the reser-
voir of oil, having a funnel by which it is filled ;
bcdefgh is a siphon which conveys the oil to
the lamp 11 ; 7, 8, 9, 10, is the tube which con-
veys the air for combustion from the gazom-
eter to the same lamp. The tube fee is formed
externally, at its lower end 6, into a male screw,
which turns in a female screw in the lid of the
reservoir of oil a; so that, by turning the reser-
voir one way or the other, it is made to rise or
fall, by which the oil is kept at the necessary
level.

When the siphon is to be filled, and the com-
munication formed between the reservoir of oil
and the lamp, the stop-cock c is shut and that
at e opened, oil is poured in by the opening/ at
the top of the siphon till it rises within three or
four lines of the upper edge of the lamp; the
stop-cock k is then shut and that at c opened;
the oil is then poured in at /, till the branch
bed of the siphon is filled, and then the stop-
cock e is closed. The two branches of the siphon
being now completely filled, a communication
is fully established between the reservoir and
the lamp.

In Plate xu, Fig. 1, all the parts of the lamp
11 (Fig. 2) are represented magnified, to show
them distinctly. The tube ik carries the oil
from the reservoir to the cavity a a a a, which
contains the wick; the tube 9, 10, brings the air
from the gazometer for keeping up the combus-
tion; this air spreads through the cavity dddd,
and, by means of the passages cccc and 6666,
is distributed on each side of the wick, after
the principles of the lamps constructed by Ar-
gand, Quinquet, and Lange.

To render the whole of this complicated ap-
paratus more easily understood, and that its
description may make all others of the same

CHEMISTRY

121

kind more readily followed, it is represented
completely connected together for use in Plate
xi. The gazometer P furnishes air for the com-
bustion by the tube and stop-cock 1, 2; the
tube 2, 3, communicates with a second gazom-
eter, which is filled whilst the first one is emp-
tying during the process, that there may be no
interruption to the combustion; 4, 5, is a tube
of glass filled with deliquescent salts, for drying
the air as much as possible in its passage; and
the weight of this tube and its contained salts,
at the beginning of the experiment being known,
it is easy to determine the quantity of water
absorbed by them from the air. From this deli-
quescent tube the air is conducted through the
pipe 5, 6, 7, 8, 9, 10, to the lamp 11, where it
spreads on both sides of the wick, as before de-
scribed, and feeds the flame. One part of this
air, which serves to keep up the combustion of
the oil, forms carbonic acid gas and water by
oxygenating its elements. Part of this water
condenses upon the sides of the pitcher A, and
another part is held in solution in the air by
means of caloric furnished by the combustion.
This air is forced by the compression of the ga-
zometer to pass through the tube 12, 13, 14,
15, into the bottle 16, and the worm 17, 18,
where the water is fully condensed from the
refrigeration of the air; and, if any water still
remains in solution, it is absorbed by deliques-
cent salts contained in the tube 19, 20.

All these precautions are solely intended for
collecting and determining the quantity of wa-
ter formed during the experiment ; the carbonic
acid and azotic gas remains to be ascertained.
The former is absorbed by caustic alkaline so-
lution in the bottles 22 and 25. 1 have only rep-
resented two of these in the figure, but nine at
least are requisite; and the last of the series may
be half filled with lime-water, which is the most
certain reagent for indicating the presence of
carbonic acid ; if the lime-water is not rendered
turbid, we may be certain that no sensible quan-
tity of that acid remains in the air.

The rest of the air which has served for com-
bustion, and which chiefly consists of azotic gas,
though still mixed with a considerable portion
of oxygen gas which has escaped unchanged
from the combustion, is carried through a third
tube 28, 29, of deliquescent salts, to deprive it
of any moisture it may have acquired in the
bottles of alkaline solution and lime-water, and
from thence by the tube 29, 30, into a gazom-
eter, where its quantity is ascertained. Small
essays are then taken from it, which are ex-
posed to a solution of sulphuret of potash, to

ascertain the proportions of oxygen and azotic
gas it contains.

In the combustion of oils the wick becomes
charred at last and obstructs the rise of the oil;
besides, if we raise the wick above a certain
height, more oil rises through its capillary tubes
than the stream of air is capable of consuming,
and smoke is produced. Hence it is necessary
to be able to lengthen or shorten the wick with-
out opening the apparatus; this is accomplished
by means of the rod 31, 32, 33, 34, which passes
through a leather-box and is connected with
the support of the wick; and that the motion
of this rod, and consequently of the wick, may
be regulated with the utmost smoothness and
facility, it is moved at pleasure by a pinion
which plays in a toothed rack. The rod, with
its appendages, are represented Plate xn, Fig.
8. It appeared to me that the combustion would
be assisted by surrounding the flame of the
lamp with a small glass jar open at both ends,
as represented in its place in Plate xi.

I shall not enter into a more detailed descrip-
tion of the construction of this apparatus, which
is still capable of being altered and modified in
many respects, but shall only add that when it
is to be used in experiment, the lamp and reser-
voir with the contained oil must be accurately
weighed, after which it is placed as before di-
rected and lighted; having then formed the
connection between the air in the gazometer
and the lamp, the external jar A (Plate xi) is
fixed over all and secured by means of the
board BC and two rods of iron which connect
this board with the lid and are screwed to it.
A small quantity of oil is burnt while the jar is
adjusting to the lid, and the product of that
combustion is lost; there is likewise a small
portion of air from the gazometer lost at the
same time. Both of these are of very inconsid-
erable consequence in extensive experiments,
and they are even capable of being valued in
our calculation of the results.

In a particular M6moire, I shall give an ac-
count to the Academy of the difficulties insep-
arable from this kind of experiment. These are
so insurmountable and troublesome that I have
not hitherto been able to obtain any rigorous
determination of the quantities of the products.
I have sufficient proof, however, that the fixed
oils are entirely resolved during combustion
into water and carbonic acid gas, and conse-
quently that they are composed of hydro-
gen and charcoal; but I have no certain know-
ledge respecting the proportions of these in-
gredients.

122

LAVOISIER

SECTION V Of the Combustion of Alcohol

The combustion of alcohol may be very read-
ilyperformedintheapparatusalreadydescribed
for the combustion of charcoal and phosphorus.
A lamp filled with alcohol is placed under the
jar A (Plate iv, Fig. #), a small morsel of phos-
phorus is placed upon the wick of the lamp,
which is set on fire by means of the hot iron, as
before directed. This process is, however, liable
to considerable inconvenience; it is dangerous
to make use of oxygen gas at the beginning of
the experiment for fear of deflagration, which
is even liable to happen when common air is
employed. An instance of this had very near
proved fatal to myself, in presence of some
members of the Academy. Instead of preparing
the experiment, as usual, at the time it was to
be performed, I had disposed everything in or-
der the evening before; the atmospheric air of
the jar had thereby sufficient time to dissolve a
good deal of the alcohol ; and this evaporation
had even been considerably promoted by the
height of the column of mercury, which I had
raised to EF (Plate iv, Fig. 3). The moment I
attempted to set the little morsel of phosphorus
on fire by means of the red hot iron, a violent
explosion took place, which threw the jar with
great violence against the floor of the labora-
tory and dashed it in a thousand pieces.

Hence we can only operate upon very small
quantities, such as ten or twelve grains of alco-
hol, in this manner; and the errors which may
be committed in experiments upon such small
quantities prevents our placing any confidence
in their results. I endeavoured to prolong the
combustion, in the experiments contained in
the Recueil de I' Academic for 1784, p. 593, by
lighting the alcohol first in common air and
furnishing oxygen gas afterwards to the jar, in
proportion as it consumed; but the carbonic
acid gas produced by the process became a
great hinderance to the combustion, the more
so that alcohol is but difficultly combustible,
especially in worse than common air; so that
even in this way very small quantities only
could be burnt.

Perhaps this combustion might succeed bet-
ter in the oil apparatus (Plate xi) ; but I have
not hitherto ventured to try it. The jar A in
which the combustion is performed is near 1400
cubic inches in dimension; and, were an explo-
sion to take place in such a vessel, its conse-
quences would be very terrible and very diffi-
cult to guard against. I have not, however, de-
spaired of making the attempt.

From all these difficulties, I have been hith-
erto obliged to confine myself to experiments
upon very small quantities of alcohol, or at
least to combustions made in open vessels, such
as that represented in Plate ix, Fig. 5, which
will be described in Section VII of this chapter.
If I am ever able to remove these difficulties, I
shall resume this investigation.

SECTION VI Of the Combustion of Ether

Tho' the combustion of ether in close vessels
does not present the same difficulties as that of
alcohol, yet it involves some of a different kind,
not more easily overcome, and which still pre-
vent the progress of my experiments. I endeav-
oured to profit by the property which ether
possesses of dissolving in atmospheric air and
rendering it inflammable without explosion. For
this purpose, I constructed the reservoir of
ether abed (Plate xu, Fig. #)> to which air is
brought from the gazometer by the tube 1, 2,
3, 4. This air spreads, in the first place, in the
double lid ac of the reservoir, from which it
passes through seven tubes e/, gh, ik, &c., which
descend to the bottom of the ether, and it is
forced by the pressure of the gazometer to boil
up through the ether in the reservoir. We may
replace the ether in this first reservoir, in pro-
portion as it is dissolved and carried off by the
air, by means of the supplementary reservoir
E, connected by a brass tube fifteen or eighteen
inches long and shut by a stop-cock. This length
of the connecting tube is to enable the descend-
ing ether to overcome the resistance occasioned
by the pressure of the air from the gazometer.

The air, thus loaded with vapours of ether,
is conducted by the tube 5, 6, 7, 8, 9, to the jar
A, into which it is allowed to escape through a
capillary opening, at the extremity of which it
is set on fire. The air, when it has served the
purpose of combustion, passes through the bot-
tle 16 (Plate xi), the worm 17, 18, and the deli-
quescent tube 19, 20, after which it passes
through the alkaline bottles; in these its car-
bonic acid gas is absorbed, the water formed
during the experiment having been previously
deposited in the former parts of the apparatus.

When I caused this apparatus constructed, I
supposed that the combination of atmospheric
air and ether formed in the reservoir abed
(Plate xu, Fig. 8) was in proper proportion for
supporting combustion; but in this I was mis-
taken; for there is a very considerable quantity
of excess of ether; so that an additional quan-
tity of atmospheric air is necessary to enable it
to burn fully. Hence a lamp constructed upon

CHEMISTRY

123

these principles will burn in common air, which
furnishes the quantity of oxygen necessary for
combustion, but will not burn in close vessels
in which the air is not renewed. From this cir-
cumstance, my ether lamp went out soon after
being lighted and shut up in the jar A (Plate
xn, Fig. 8). To remedy this defect, I endeav-
oured to bring atmospheric air to the lamp by
the lateral tube 10, 11, 12, 13, 14, 15, which I
distributed circularly round the flame; but the
flame is so exceedingly rare that it is blown out
by the gentlest possible stream of air, so that I
have not hitherto succeeded in burning ether.
I do not, however, despair of being able to ac-
complish it by means of some changes I am
about to have made upon this apparatus.

SECTION VII Of the Combustion of Hydrogen
Gas and the Formation of Water

In the formation of water, two substances,
hydrogen and oxygen, which are both in the
aeriform state before combustion, are trans-
formed into liquid or water by the operation.
This experiment would be very easy and would
require very simple instruments, if it were pos-
sible to procure the two gases perfectly pure,
so that they might burn without any residuum.
We might, in that case, operate in very small
vessels and, by continually furnishing the two
gases in proper proportions, might continue the
combustion indefinitely. But, hitherto, chem-
ists have only employed oxygen gas mixed with
azotic gas; from which circumstance, they have
only been able to keep up the combustion of
hydrogen gas for a very limited time in close
vessels, because, as the residuum of azotic gas
is continually increasing, the air becomes at
last so much contaminated that the flame weak-
ens and goes out. This inconvenience is so much
the greater in proportion as the oxygen gas em-
ployed is less pure. From this circumstance, we
must either be satisfied with operating upon
small quantities or must exhaust the vessels at
intervals, to get rid of the residuum of azotic
gas; but, in this case, a portion of the water
formed during the experiment is evaporated by
the exhaustion; and the resulting error is the
more dangerous to the accuracy of the process,
so that we have no certain means of valuing it.

These considerations make me desirous to
repeat the principal experiments of pneumatic
chemistry with oxygen gas entirely free from
any admixture of azotic gas; and this may be
procured from oxygenated muriate of potash.
The oxygen gas extracted from this salt does
not appear to contain azote, unless accident-

ally, so that, by proper precautions, it may be
obtained perfectly pure. In the mean time, the
apparatus employed by M. Meusnier and me
for the combustion of hydrogen gas, which is
described in the experiment for recornposition
of water, Part I, Chapter VIII, and need not
be here repeated, will answer the purpose ; when
pure gases are procured, this apparatus will re-
quire no alterations, except that the capacity
of the vessels may then be diminished. See
Plate iv, Fig. 5.

The combustion, when once begun, continues
for a considerable time but weakens gradually,
in proportion as the quantity of azotic gas re-
maining from the combustion increases, till at
last the azotic gas is in such over proportion
that the combustion can no longer be support-
ed, and the flame goes out. This spontaneous
extinction must be prevented, because, as the
hydrogen gas is pressed upon in its reservoir,
by an inch and a half of water, whilst the oxy-
gen gas suffers a pressure only of three lines,
a mixture of the two would take place in the
balloon, which would at last be forced by the
superior pressure into the reservoir of oxygen
gas. Wherefore the combustion must be stop-
ped by shutting the stop-cock of the tube dDd
whenever the flame grows very feeble; for
which purpose it must be attentively watched.

There is another apparatus for combustion,
which, though we cannot with it perform ex-
periments with the same scrupulous exactness
as with the preceding instruments, gives very
striking results that are extremely proper to be
shown in courses of philosophical chemistry. It
consists of a worm EF (Plate ix, Fig. 5) con-
tained in a metallic cooler ABCD. To the up-
per part of this worm E, the chimney GH is
fixed, which is composed of two tubes, the in-
ner of which is a continuation of the worm, and
the outer one is a case of tin-plate, which sur-
rounds it at about an inch distance, and the in-
terval is filled up with sand. At the inferior ex-
tremity K of the inner tube, a glass tube is
fixed, to which we adopt the Argand lamp LM
for burning alcohol, &c.

Things being thus disposed, and the lamp
being filled with a determinate quantity of al-
cohol, it is set on fire ; the water which is formed
during the combustion rises in the chimney KE,
and, being condensed in the worm, runs out at
its extremity F into the bottle P. The double
tube of the chimney, filled with sand in the in-
terstice, is to prevent the tube from cooling in
its upper part and condensing the water; other-
wise, it would fall back in the tube, and we

124

LAVOISIER

should not be able to ascertain its quantity,
and besides it might fall in drops upon the wick
and extinguish the flame. The intention of this
construction is to keep the chimney always hot
and the worm always cool, that the water may
be preserved in the state of vapour whilst ris-
ing and may be condensed immediately upon
getting into the descending part of the appara-
tus. By this instrument, which was contrived
by M. Meusnier, and which is described by
me in the Eecueil de I'Academie for 1784, p.
593, we may, with attention to keep the worm
always cold, collect nearly seventeen ounces of
water from the combustion of sixteen ounces
of alcohol.

SECTION VIII Of the Oxidation of Metals

The term oxidation or calcination is chiefly
used to signify the process by which metals ex-
posed to a certain degree of heat are converted
into oxides by absorbing oxygen from the air.
This combination takes place in consequence
of oxygen possessing a greater affinity to met-
als, at a certain temperature, than to caloric,
which becomes disengaged in its free state ; but,
as this disengagement, when made in common
air, is slow and progressive, it is scarcely evi-
dent to the senses. It is quite otherwise, how-
ever, when oxidation takes place in oxygen gas;
for, being produced with much greater rapidity,
it is generally accompanied with heat and light,
so as evidently to show that metallic substances
are real combustible bodies.

All the metals have not the same degree of
affinity to oxygen. Gold, silver, and platinum,
for instance, are incapable of taking it away
from its combination with caloric, even in the
greatest known heat ; whereas the other metals
absorb it in a larger or smaller quantity, until
the affinities of the metal to oxygen, and of the
latter to caloric, are in exact equilibrium. In-
deed, this state of equilibrium of affinities may
be assumed as a general law of nature in all
combinations.

In all operations of this nature, the oxidation
of metals is accelerated by giving free access to
the air; it is sometimes much assisted by join-
ing the action of a bellows, which directs a
stream of air over the surface of the metal. This
process becomes greatly more rapid if a stream
of oxygen gas be used, which is readily done by
means of the gazometer formerly described. The
metal, in this case, throws out a brilliant flame,
and the oxidation is very quickly accomplished ;
but this method can only be used in very con-
fined experiments, on account of the expense of

procuring oxygen gas. In the essay of ores, and
in all the common operations of the laboratory,
the calcination or oxidation of metals is usual-
ly performed in a dish of baked clay (Plate iv,
Fig. 6), commonly called a roasting test, placed
in a strong furnace. The substances to be oxi-
dated are frequently stirred, on purpose to pre-
sent fresh surfaces to the air.

Whenever this operation is performed upon
a metal which is not volatile, and from which
nothing flies off into the surrounding air during
the process, the metal acquires additional
weight; but the cause of this increased weight
during oxidation could never have been discov-
ered by means of experiments performed in free
air; and it is only since these operations have
been performed in close vessels, and in deter-
minate quantities of air, that any just conjec-
tures have been formed concerning the cause of
this phenomenon. The first method for this
purpose is due to Dr. Priestley, who exposes the
metal to be calcined in a porcelain cup N (Plate
iv, Fig. 11), placed upon the stand IK, under
a jar A, in the basin BCDE, full of water; the
water is made to rise up to GH, by sucking out
the air with a siphon, and the focus of a burn-
ing glass is made to fall upon the metal. In a
few minutes the oxidation takes place, a part of
the oxygen contained in the air combines with
the metal, and a proportional diminution of the
volume of air is produced; what remains is
nothing more than azotic gas, still however
mixed with a small quantity of oxygen gas. I
have given an account of a series of experiments
made with this apparatus in my Physical and
Chemical Essays, first published in 1773. Mer-
cury may be used instead of water in this ex-
periment, whereby the results are rendered still
more conclusive.

Another process for this purpose was invent-
ed by M. Boyle, of which I gave an account in
the Eecueil de VAcad6mie for 1774, p. 351. The
metal is introduced into a retort (Plate in, Fig.
20), the beak of which is hermetically sealed;
the metal is then oxidated by means of heat ap-
plied with great precaution. The weight of the
vessel and its contained substances is not at ail
changed by this process, until the extremity of
the neck of the retort is broken; but, when that
is done, the external air rushes in with a hissing
noise. This operation is attended with danger,
unless a part of the air is driven out of the re-
tort by means of heat before it is hermetically
sealed, as otherwise the retort would be apt to
burst by the dilation of the air when placed in
the furnace. The quantity of air driven out

CHEMISTRY

125

may be received under a jar in the pneumato-
chemical apparatus, by which its quantity and
that of the air remaining in the retort is ascer-
tained. I have not multiplied my experiments
upon oxidation of metals so much as I could
have wished; neither have I obtained satisfac-
tory results with any metal except tin. It is
much to be wished that some person would
undertake a series of experiments upon oxida-
tion of metals in the several gases; the subject
is important and would fully repay any trouble
which this kind of experiment might occasion.

As all the oxides of mercury are capable of
revivifying without addition and restore the
oxygen gas they had before absorbed, this seem-
ed to be the most proper metal for becoming the
subject of conclusive experiments upon oxida-
tion. I formerly endeavoured to accomplish the
oxidation of mercury in close vessels, by filling
a retort, containing a small quantity of mer-
cury, with oxygen gas, and adapting a bladder
half full of the same gas to its beak; See Plate
iv, Fig. 12. Afterwards, by heating the mer-
cury in the retort for a very long time, I suc-
ceeded in oxidating a very small portion, so as
to form a little red oxide floating upon the sur-
face of the running mercury; but the quantity
was so small that the smallest error committed
in the determination of the quantities of oxy-
gen gas before and after the operation must
have thrown very great uncertainty upon the
results of the experiment. I was, besides, dis-
satisfied with this process, and not without
cause, lest any air might have escaped through
the pores of the bladder, more especially as it
becomes shrivelled by the heat of the furnace
unless covered over with cloths kept constant-
ly wet.

This experiment is performed with more cer-
tainty in the apparatus described in the Recueil
de I'Acadtmie for 1775, p. 580. This consists of
a retort A (Plate iv, Fig. 2), having a crooked
glass tube BCDE of ten or twelve lines internal
diameter melted on to its beak, and which is
engaged under the bell glass FG, standing with
its mouth downwards in a basin filled with wa-
ter or mercury. The retort is placed upon the
bars of the furnace MMNN (Plate iv, Fig. 2),
or in a sand bath, and by means of this appa-
ratus we may, in the course of several days,
oxidate a small quantity of mercury in com-
mon air; the red oxide floats upon the surface,
from which it may be collected and revivified,
so as to compare the quantity of oxygen gas
obtained in revivification with the absorption
which took place during oxidation. This kind

of experiment can only be performed upon a
small scale, so that no very certain conclusions
can be drawn from them. 1

The combustion of iron in oxygen gas being
a true oxidation of that metal, ought to be men-
tioned in this place. The apparatus employed
by M. Ingenhousz for this operation is repre-
sented in Plate iv, Fig. 17; but, having already
described it sufficiently in Chapter III, I shall
refer the reader to what is said of it in that
place. Iron may likewise be oxidated by com-
bustion in vessels filled with oxygen gas, in the
way already directed for phosphorus and char-
coal. This apparatus is represented in Plate iv,
Fig. 8, and described in the fifth chapter of the
first part of this work. We learn from M. In-
genhousz that all the metals, except gold, sil-
ver, and mercury, may be burnt or oxidated in
the same manner, by reducing them into very
fine wire or very thin plates cut into narrow
slips; these are twisted round with iron-wire,
which communicates the property of burning
to the other metals.

Mercury is even with difficulty oxidated in
free air. In chemical laboratories, this process
is usually carried on in a matrass A (Plate iv,
Fig. 10), having a very flat body and a very
long neck BC, which vessel is commonly called
Boyle 1 s hell. A quantity of mercury is intro-
duced sufficient to cover the bottom, and it is
placed in a sand bath, which keeps up a con-
stant heat approaching to that of boiling mer-
cury. By continuing this operation with five or
six similar matrasses during several months,
and renewing the mercury from time to time, a
few ounces of red oxide are at last obtained.
The great slowness and inconvenience of this
apparatus arises from the air not being suffici-
ently renewed; but if, on the other hand, too
free a circulation were given to the external air,
it would carry off the mercury in solution in
the state of vapour, so that in a few days none
would remain in the vessel.

As, of all the experiments upon the oxidation
of metals, those with mercury are the most
conclusive, it were much to be wished that a
simple apparatus could be contrived by which
this oxidation and its results might be demon-
strated in public courses of chemistry. This
might, in my opinion, be accomplished by meth-
ods similar to those I have already described
for the combustion of charcoal and the oils ; but,
from other pursuits, I have not been able hith-
erto to resume this kind of experiment.

See an account of this experiment, Part I, Chap-
ter III. AUTHOB.

126

LAVOISIER

The oxide of mercury revives without addi-
tion, by being heated to a slightly red heat. In
this degree of temperature, oxygen has greater
affinity to caloric than to mercury, and forms
oxygen gas. This is always mixed with a small
portion of azotic gas, which indicates that the
mercury absorbs a small portion of this latter
gas during oxidation. It almost always con-
tains a little carbonic acid gas, which must un-
doubtedly be attributed to the foulnesses of the
oxide; these are charred by the heat, and con-
vert a part of the oxygen gas into carbonic acid.

If chemists were reduced to the necessity of
procuring all the oxygen gas employed in their
experiments from mercury oxidated by heat
without addition, or, as it is called, calcined or
precipitated per se y the excessive dearness of that
preparation would render experiments, even
upon a moderate scale, quite impracticable.
But mercury may likewise be oxidated by means
of nitric acid; and in this way we procure a red
oxide even more pure than that produced by
calcination. I have sometimes prepared this ox-
ide by dissolving mercury in nitric acid, evap-
orating to dryness, and calcining the salt, either
in a retort or in capsules formed of pieces of
broken matrasses and retorts, in the manner
formerly described; but I have never succeed-
ed in making it equally beautiful with what is
sold by the druggists, and which is, I believe,
brought from Holland. In choosing this, we
ought to prefer what is in solid lumps composed
of soft adhering scales, as when in powder it is
sometimes adulterated with red oxide of lead.

To obtain oxygen gas from the red oxide of
mercury, I usually employ a porcelain retort
having a long glass tube adapted to its beak,
which is engaged under jars in the water pneu-
mato-chemical apparatus, and I place a bottle
in the water, at the end of the tube, for receiv-
ing the mercury, in proportion as it revives and
distils over. As the oxygen gas never appears
till the retort becomes red, it seems to prove
the principle established by M. Berthollet that
an obscure heat can never form oxygen gas and
that light is one of its constituent elements. We
must reject the first portion of gas which comes
over as being mixed with common air, from
what was contained in the retort at the begin-
ning of the experiment; but, even with this
precaution, the oxygen gas procured is usually
contaminated with a tenth part of azotic gas
and with a very small portion of carbonic acid
gas. This latter is readily got rid of, by making
the gas pass through a solution of caustic alka-
li; but we know of no method for separating the

azotic gas; its proportions may however be as-
certained, by leaving a known quantity of the
oxygen gas contaminated with it for a fort-
night, in contact with sulphuret of soda or pot-
ash, which absorbs the oxygen gas so as to con-
vert the sulphur into sulphuric acid and leaves
the azotic gas remaining pure.

We may likewise procure oxygen gas from
black oxide of manganese or nitrate of potash,
by exposing them to a red heat in the appara-
tus already described for operating upon red
oxide of mercury; only, as it requires such a
heat as is at least capable of softening glass, we
must employ retorts of stone or of porcelain.
But the purest and best oxygen gas is what is
disengaged from oxygenated muriate of potash
by simple heat. This operation is performed in
a glass retort, and the gas obtained is perfectly
pure, provided that the first portions, which
are mixed with the common air of the vessels,
be rejected.

CHAPTER IX

Of Deflagration

I HAVE already shown, Part I, Chapter IX,
that oxygen does not always part with the
whole of the caloric it contained in the state of
gas when it enters into combination with other
bodies. It carries almost the whole of its caloric
alongst with it in entering into the combina-
tions which form nitric acid and oxygenated
muriatic acid; so that in nitrates, and more es-
pecially in oxygenated muriates, the oxygen is,
in a certain degree, in the state of oxygen gas,
condensed, and reduced to the smallest volume
it is capable of occupying.

In these combinations, the caloric exerts a
constant action upon the oxygen to bring it
back to the state of gas; hence the oxygen ad-
heres but very slightly, and the smallest addi-
tional force is capable of setting it free; and,
when such force is applied, it often recovers the
state of gas instantaneously. This rapid passage
from the solid to the aeriform state is called
detonation, or f ulmination, because it is usually
accompanied with noise and explosion. Defla-
grations are commonly produced by means of
combinations of charcoal either with nitre or
oxygenated muriate of potash; sometimes, to
assist the inflammation, sulphur is added; and,
upon the just proportion of these ingredients,
and the proper manipulation of the mixture,
depends the art of making gun-powder.

As oxygen is changed, by deflagration with
charcoal, into carbonic acid, instead of oxygen

CHEMISTRY

127

gas, carbonic acid gas is disengaged, at least
when the mixture has been made in just pro-
portions. In deflagration with nitre, azotic gas
is likewise disengaged, because azote is one of
the constituent elements of nitric acid.

The sudden and instantaneous disengage-
ment and expansion of these gases is not, how-
ever, sufficient for explaining all the phenom-
ena of deflagration; because, if this were the
sole operating power, gun-powder would always
be so much the stronger in proportion as the
quantity of gas disengaged in a given time was
the more considerable, which does not always
accord with experiment. I have tried some kinds
which produced almost double the effect of or-
dinary gun-powder, although they gave out a
sixth part less of gas during deflagration. It
would appear that the quantity of caloric dis-
engaged at the moment of detonation contrib-
utes considerably to the expansive effects pro-
duced; for, although caloric penetrates freely
through the pores of every body in nature, it
can only do so progressively, and in a given
time; hence, when the quantity disengaged at
once is too large to get through the pores of
the surrounding bodies, it must necessarily act
in the same way with ordinary elastic fluids
and overturn everything that opposes its pas-
sage. This must, at least in part, take place
when gun-powder is set on fire in a cannon; as,
although the metal is permeable to caloric, the
quantity disengaged at once is too large to find
its way through the pores of the metal, it must
therefore make an effort to escape on every
side ; and, as the resistance all around, excepting
towards the muzzle, is too great to be overcome,
this effort is employed for expelling the bullet.

The caloric produces a second effect, by
means of the repulsive force exerted between
its particles ; it causes the gases, disengaged at
the moment of deflagration, to expand with a
degree of force proportioned to the tempera-
ture produced.

It is very probable that water is decomposed
during the deflagration of gun-powder, and that
part of the oxygen furnished to the nascent car-
bonic acid gas is produced from it. If so, a con-
siderable quantity of hydrogen gas must be
disengaged in the instant of deflagration which
expands and contributes to the force of the ex-
plosion. It may readily be conceived how great-
ly this circumstance must increase the effect of
powder, if we consider that a pint of hydrogen
gas weighs only one grain and two thirds ; hence
a very small quantity in weight must occupy a
very large space, and it must exert a prodigious

expansive force in passing from the liquid to
the aeriform state of existence.

In the last place, as a portion of undecom-
posed water is reduced to vapour during the
deflagration of gun-powder, and as water, in
the state 'of gas, occupies seventeen or eighteen
hundred times more space than in its liquid
state, this circumstance must likewise contrib-
ute largely to the explosive force of the powder.

I have already made a considerable series of
experiments upon the nature of the elastic fluids
disengaged during the deflagration of nitre with
charcoal and sulphur, and have made some,
likewise, with the oxygenated muriate of pot-
ash. This method of investigation leads to tol-
erably accurate conclusions with respect to the
constituent elements of these salts. Some of
the principal results of these experiments, and
of the consequences drawn from them respect-
ing the analysis of nitric acid, are reported in
the collection of Mtmoires presented to the
Academy by foreign philosophers, Vol. XI, p.
625. Since then I have procured more conven-
ient instruments, and I intend to repeat these
experiments upon a larger scale, by which I
shall procure more accurate precision in their
results ; the following, however, is the process I
have hitherto employed. I would very earnest-
ly advise such as intend to repeat some of these
experiments to be very much upon their guard
in operating upon any mixture which contains
nitre, charcoal, and sulphur, and more especi-
ally with those in which oxygenated muriate of
potash is mixed with these two materials.

I make use of pistol barrels, about six inches
long and of five or six lines diameter, having
the touch-hole spiked up with an iron nail
strongly driven in and broken in the hole, and
a little tin-smith's solder run in to prevent any
possible issue for the air. These are charged
with a mixture of known quantities of nitre and
charcoal, or any other mixture capable of de-
flagration, reduced to an impalpable powder
and formed into a paste with a moderate quan-
tity of water. Every portion of the materials
introduced must be rammed down with a ram-
mer nearly of the same caliber with the barrel,
four or five lines at the muzzle must be left
empty, and about two inches of quick match
are added at the end of the charge. The only
difficulty in this experiment, especially when
sulphur is contained in the mixture, is to dis-
cover the proper degree of moistening; for, if
the paste be too much wetted, it will not take
fire, and if too dry, the deflagration is apt to
become too rapid and even dangerous.

128

LAVOISIER

When the experiment is not intended to be
rigorously exact, we set fire to the match, and,
when it is just about to communicate with the
charge, we plunge the pistol below a large bell-
glass full of water in the pneumato-chemical
apparatus. The deflagration begins and con-
tinues in the water, and gas is disengaged with
less or more rapidity, in proportion as the mix-
ture is more or less dry. So long as the defla-
gration continues, the muzzle of the pistol must
be kept somewhat inclined downwards, to pre-
vent the water from getting into its barrel. In
this manner I have sometimes collected the gas
produced from the deflagration of an ounce and
half, or two ounces, of nitre.

In this manner of operating it is impossible
to determine the quantity of carbonic acid gas
disengaged, because a part of it is absorbed by
the water while passing through it; but, when
the carbonic acid is absorbed, the azotic gas re-
mains; and, if it be agitated for a few minutes
in caustic alkaline solution, we obtain it pure
and can easily determine its volume and weight.
We may even, in this way, acquire a tolerably
exact knowledge of the quantity of carbonic
acid by repeating the experiment a great many
times, and varying the proportions of charcoal,
till we find the exact quantity requisite to defla-
grate the whole nitre employed. Hence, by
means of the weight of charcoal employed, we
determine the weight of oxygen necessary for
saturation and deduce the quantity of oxygen
contained in a given weight of nitre.

I have used another process, by which the
results of this experiment are considerably more
accurate, which consists in receiving the disen-
gaged gases in bell-glasses filled with mercury.
The mercurial apparatus I employ is large
enough to contain jars of from twelve to fifteen
pints in capacity, which are not very readily
managed when full of mercury and even re-
quire to be filled by a particular method. When
the jar is placed in the cistern of mercury, a
glass siphon is introduced, connected with a
small air-pump by means of which the air is
exhausted, and the mercury rises so as to fill
the jar. After this, the gas of the deflagration
is made to pass into the jar in the same manner
as directed when water is employed.

I must again repeat that this species of ex-
periment requires to be performed with the
greatest possible precautions. I have sometimes
seen, when the disengagement of gas proceeded
with too great rapidity, jars filled with more
than an hundred and fifty pounds of mercury
driven off by the force of the explosion and

broken to pieces, while the mercury was scat-
tered about in great quantities.

When the experiment has succeeded and the
gas is collected under the jar, its quantity in
general, and the nature and quantities of the
several species of gases of which the mixture is
composed, are accurately ascertained by the
methods already pointed out in the second chap-
ter of this part of my work. I have been pre-
vented from putting the last hand to the exper-
iments I had begun upon deflagration, from
their connection with the objects I am at pres-
ent engaged in; and I am in hopes they will
throw considerable light upon the operations
belonging to the manufacture of gun-powder.

CHAPTER X

Of the Instruments Necessary for Operating upon
Bodies in Very High Temperatures

SECTION I Of Fusion

WE have already seen that, by aqueous solu-
tion in which the particles of bodies are sepa-
rated from each other, neither the solvent nor
the body held in solution are at all decomposed ;
so that, whenever the cause of separation ceases,
the particles reunite, and the saline substance
recovers precisely the same appearance and
properties it possessed before solution. Real
solutions are produced by fire, or by introduc-
ing and accumulating a great quantity of caloric
between the particles of bodies ; and this species
of solution in caloric is usually called fusion.

This operation is commonly performed in
vessels called crucibles, which must necessarily
be less fusible than the bodies they are intend-
ed to contain. Hence, in all ages, chemists have
been extremely solicitous to procure crucibles
of very refractory materials, or such as are ca-
pable of resisting a very high degree of heat.
The best are made of very pure clay or of porce-
lain earth; whereas such as are made of clay
mixed with calcareous or silicious earth are very
fusible. All the crucibles made in the neighbour-
hood of Paris are of this kind and consequent-
ly unfit for most chemical experiments. The
Hessian crucibles are tolerably good; but the
best are made of Limoges earth, which seems
absolutely infusible. We have, in France, a
great many clays very fit for making crucibles;
such, for instance, is the kind used for making
melting-pots at the glass-manufactory of St.
Gobin.

Crucibles are made of various forms, accord-
ing to the operations they are intended to per-

CHEMISTRY

129

form. Several of the most common kinds are
represented Plate vn, Figs. 7, 8, 9, and 10; the
one represented at Fig. 9 is almost shut at its
mouth.

Though fusion may often take place without
changing the nature of the fused body, this op-
eration is frequently employed as a chemical
means of decomposing and recompounding bod-
ies. In this way all the metals are extracted
from their ores; and, by this process, they are
revivified, moulded, and alloyed with each oth-
er. By this process sand and alkali are combined
to form glass, and by it likewise pastes, or col-
oured stones, enamels, &c. are formed.

The action of violent fire was much more
frequently employed by the ancient chemists
than it is in modern experiments. Since greater
precision has been employed in philosophical
researches, the humid has been preferred to the
dry method of process, and fusion is seldom
had recourse to until all the other means of
analysis have failed.

SECTION II Of Furnaces

These are instruments of most universal use
in chemistry; and, as the success of a great
number of experiments depends upon their be-
ing well or ill constructed, it is of great import-
ance that a laboratory be well provided in this
respect. A furnace is a kind of hollow cylindri-
cal tower, sometimes widened above (Plate
xiu, Fig. 1). ABCD, which must have at least
two lateral openings; one in its upper part F,
which is the door of the fire-place, and one be-
low G, leading to the ash-hole. Between these
the furnace is divided by a horizontal grate, in-
tended for supporting the fuel, the situation of
which is marked in the figure by the line HI.
Though this be the least complicated of all the
chemical furnaces, yet it is applicable to a great
number of purposes. By it lead, tin, bismuth,
and, in general, every substance which does
not require a very strong fire, may be melted in
crucibles; it will serve for metallic oxidations,
for evaporatory vessels, and for sand baths, as
in Plate in, Figs. 1 and 2. To render it proper
for these purposes, several notches, mm mm
(Plate xin, Fig. 1), are made in its upper edge,
as otherwise any pan which might be placed
over the fire would stop the passage of the air,
and prevent the fuel from burning. This fur-
nace can only produce a moderate degree of
heat, because the quantity of charcoal it is
capable of consuming is limited by the quan-
tity of air which is allowed to pass through the
opening G of the ash-hole. Its power might be

considerably augmented by enlarging this op-
ening, but then the great stream of air which is
convenient for some operations might be hurt-
ful in others; wherefore we must have furnaces
of different forms, constructed for different pur-
poses, in our laboratories. There ought espe-
cially to be several of the kind now described
of different sizes.

The reverberatory furnace (Plate xin, Fig.
2) is perhaps more necessary. This, like the
common furnace, is composed of the ash-hole
HIKL, the fire-place KLMN, the laboratory
MNOP, and the dome RRSS, with its funnel
or chimney TTVV; and to this last several ad-
ditional tubes may be adapted, according to
the nature of the different experiments. The
retort A is placed in the division called the lab-
oratory and supported by two bars of iron
which run across the furnace, and its beak
comes out at a round hole in the side of the
furnace, one half of which is cut in the piece
called the laboratory and the other in the dome.
In most of the ready-made reverberatory fur-
naces which are sold by the potters at Paris,
the openings both above and below are too
small. These do not allow a sufficient volume
of air to pass through; hence, as the quantity
of charcoal consumed, or, which is much the
same thing, the quantity of caloric disengaged
is nearly in proportion to the quantity of air
which passes through the furnace, these fur-
naces do not produce a sufficient effect in a
great number of experiments. To remedy this
defect, there ought to be two openings GG to
the ash-hole; one of these is shut up when only
a moderate fire is required ; and both are kept
open when the strongest power of the furnace
is to be exerted. The opening of the dome SS
ought likewise to be considerably larger than
is usually made.

It is of great importance not to employ re-
torts of too large size in proportion to the fur-
nace, as a sufficient space ought always to be
allowed for the passage of the air between the
sides of the furnace and the vessel. The retort
A in the figure is too small for the size of the
furnace, yet I find it more easy to point out the
error than to correct it. The intention of the
dome is to oblige the flame and heat to sur-
round and strike back or reverberate upon ev-
ery part of the retort, whence the furnace gets
the name of reverberatory. Without this cir-
cumstance the retort would only be heated in
its bottom, the vapours raised from the con-
tained substance would condense in the upper
part, and a continual cohabitation would take

130

LAVOISIER

place without anything passing over into the
receiver; but, by means of the dome, the retort
is equally heated in every part, and the vapours
being forced out can only condense in the neck
of the retort or in the recipient.

To prevent the bottom of the retort from be-
ing either heated or cooled too suddenly, it is
sometimes placed in a small sand bath of baked
clay, standing upon the cross bars of the fur-
nace. Likewise, in many operations, the retorts
are coated over with lutes, some of which are
intended to preserve them from the too sudden
influence of heat or of cold, while others are for
sustaining the glass, or forming a kind of sec-
ond retort, which supports the glass one during
operations wherein the strength of the fire might
soften it. The former is made of brick-clay with
a little cow's hair beat up along with it, into a
paste or mortar, and spread over the glass or
stone retorts. The latter is made of pure clay
and pounded stone-ware mixed together and
used in the same manner. This dries and hard-
ens by the fire, so as to form a true supplemen-
tary retort capable of retaining the materials,
if the glass retort below should crack or soften.
But, in experiments which are intended for col-
lecting gases, this lute, being porous, is of no
manner of use.

In a great many experiments wherein very
violent fire is not required, the reverberatory
furnace may be used as a melting one, by leav-
ing out the piece called the laboratory and plac-
ing the dome immediately upon the fireplace,
as represented Plate xin, Fig. 3. The furnace
represented in Fig. 4 is very convenient for fus-
ions; it is composed of the fire-place and ash-
hole ABD, without a door, and having a hole
E, which receives the muzzle of a pair of bel-
lows strongly luted on, and the dome ABGH,
which ought to be rather lower than is repre-
sented in the figure. This furnace is not capa-
ble of producing a very strong heat but is suf-
ficient for ordinary operations and may be read-
ily moved to any part of the laboratory where
it is wanted. Though these particular furnaces
are very convenient, every laboratory must be
provided with a forge furnace, having a good
pair of bellows, or, what is more necessary, a
powerful melting furnace. I shall describe the
one I use, with the principles upon which it is
constructed.

The air circulates in a furnace in consequence
of being heated in its passage through the burn-
ing coals; it dilates and, becoming lighter than
the surrounding air, is forced to rise upwards
by the pressure of the lateral columns of air,

and is replaced by fresh air from all sides, espe-
cially from below. This circulation of air even
takes place when coals are burnt in a common
chaffing dish ; but we can readily conceive, that,
in a furnace open on all sides, the mass of air
which passes, all other circumstances being
equal, cannot be so great as when it is obliged
to pass through a furnace in the shape of a hol-
low tower, like most of the chemical furnaces,
and consequently that the combustion must be
more rapid in a furnace of this latter con-
struction. Suppose, for instance, the furnace
ABCDEF open above and filled with burning
coals, the force with which the air passes through
the coals will be in proportion to the difference
between the specific gravity of two columns
equal to AC, the one of cold air without, and
the other of heated air within the furnace.
There must be some heated air above the open-
ing AB, and the superior levity of this ought
likewise to be taken into consideration; but, as
this portion is continually cooled and carried
off by the external air, it cannot produce any
great effect.

But, if we add to this furnace a large hollow
tube GHAB of the same diameter, which pre-
serves the air which has been heated by the
burning coals from being cooled and dispersed
by the surrounding air, the difference of specific
gravity which causes the circulation will then
be between two columns equal to GC. Hence,
if GC be three times the length of AC, the cir-
culation will have treble force. This is upon the
supposition that the air in GHCD is as much
heated as what is contained in ABCD, which
is not strictly the case, because the heat must
decrease between AB and GH; but, as the air
in GHAB is much warmer than the external
air, it follows that the addition of the tube must
increase the rapidity of the stream of air, that
a larger quantity must pass through the coals,
and consequently that a greater degree of com-
bustion must take place.

We must not, however, conclude from these
principles, that the length of this tube ought to
be indefinitely prolonged; for, since the heat of
the air gradually diminishes in passing from
AB to GH, even from the contact of the sides
of the tube, if the tube were prolonged to a
certain degree, we would at last come to a point
where the specific gravity of the included air
would be equal to the air without; and, in this
case, as the cool air would no longer tend to rise
upwards, it would become a gravitating mass,
resisting the ascension of the air below. Be-
sides, as this air, which has served for combus-

CHEMISTRY

131

tion, is necessarily mixed with carbonic acid
gas, which is considerably heavier than com-
mon air, if the tube were made long enough,
the air might at last approach so near to the
temperature of the external air as even to grav-
itate downwards; hence we must conclude that
the length of the tube added to a furnace must
have some limit beyond which it weakens in-
stead of strengthening the force of the fire.

From these reflections it follows that the first
foot of tube added to a furnace produces more
effect than the sixth, and the sixth more than
the tenth; but we have no data to ascertain at
what height we ought to stop. This limit of use-
ful addition is so much the farther in propor-
tion as the materials of the tube are weaker
conductors of heat, because the air will thereby
be so much less cooled; hence baked earth is
much to be preferred to plate iron. It would be
even of consequence to make the tube double,
and to fill the interval with rammed charcoal,
which is one of the worst conductors of heat
known; by this the refrigeration of the air will
be retarded, and the rapidity of the stream of
air consequently increased; and, by this means,
the tube may be made so much the longer.

As the fire-place is the hottest part of a fur-
nace, and the part where the air is most dilated
in its passage, this part ought to made with a
considerable widening or belly. This is the more
necessary, as it is intended to contain the
charcoal and crucible, as well as for the pass-
age of the air which supports, or rather pro-
duces the combustion; hence we only allow the
interstices between the coals for the passage
of the air.

From these principles my melting furnace is
constructed, which I believe is at least equal in
power to any hitherto made, though I by no
means pretend that it possesses the greatest
possible intensity that can be produced in chem-
ical furnaces. The augmentation of the volume
of air produced during its passage through a
melting furnace not being hitherto ascertained
from experiment, we are still unacquainted with
the proportions which should exist between the
inferior and superior apertures, and the abso-
lute size of which these openings should be
made is still less understood; hence data are
wanting by which to proceed upon principle,
and we can only accomplish the end in view by
repeated trials.

This furnace, which, according to the above
stated rules, is in form of an eliptical spheroid,
is represented Plate xm, Fig. 6, ABCD; it is
cut off at the two ends by two planes, which

pass, perpendicular to the axis, through the fo-
ci of the elipse. From this shape it is capable of
containing a considerable quantity of charcoal,
while it leaves sufficient space in the intervals
for the passage of the air. That no obstacle may
oppose the free access of external air, it is per-
fectly open below, after the model of M. Mac-
quer's melting furnace, and stands upon an iron
tripod. The grate is made of flat bars set on
edge, and with considerable interstices. To the
upper part is added a chimney, or tube, of baked
earth, ABFG, about eighteen feet long, and al-
most half the diameter of the furnace. Though
this furnace produces a greater heat than any
hitherto employed by chemists, it is still sus-
ceptible of being considerably increased in pow-
er by the means already mentioned, the princi-
pal of which is to render the tube as bad a
conductor of heat as possible, by making it
double, and filling the interval with rammed
charcoal.

When it is required to know if lead contains
any mixture of gold or silver, it is heated in a
strong fire in capsules of calcined bones, which
are called cupels. The lead is oxidated, becomes
vitrified, and sinks into the substance of the
cupel, while the gold or silver, being incapable
of oxidation, remain pure. As lead will not oxi-
date without free access of air, this operation
cannot be performed in a crucible placed in the
middle of the burning coals of a furnace, be-
cause the internal air, being mostly already re-
duced by the combustion into azotic and car-
bonic acid gas, is no longer fit for the oxidation
of metals. It was therefore necessary to con-
trive a particular apparatus, in which the metal
should be at the same time exposed to the in-
fluence of violent heat and defended from con-
tact with air rendered incombustible by its pas-
sage through burning coals. The furnace in-
tended for answering this double purpose is
called the cupelling or essay furnace. It is usu-
ally made of a square form, as represented
Plate xm, Figs. 8 and 10, having an ash-hole
AABB, a fire-place BBCC, a laboratory CCDD,
and a dome DDEE. The muffle or small oven
of baked earth GH (Fig. 9) being placed in the
laboratory of the furnace upon cross bars of
iron, is adjusted to the opening GG, and luted
with clay softened in water. The cupels are
placed in this oven or muffle, and charcoal is
conveyed into the furnace through the open-
ings of the dome and fire-place. The external
air enters through the openings of the ash-hole
for supporting the combustion, and escapes by
the superior opening or chimney at EE; and

132

LAVOISIER

air is admitted through the door of the muffle
GG for oxidating the contained metal.

Very little reflection is sufficient to discover
the erroneous principles upon which this fur-
nace is constructed. When the opening GG is
shut, the oxidation is produced slowly and with
difficulty, for want of air to carry it on; and,
when this hole is open, the stream of cold air
which is then admitted fixes the metal and ob-
structs the process. These inconveniences may
be easily remedied, by constructing the muffle
and furnace in such a manner that a stream of
fresh external air should always play upon the
surface of the metal, and this air should be
made to pass through a pipe of clay kept con-
tinually red hot by the fire of the furnace. By
this means the inside of the muffle will never
be cooled, and processes will be finished in a
few minutes which at present require a consid-
erable space of time.

M. Sage remedies these inconveniences in a
different manner; he places the cupel contain-
ing lead, alloyed with gold or silver, amongst
the charcoal of an ordinary furnace and cov-
ered by a small porcelain muffle; when the
whole is sufficiently heated, he directs the blast
of a common pair of hand-bellows upon the
surface of the metal and completes the cu-
pellation in this way with great ease and
exactness.

SECTION III Of Increasing the Action of Fire
by Using Oxygen Gas Instead of Atmospher-
ic Air

By means of large burning glasses, such as
those of Tchirnausen and M. de Trudaine, a
degree of heat is obtained somewhat greater
than has hitherto been produced in chemical
furnaces, or even in the ovens of furnaces used
for baking hard porcelain. But these instru-
ments are extremely expensive, and do not
even produce heat sufficient to melt crude plat-
inum ; so that their advantages are by no means
sufficient to compensate for the difficulty of
procuring, and even of using them. Concave
mirrors produce somewhat more effect than
burning glasses of the same diameter, as is
proved by the experiments of MM. Macquer
and Beaume 1 with the speculum of the Abbe*
Bouriot; but, as the direction of the reflected
rays is necessarily from below upwards, the
substance to be operated upon must be placed
in the air without any support, which renders
most chemical experiments impossible to be
performed with this instrument.

For these reasons, I first endeavoured to em-

ploy oxygen gas for combustion, by filling large
bladders with it, and making it pass through a
tube capable of being shut by a stop cock; and
in this way I succeeded in causing it to support
the combustion of lighted charcoal. The inten-
sity of the heat produced, even in my first at-
tempt, was so great as readily to melt a small
quantity of crude platinum. To the success of
this attempt is owing the idea of the gazometer,
described p. 91 et seq., which I substituted in-
stead of the bladders; and, as we can give the
oxygen gas any necessary degree of pressure,
we can with this instrument keep up a contin-
ued stream and give it even a very considerable
force.

Theonlyapparatusnecessaryforexperiments
of this kind consists of a small table ABCD
(Plate xn, Fig. 15), with a hole F, through
which passes a tube of copper or silver, ending
in a very small opening at G, and capable of
being opened or shut by the stop-cock H. This
tube is continued below the table &tlmno and
is connected with the interior cavity of the ga-
zometer. When we mean to operate, a hole of a
few lines deep must be made with a chisel in a
piece of charcoal, into which the substance to
be treated is laid; the charcoal is set on fire by
means of a candle and blow-pipe, after which
it is exposed to a rapid stream of oxygen gas
from the extremity G of the tube FG.

This manner of operating can only be used
with such bodies as can be placed, without in-
convenience, in contact with charcoal, such as
metals, simple earths, &c. But, for bodies whose
elements have affinity to charcoal, and which
are consequently decomposed by that sub-
stance, such as sulphates, phosphates, and most
of the neutral salts, metallic glasses, enamels,
&c., we must use a lamp and make the stream
of oxygen gas pass through its flame. For this
purpose, we use the elbowed blow-pipe ST, in-
stead of the bent one FG, employed with char-
coal. The heat produced in this second manner
is by no means so intense as in the former way
and is very difficultly made to melt platinum.
In this manner of operating with the lamp, the
substances are placed in cupels of calcined
bones, or little cups of porcelain, or even in me-
tallic dishes. If these last are sufficiently large,
they do not melt, because, metals being good
conductors of heat, the caloric spreads rapidly
through the whole mass, so that none of its
parts are very much heated.

In the Recueil de VAcademie for 1782, p. 476,
and for 1783, p. 573, the series of experiments
I have made with this apparatus may be seen

CHEMISTRY

133

at large. The following are some of the princi-
pal results.

1. Rock crystal, or pure silicious earth, is in-
fusible, but becomes capable of being softened
or fused when mixed with other substances.

2. Lime, magnesia, and barytes, are infusi-
ble, either when alone, or when combined to-
gether; but, especially lime, they assist the fu-
sion of every other body.

3. Argill, or pure base of alum, is completely
fusible per se into a very hard opaque vitreous
substance, which scratches glass like the preci-
ous stones.

4. All the compound earths and stones are
readily fused into a brownish glass.

5. All the saline substances, even fixed alkali,
are volatilized in a few seconds.

6. Gold, silver, and probably platinum, are
slowly volatilized without any particular phe-
nomenon.

7. All other metallic substances, except mer-
cury, become oxidated, though placed upon
charcoal, and burn with different coloured
flames and at last dissipate altogether.

8. The metallic oxides likewise all burn with
flames. This seems to form a distinctive char-
acter for these substances, and even leads me
to believe, as was suspected by Bergman, that
barytes is a metallic oxide, though we have not
hitherto been able to obtain the metal in its
pure or reguline state.

9. Some of the precious stones, as rubies, are
capable of being softened and soldered togeth-
er, without injuring their colour or even dimin-
ishing their weights. The hyacinth, tho' almost
equally fixed with the ruby, loses its colour
very readily. The Saxon and Brazilian topaz,
and the Brazilian ruby, lose their colour very

quickly and lose about a fifth of their weight,
leaving a white earth, resembling white quartz
or unglazed china. The emerald, chrysolite,
and garnet, are almost instantly melted into
an opaque and coloured glass.

10. The diamond presents a property peculi-
ar to itself; it burns in the same manner with
combustible bodies and is entirely dissipated.

There is yet another manner of employing
oxygen gas for considerably increasing the force
of fire, by using it to blow a furnace. M. Achard
first conceived this idea; but the process he
employed, by which he thought to dephlogist-
icate, as it is called, atmospheric air, or to de-
prive it of azotic gas, is absolutely unsatisfac-
tory. I propose to construct a very simple fur-
nace for this purpose, of very refractory earth,
similar to the one represented Plate xm, Fig.
4, but smaller in all its dimensions. It is to have
two openings, as at E, through one of which
the nozzle of a pair of bellows is to pass, by
which the heat is to be raised as high as pos-
sible with common air; after which, the stream
of common air from the bellows being sudden-
ly stopped, oxygen gas is to be admitted by a
tube at the other opening, communicating with
a gazometer having the pressure of four or five
inches of water. I can in this manner unite
the oxygen gas from several gazometers, so
as to make eight or nine cubic feet of gas pass
through the furnace; and in this way I expect to
produce a heat greatly more intense than any
hitherto known. The upper orifice of the furnace
must be carefully made of considerable dimen-
sions, that the caloric produced may have free
issue, lest the too sudden expansion of that
highly elastic fluid should produce a dangerous
explosion.

PLATE I

Fig. i

Fig. 2

Fig. 4

Fig. 5

Fig. 7

Fig. 11

Fig. 8

Fig. 12

Fig. 13

Fig. 6

Fig. 15

Fig. 9

Fig. 10

Fig. 14

Fig. 16

PLATE II

Fig. 15

Fig. 16

PLATE III

Fig. 21

Fig. 22

Fig. 23

PLATE

Fig. i

Fig. 8

J-"

Fig. 4

Fig. 12

Fig. 17

Fig. 13

Fig. 14

Fig. 15

Fig. 11

PLATE V

Fig. i

PLATE VI

Fig. 8

Fig. 9

PLATE VII

Fig. 8 Fig. 9 Fig. 10

Fig. 15

Fig. 17

PLATE VIII

Fig. 2

Fig. 6

Fig. 7

Fig. 3 Fig. 5

Fig. 8

Fig. 10

PLATE IX

PLATE

Fig. 11

XII

Fig. II 15

Fig. 18

Fig. 17

PLATE XIII

Fig. 9

Fig. 10

Fig. 5 Fig. 6

THEORY OF HEAT

BIOGRAPHICAL NOTE

JOSEPH FOUKIER, 1768-1830

FOURIER was born at Auxerre March 21, 1768,
the son of a poor tailor. An orphan at eight, he
was recommended by a friend to the Bishop of
Auxerre, who obtained admission for him in
the local military school conducted by the
Benedictines of Saint-Maur. He quickly dis-
tinguished himself as a student and showed
distinct literary ability; at twelve he was writ-
ing sermons which were often used with great
effect in Paris. At the age of thirteen mathema-
tics began to attract him strongly. The pre-
scribed hours of study did not suffice; he arose
at night, concealed himself behind a screen,
and by the light of candle-ends carefully col-
lected during the day, pursued his mathemat-
ical studies. When he was twenty-one he de-
livered his first memoir before the Academy of
Sciences on the resolution of numerical equa-
tions of all degrees.

Educated by monks in a military school,
Fourier seems to have considered that only the
army or the church could provide a career.
With a strong recommendation from Legendre
he applied for admission to the artillery. He
was refused with the statement, "Fourier, not
being of noble birth, cannot enter the artillery,
not even if he is a second Newton." He then
entered the Benedictine Order, where he re-
mained as a novice from 1787 to 1789. Upon
the outbreak of the Revolution he left the con-
vent, although this did not result in any break
with the Benedictines, since they immediately
appointed him to the principal chair of math-
ematics at their school in Auxerre. When his
colleagues became ill, he took their place, and
besides teaching mathematics he also lectured
on rhetoric, history, and philosophy.

At Auxerre, Fourier embraced the cause of
the Revolution, joined the peoples' party, and
served as publicist, recruiting agent, and mem-
ber of the Citizens' Committee of Surveillance;
in this last function he exercised such modera-
tion that he was himself in danger from the
Terror. When, in 1794, the Normal School was
instituted at Paris to train a specially selected
group of new teachers, Fourier was among the

fifteen hundred that were chosen, and, although
he began as a student, he was soon made a
"master of conference." The school failed after
a short time, but Fourier had so impressed the
authorities that when the Polytechnic School
was founded, he was appointed to its faculty,
first as "superintendent of lectures on fortifica-
tion" and then as "lecturer on analysis."

Napoleon sometimes attended the sessions
at the Polytechnic School, and when he organ-
ized the expedition to Egypt in 1798, Fourier
was asked to be a part of it, although he was
not informed of the role he was expected to
play. Fourier was in Egypt for three years, en-
gaged in the most varied activities: organizing
factories for the army, constructing machines,
leading scientific expeditions, and executing
numerous administrative tasks. He acted as
the representative of the general-in-chief, re-
ceiving complaints from the Egyptian popu-
lace, and for one period was virtually governor
of half of Egypt. On the death of General K16ber
he was called upon to present a eulogy before
the French Army. As secretary of the Institute
of Cairo he instigated the collection of materi-
als for the famous Description of Egypt. In col-
laboration with Napoleon he wrote the histor-
ical introduction to this work, which established
his literary reputation and eventually won him
membership in the French Academy.

On his return to France in 1802 Fourier was
appointed prefect of the D6partement of Is&re
and for the next thirteen years lived at Gren-
oble. He composed the disputes between the
different parties and brought order out of the
confusion left by the Revolution in his province.
As part of a general policy of public improve-
ments, he initiated an extensive road-building
project and undertook the reclamation of
marsh-lands which had been the source of in-
fection for thirty-seven communes. In recog-
nition of his services he was created Baron of
the Empire in 1808.

His many administrative duties as prefect of
Is&re did not interrupt his work as a mathema-
tician and man of letters. He conducted inves-

163

164

BIOGRAPHICAL NOTE

tigations into the motions of heat in solid bodies
with the aim of reducing them to mathematical
formulation, and in 1807 submitted his first
paper on the subject to the Academy of Sci-
ences. To induce the author to extend and im-
prove his researches the Academy assigned as
the problem for its prize competition of 1812,
"The mathematical theory of the laws of the
propagation of heat and the comparison of the
results of this theory with exact experiment."
The judges were Laplace, Lagrange, and Le-
gendre, and they awarded the prize to Fourier
for his memoir in two parts, TMorie des mouve-
ments de la chaleur dans Us corps solides. The
first part was repubiished in 1822 as the Thi-
orie Analytique de la Chaleur.

Fourier continued to hold his position as pre-
fect through the Revolution of 1814, but Na-
poleon's return from Elba proved to be his polit-
ical downfall. As Napoleon was approaching
Grenoble, Fourier went to Lyons to notify the
Bourbons that the city would undoubtedly ca-
pitulate. They refused to believe him and made
him responsible for the safety of the city. Upon
his return to Grenoble, which had surrendered,
he was taken prisoner and brought before the
Emperor. Napoleon confronted him : "You also
have declared war against me? ... It only
grieves me to see among my enemies an Egyp-
tian, a man who has eaten along with me the

bread of the bivouac, an old friend. How, more-
over, could you have forgotten, Monsieur
Fourier, that I have made you what you are?"
Fourier 's loyalty was re-established, although
he did not share Napoleon's confidence of vic-
tory. The end of the Hundred Days and the
Restoration found him deprived of political of-
fice, in disgrace, and almost penniless.

A friend and former pupil who was prefect of
Paris made it possible for him to become Direc-
tor of the Bureau of Statistics, which he re-
mained until his death. His political past, how-
ever, did not prevent renewed recognition of
his scientific abilities. In 1816 he was proposed
for membership in the Academy of Sciences,
and although Louis XVIII refused his consent
at that time, he became a member the follow-
ing year. He was made permanent secretary of
the Division of Mathematical Sciences in 1822,
member of the French Academy in 1826, and
a year later succeeded Laplace as President of
the Council for Improving the Polytechnic
School. In 1828 he became a member of the
government commission established for the en-
couragement of literature.

He died May 16, 1830, of aneurism of the
heart, which had been aggravated by his habit
of wrapping himself in all seasons like "an
Egyptian mummy" and living in airless rooms
at an excessively high temperature.

CONTENTS

BIOGRAPHICAL NOTE, 163 PRELIMINARY DISCOURSE, 169
CHAPTER I. INTRODUCTION

SECTION I. Statement of the Object of the Work

I. Object of the Theoretical Researches, 177

2-10. Different Examples, Ring, Cube, Sphere, Infi-
nite Prism; the Variable Temperature at Any
Point Whatever Is a Function of the Coordinates
and of the Time, The Quantity of Heat, Which
During Unit of Time Crosses a Given Surface in
the Interior of the Solid, Is Also a Function of the
Time Elapsed, and of Quantities Which Deter-
mine the Form and Position of the Surface. The
Object of the Theory is to Discover These Func-
tions, 177

II. The Three Specific Elements Which Must Be
Observed are the Capacity, the Conductivity
Proper or Permeability, and the External Con-
ductivity or Penetrability. The Coefficients Which
Express Them May Be Regarded at First as Con-
stant Numbers, Independent of the Temperatures,
180

12. First Statement of the Problem of the Terrestrial
Temperatures, 180

13-15. Conditions Necessary to Applications of the
Theory. Object of the Experiments, 181

16-21. The Rays of Heat Which Escape from the
Same Point of a Surface Have Not the Same In-
tensity. The Intensity of Each Ray is Proportion-
al to the Cosine of the A ngle Which Its Direction
Makes with the Normal to the Surface. Divers re-
marks, and Considerations on the Object and Ex-
tent of Thermological Problems, and on the Rela-
tions of General Analysis with the Study of
Nature, 182

SECTION II. Preliminary Definitions and General
Notions

22-24. Permanent Temperature, Thermometer. The
Temperature Denoted byQIs That of Melting Ice.
The Temperature of Water Boiling in a Given
Vessel under a Given Pressure Is Denoted by 1, 184

25. The Unit Which Serves to Measure Quantities of
Heat Is the Heat Required to Liquify a Certain
Mass of Ice, 184

26. Specific Capacity for Heat, 185

27-29. Temperatures Measured by Increments of Vol-
ume or by the Additional Quantities of Heat.
Those Cases Only Are Here Considered, in Which
the Increments of Volume Are Proportional to the
Increments of the Quantity of Heat. This Condi-
tion Does Not in General Exist in Liquids; It Is
Sensibly True for Solid Bodies Whose Tempera-
tures Differ Very Much from Those Which Cause
the Change of State, 185

30. Notion of External Conductivity, 185

31. We May at First Regard the Quantity of Heat
Lost as Proportional to the Temperature. This
Proposition Is Not Sensibly True Except for
Certain Limits of Temperature, 186

32-35. The Heat Lost into the Medium Consists of
Several Parts. The Effect Is Compound and Vari-
able. Luminous Heat, 186

36. Measure of the External Conductivity, 187

37. Notion of the Conducibility Proper. This Property
Also May Be Observed in Liquids, 187

38. 39. Equilibrium of Temperatures. The Effect Is

Independent of Contact, 187

40-49. First Notions of Radiant Heat, and of the Equi-
librium Which Is Established in Spaces Void of
Air; of the Cause of the Reflection of Rays of Heat,
or of Their Retention in Bodies; of the Mode of
Communication Between the Internal Molecules;
of the Law Which Regulates the Intensity of the
Rays Emitted. The Law Is Not Disturbed by the
Reflection of Heat, 188

50,51. First Notion of the Effects of Reflected Heat, 190
52-56. Remarks on the Statical or Dynamical Proper-
ties of Heat. It Is the Principle of Elasticity. The
Elastic Force of Aeriform Fluids Exactly Indi-
cates Their Temperatures, 192

SECTION III. Principle of the Communication of
Heat

57-59. When Two Molecules of the Same Solid Are
Extremely Near and at Unequal Temperatures,
the Most Heated Molecule Communicates to That
Which Is Less Heated a Quantity of Heat Exactly
Expressed by the Product of the Duration of the
Instant, of the Extremely Small Difference of the
Temperatures, and of a Certain Function of the
Distance of the Molecules, 193

60. When a Heated Body Is Placed in an Aeriform
Medium at a Lower Temperature, It Loses at
Each Instant a Quantity of Heat Which May Be
Regarded in the First Researches as Proportional
to the Excess of the Temperature of the Surface
over the Temperature of the Medium, 194

61-64. The Propositions Enunciated in the Two Pre-
ceding Articles Are Founded on Divers Observa-
tions. The Primary Object of the Theory / to Dis-
cover All the Exact Consequences of These Propo-
sitions. We Can Then Measure the Variations of
the Coefficients, by Comparing the Results of Cal-
culation with Very Exact Experiments, 194

SECTION IV. Of the Uniform and Linear Movement

of Heat
65. The Permanent Temperatures of an Infinite Solid

Included Between Two Parallel Planes Main-

165

166

FOURIER

tained at Fixed Temperatures Are Expressed
by the Equation (o - a) e - (6 - a) z; a and b Are
the Temperatures of the Two Extreme Planes, e
Their Distance, and v the Temperature of the Sec-
tion, Whose Distance from the Lower Plane is z,
196

66, 67. Notion and Measure of the Flow of Heat, 198
68, 69. Measure of the Conductivity Proper, 200

70. Remarks on the Case in Which the Direct Action
of the Heat Extends to a Sensible Distance, 200

71. State of the Same Solid When the Upper Plane Is
Exposed to the Air, 201

72. General Conditions of the Linear Movement of
Heat, 202

SECTION V. Law of the Permanent Temperatures in

a Prism of Small Thickness
73-80. Equation of the Linear Movement of Heat in

the Prism. Different Consequences of This Equa-

tion, 203

SECTION VI. On the Heating of Closed Spaces
81-84. The Final State of the Solid Boundary Which
Encloses the Space Heated by a Surface b, Main-
tained at the Temperature a, Is Expressed by the
Following Equation:

, m Is the Tem-

The Value of P is -i+~+
s\n K H

perature of the Internal Air, n the Temperature of
the External Air, g, h, H Measure Respectively
the Penetrability of the Heated Surface a, That of
the Inner Surface of the Boundary s, and That of
the External Surface s; e Is the Thickness of the
Boundary, and K its Conductivity Proper, 206

85, 86. Remarkable Consequences of the Preceding
Equation, 208

87-91. Measure of the Quantity of Heat Requisite to
Retain at a Constant Temperature a Body Whose
Surface Is Protected from the External Air by
Several Successive Envelopes. Remarkable Effects
of the Separation of the Surfaces. These Results
Applicable to Many Different Problems, 209

SECTION VII. Of the Uniform Movement of Heat in

Three Dimensions
92, 93. The Permanent Temperatures of a Solid En-

closed Between Six Rectangular Planes Are Ex-

pressed by the Equation

x, y, z Are the Coordinates of Any Point, Whose
Temperature is v; A, a, b, c are Constant Num-
bers. If the Extreme Planes Are Maintained by
Any Causes at Fixed Temperatures Which Satis-
fy the Preceding Equation, the Final System of
All the Internal Temperatures Will Be Expressed
by the Same Equation, 213

94, 95. Measure of the Flow of Heat in This Prism,
215

SECTION VIII. Measure of the Movement of Heat
at a Given Point of a Solid Mass

96-99. The Variable System of Temperatures of a
Solid Is Supposed to Be Expressed by the Equa-
tion v = F (x, y, z, t) , Where v Denotes the Variable
Temperature Which Would Be Observed After the
Time t Had Elapsed, at the Point Whose Coordi-
nates are x,y, z. Formation of the Analytical Ex-
pression of the Flow of Heat in a Given Direction
Within the Solid, 216

1 00. A pplication of the Preceding Theorem to the Case in
Which the Function F is e- gt cos x cos y cos z, 219

CHAPTER II. EQUATIONS OP THE MOVEMENT OF HEAT

SECTION I. Equation of the Varied Movement of
Heat in a Ring

101-105. The Variable Movement of Heat in a Ring
Is Expressed by the Equation

do K d*v hi
dt~ CDdx*~CDS V '

The Arcx Measures the Distance of a Section from
the Origin O; v Is the Temperature Which That
Section Acquires After the Lapse of Time t; K, C,
D, h Are the Specific Coefficients; S Is the Area
of the Section, by the Revolution of Which the
Ring Is Generated; I Is the Perimeter of the Sec-
tion, 221

106-110. The Temperatures at Points Situated at
Equal Distances Are Represented by the Terms of
a Recurring Series. Observation of the Tempera-
tures vi, v*, v* of Three Consecutive Points Gives

the Measure of the ratio : We Have - - ' * q,
K v%

A s * S/loo<*\*
0, and = 7 I -~ I .
K I \\log e/

The Distance Between Two Consecutive Points Is
\, and log w Is the Decimal Logarithm of One of
the Two Values o/w, 223

SECTION II. Equation of the Varied Movement of

Heat in a Solid Sphere
111-113. x Denoting the Radius of Any Shell, the

Movement of Heat in the Sphere Is Expressed by

the Equation

_ + 224

dt CD\dx*^'

114-117. Conditions Relative to the State of the Sur-
face and to the Initial Slate of the Solid, 225

SECTION III. Equations of the Varied Movement of
Heat in a Solid Cylinder

118-120. The Temperatures of the Solid Are Deter-
mined by Three Equations; the First Relates to the
Internal Temperatures, the Second Expresses the
Continuous State of the Surface, the Third Ex-
presses the Initial State of the Solid, 227

SECTION IV. Equations of the Uniform Movement

of Heat in a Solid Prism of Infinite Length
121-123. The System of Fixed Temperatures Satisfies
the Equation

d*v do d*v
dx* dy* <fc '*

v Is the Temperature at a Point Whose Coordi-
nates Are x, y z, 229

CONTENTS

167

124. 125. Equation Relative to the State of the Surface
and to That of the First Section, 230

SECTION V. Equations of the Varied Movement of
Heat in a Solid Cube

126-131. The System of Variable Temperatures Is
Determined by Three Equations; One Expresses
the Internal State, the Second Relates to the State
of the Surface, and the Third Expresses the Initial
Slate, 231

SECTION VI. General Equation of the Propagation
of Heat in the Interior of Solids

132-139. Elementary Proof of Properties of the Uniform
Movement of Heat in a Solid Enclosed Between
Six Orthogonal Planes, the Constant Tempera-
tures Being Expressed by the Linear Equation,

v A ax by cz.

The Temperatures Cannot Change, Since Each
Point of the Solid Receives as Much Heat as It
Gives Off. The Quantity of Heat Which During
the Unit of Time Crosses a Plane at Right Angles
to the Axis of z Is the Same, Through Whatever
Point of That Axis the Plane Passes. The Value
of This Common Flow Is That Which Would Ex-
ist, If the Coefficients a and b Were Nul, 233
140, 141. Analytical Expression of the Flow in the
Interior of Any Solid. The Equation of the Tem-
peratures Being v=f(x t y, z, t) the Function

ar-r-

Expresses the Quantity of Heat Which

During the Instant dt Crosses an Infinitely Small
Area o> Perpendicular to the Axis ofz, at the Point
Whose Coordinates Are x, y, z, and Whose Tem-
perature Is v After the Time t Has Elapsed, 237
142-145. It Is Easy to Derive from the Foregoing
Theorem the General Equation of the Movement
of Heat, Namely

^ (++)">

SECTION VII. General Equation Relative to the
Surface

146-154. It Is Proved That the Variable Tempera-
tures at Points on the Surface of a Body, Which IB
Cooling in Air, Satisfy the Equation

dv dv dv h

m- \-n- hp~r~ {--7703=0; rndx+ndy+pdz^Q,
ax ay az K.

Being the Differential Equation of the Surface
Which Bounds the Solid, and q Being Equal to
(m-f n'+P 2 )*. To Discover This Equation We
Consider a Molecule of the Envelop Which
Bounds the Solid, and We Express the Fact That
the Temperature of This Element Does Not
Change by a Finite Magnitude During an Infi-
nitely Small Instant. This Condition Holds and
Continues to Exist After That the Regular Action
of the Medium Has Been Exerted During a Very
Small Instant. Any Form May Be Given to the
Element of the Envelop. The Case in Which the
Molecule Is Formed by Rectangular Sections Pre-
sents Remarkable Properties. In the Most Simple
Case, Which Is That in Which the Base Is Paral-
lel to the Tangent Plane, the Truth of the Equation
Is Evident, 240

SECTION VIII. Application of the General Equa-
tions

155, 156. In Applying the General Equation (A) to
the Case of the Cylinder and of the Sphere, We
Find the Same Equations as Those of Section III
and of Section II of This Chapter, 246

SECTION IX. General Remarks

157-162. Fundamental Considerations on the Nature
of the Quantities x, t, v, K, h, C, D, Which Enter
into All the Analytical Expressions of the Theory
of Heat. Each of These Quantities Has an Expo-
nent of Dimension Which Relates to the Length,
or to the Duration, or to the Temperature. These
Exponents Are Found by Making the Units of
Measure Vary, 249

PRELIMINARY DISCOURSE

PRIMARY causes are unknown to us; but are subject to simple and constant
laws, which may be discovered by observation, the study of them being the
object of natural philosophy.

Heat, like gravity, penetrates every substance of the universe, its rays occu-
py all parts of space. The object of our work is to set forth the mathematical
laws which this element obeys. The theory of heat will hereafter form one of
the most important branches of general physics.

The knowledge of rational mechanics, which the most ancient nations had
been able to acquire, has not come down to us, and the history of this science,
if we except the first theorems in harmony, is not traced up beyond the dis-
coveries of Archimedes. This great geometer explained the mathematical
principles of the equilibrium of solids and fluids. About eighteen centuries
elapsed before Galileo, the originator of dynamical theories, discovered the
laws of motion of heavy bodies. Within this new science Newton comprised the
whole system of the universe. The successors of these philosophers have ex-
tended these theories, and given them an admirable perfection: they have
taught us that the most diverse phenomena are subject to a small number of
fundamental laws which are reproduced in all the acts of nature. It is recog-
nised that the same principles regulate all the movements of the stars, their
form, the inequalities of their courses, the equilibrium and the oscillations of
the seas, the harmonic vibrations of air and sonorous bodies, the transmission
of light, capillary actions, the undulations of fluids, in fine the most complex
effects of all the natural forces, and thus has the thought of Newton been con-
firmed : quod tarn paucis tarn multa proestet geometria gloriatur.

But whatever may be the range of mechanical theories, they do not apply
to the effects of heat. These make up a special order of phenomena, which can-
not be explained by the principles of motion and equilibrium. We have for a
long time been in possession of ingenious instruments adapted to measure
many of these effects; valuable observations have been collected; but in this
manner partial results only have become known, and not the mathematical
demonstration of the laws which include them all.

I have deduced these laws from prolonged study and attentive comparison
of the facts known up to this time: all these facts I have observed afresh in the
course of several years with the most exact instruments that have hitherto
been used.

To found the theory, it was in the first place necessary to distinguish and
define with precision the elementary properties which determine the action of

169

170 FOURIER

heat. I then perceived that all the phenomena which depend on this action re-
solve themselves into a very small number of general and simple facts; where-
by every physical problem of this kind is brought back to an investigation of
mathematical analysis. From these general facts I have concluded that to de-
termine numerically the most varied movements of heat, it is sufficient to sub-
mit each substance to three fundamental observations. Different bodies in fact
do not possess in the same degree the power to contain heat, to receive or trans-
mit it across their surfaces, nor to conduct it through the interior of their masses.
These are the three specific qualities which our theory clearly distinguishes
and shews how to measure.

It is easy to judge how much these researches concern the physical sciences
and civil economy, and what may be their influence on the progress of the arts
which require the employment and distribution of heat. They have also a
necessary connection with the system of the world, and their relations become
known when we consider the grand phenomena which take place near the sur-
face of the terrestrial globe.

In fact, the radiation of the sun in which this planet is incessantly plunged,
penetrates the air, the earth, and the waters; its elements are divided, change
in direction every way, and, penetrating the mass of the globe, would raise its
mean temperature more and more, if the heat acquired were not exactly bal-
anced by that which escapes in rays from all points of the surface and expands
through the sky.

Different climates, unequally exposed to the action of solar heat, have, after
an immense time, acquired the temperatures proper to their situation. This
effect is modified by several accessory causes, such as elevation, the form of the
ground, the neighbourhood and extent of continents and seas, the state of the
surface, the direction of the winds.

The succession of day and night, the alternations of the seasons occasion in
the solid earth periodic variations, which are repeated every day or every year:
but these changes become less and less sensible as the point at which they are
measured recedes from the surface. No diurnal variation can be detected at the
depth of about three metres [ten feet] ; and the annual variations cease to be
appreciable at a depth much less than sixty metres. The temperature at great
depths is then sensibly fixed at a given place: but it is not the same at all points
of the same meridian; in general it rises as the equator is approached.

The heat which the sun has communicated to the terrestrial globe, and
which has produced the diversity of climates, is now subject to a movement
which has become uniform. It advances within the interior of the mass which
it penetrates throughout, and at the same time recedes from the plane of the
equator, and proceeds to lose itself across the polar regions.

In the higher regions of the atmosphere the air is very rare and transparent,
and retains but a minute part of the heat of the solar rays : this is the cause of
the excessive cold of elevated places. The lower layers, denser and more heat-
ed by the land and water, expand and rise up : they are cooled by the very fact
of expansion. The great movements of the air, such as the trade winds which
blow between the tropics, are not determined by the attractive forces of the
moon and sun. The action of these celestial bodies produces scarcely percepti-
ble oscillations in a fluid so rare and at so great a distance. It is the changes of
temperature which periodically displace every part of the atmosphere.

The waters of the ocean are differently exposed at their surface to the rays

PRELIMINARY DISCOURSE 171

of the sun, and the bottom of the basin which contains them is heated very
unequally from the poles to the equator. These two causes, ever present, and
combined with gravity and the centrifugal force, keep up vast movements in
the interior of the seas. They displace and mingle all the parts, and produce
those general and regular currents which navigators have noticed.

Radiant heat which escapes from the surface of all bodies, and traverses
elastic media, or spaces void of air, has special laws, and occurs with widely
varied phenomena. The physical explanation of many of these facts is already
known ; the mathematical theory which I have formed gives an exact measure of
them. It consists, in a manner, in a new catoptrics which has its own theorems,
and serves to determine by analysis all the effects of heat direct or reflected.

The enumeration of the chief objects of the theory sufficiently shews the na-
ture of the questions which I have proposed to myself. What are the elemen-
tary properties which it is requisite to observe in each substance, and what are
the experiments most suitable to determine them exactly? If the distribution
of heat in solid matter is regulated by constant laws, what is the mathematical
expression of those laws, and by what analysis may we derive from this expres-
sion the complete solution of the principal problems? Why do terrestrial tem-
peratures cease to be variable at a depth so small with respect to the radius of
the earth? Every inequality in the movement of this planet necessarily occa-
sioning an oscillation of the solar heat beneath the surface, what relation is
there between the duration of its period, and the depth at which the tempera-
tures become constant?

What time must have elapsed before the climates could acquire the different
temperatures which they now maintain; and what are the different causes
which can now vary their mean heat? Why do not the annual changes alone in
the distance of the sun from the earth, produce at the surface of the earth very
considerable changes in the temperatures?

From what characteristic can we ascertain that the earth has not entirely
lost its original heat; and what are the exact laws of the loss?

If, as several observations indicate, this fundamental heat is not wholly dis-
sipated, it must be immense at great depths, and nevertheless it has no sensible
influence at the present time on the mean temperature of the climates. The
effects which are observed in them are due to the action of the solar rays. But
independently of these two sources of heat, the one fundamental and primitive
proper to the terrestrial globe, the other due to the presence of the sun, is there
not a more universal cause, which determines the temperature of the heavens, in
that part of space which the solar system now occupies? Since the observed
facts necessitate this cause, what are the consequences of an exact theory in
this entirely new question; how shall we be able to determine that constant
value of the temperature of space, and deduce from it the temperature which
belongs to each planet?

To these questions must be added others which depend on the properties of
radiant heat. The physical cause of the reflection of cold, that is to say the
reflection of a lesser degree of heat, is very distinctly known; but what is the
mathematical expression of this effect?

On what general principles do the atmospheric temperatures depend,
whether the thermometer which measures them receives the solar rays direct-
ly, on a surface metallic or unpolished, or whether this instrument remains ex-
posed, during the night, under a sky free from clouds, to contact with the air,

172 FOURIER

to radiation from terrestrial bodies, and to that from the most distant and
coldest parts of the atmosphere?

The intensity of the rays which escape from a point on the surface of any
heated body varying with their inclination according to a law which experi-
ments have indicated, is there not a necessary mathematical relation between
this law and the general fact of the equilibrium of heat; and what is the physi-
cal cause of this inequality in intensity?

Lastly, when heat penetrates fluid masses, and determines in them internal
movements by continual changes of the temperature and density of each mole-
cule, can we still express, by differential equations, the laws of such a com-
pound effect; and what is the resulting change in the general equations of hy-
drodynamics?

Such are the chief problems which I have solved, and which have never yet
been submitted to calculation. If we consider further the manifold relations of
this mathematical theory to civil uses and the technical arts, we shall recognize
completely the extent of its applications. It is evident that it includes an en-
tire series of distinct phenomena, and that the study of it cannot be omitted
without losing a notable part of the science of nature.

The principles of the theory are derived, as are those of rational mechanics,
from a very small number of primary facts, the causes of which are not consid-
ered by geometers, but which they admit as the results of common observa-
tions confirmed by all experiment.

The differential equations of the propagation of heat express the most gen-
eral conditions, and reduce the physical questions to problems of pure analysis,
and this is the proper object of theory. They are not less rigorously established
than the general equations of equilibrium and motion. In order to make this
comparison more perceptible, we have always preferred demonstrations ana-
logous to those of the theorems which serve as the foundation of statics and
dynamics. These equations still exist, but receive a different form, when they
express the distribution of luminous heat in transparent bodies, or the move-
ments which the changes of temperature and density occasion in the interior of
fluids. The coefficients which they contain are subject to variations whose ex-
act measure is not yet known, but in all the natural problems which it most
concerns us to consider, the limits of temperature differ so little that we may
omit the variations of these coefficients.

The equations of the movement of heat, like those which express the vibra-
tions of sonorous bodies, or the ultimate oscillations of liquids, belong to one
of the most recently discovered branches of analysis, which it is very important
to perfect. After having established these differential equations their integrals
must be obtained; this process consists in passing from a common expression to
a particular solution subject to all the given conditions. This difficult investiga-
tion requires a special analysis founded on new theorems, whose object we
could not in this place make known. The method which is derived from them
leaves nothing vague and indeterminate in the solutions, it leads them up to
the final numerical applications, a necessary condition of every investigation,
without which we should only arrive at useless transformations.

The same theorems which have made known to us the equations of the
movement of heat, apply directly to certain problems of general analysis and
dynamics whose solution has for a long time been desired.

Profound study of nature is the most fertile source of mathematical discov-

PRELIMINARY DISCOURSE 173

eries. Not only has this study, in offering a determinate object to investigation,
the advantage of excluding vague questions and calculations without issue; it is
besides a sure method of forming analysis itself, and of discovering the ele-
ments which it concerns us to know, and which natural science ought always to
preserve: these are the fundamental elements which are reproduced in all
natural effects.

We see, for example, that the same expression whose abstract properties
geometers had considered, and which in this respect belongs to general analy-
sis, represents as well the motion of light in the atmosphere, as it determines
the laws of diffusion of heat in solid matter, and enters into all the chief prob-
lems of the theory of probability.

The analytical equations, unknown to the ancient geometers, which Des-
cartes was the first to introduce into the study of curves and surfaces, are not
restricted to the properties of figures, and to those properties which are the
object of rational mechanics; they extend to all general phenomena. There can-
not be a language more universal and more simple, more free from errors and
from obscurities, that is to say more worthy to express the invariable relations
of natural things.

Considered from this point of view, mathematical analysis is as extensive as
nature itself; it defines all perceptible relations, measures times, spaces, forces,
temperatures; this difficult science is formed slowly, but it preserves every
principle which it has once acquired; it grows and strengthens itself incessantly
in the midst of the many variations and errors of the human mind.

Its chief attribute is clearness; it has no marks to express confused notions.
It brings together phenomena the most diverse, and discovers the hidden anal-
ogies which unite them. If matter escapes us, as that of air and light, by its ex-
treme tenuity, if bodies are placed far from us in the immensity of space, if man
wishes to know the aspect of the heavens at successive epochs separated by a
great number of centuries, if the actions of gravity and of heat are exerted in
the interior of the earth at depths which will be always inaccessible, mathe-
matical analysis can yet lay hold of the laws of these phenomena. It makes
them present and measurable, and seems to be a faculty of the human mind
destined to supplement the shortness of life and the imperfection of the senses;
and what is still more remarkable, it follows the same course in the study of all
phenomena; it interprets them by the same language, as if to attest the unity
and simplicity of the plan of the universe, and to make still more evident that
unchangeable order which presides over all natural causes.

The problems of the theory of heat present so many examples of the simple
and constant dispositions which spring from the general laws of nature; and
if the order which is established in these phenomena could be grasped by our
senses, it would produce in us an impression comparable to the sensation of
musical sound.

The forms of bodies are infinitely varied ; the distribution of the heat which
penetrates them seems to be arbitrary and confused; but all the inequalities
are rapidly cancelled and disappear as time passes on. The progress of the
phenomenon becomes more regular and simpler, remains finally subject to a.
definite law which is the same in all cases, and which bears no sensible impress
of the initial arrangement.

All observation confirms these consequences. The analysis from which they
are derived separates and expresses clearly : first, the general conditions, that is

174 FOURIER

to say those which spring from the natural properties of heat ; second, the effect,
accidental but continued, of the form or state of the surfaces; third, the effect,
not permanent, of the primitive distribution.

In this work we have demonstrated all the principles of the theory of heat,
and solved all the fundamental problems. They could have been explained
more concisely by omitting the simpler problems, and presenting in the first
instance the most general results; but we wished to shew the actual origin of
the theory and its gradual progress. When this knowledge has been acquired
and the principles thoroughly fixed, it is preferable to employ at once the most
extended analytical methods, as we have done in the later investigations. This
is also the course which we shall hereafter follow in the memoirs which will be
added to this work, and which will form in some manner its complement; and
by this means we shall have reconciled, so far as it can depend on ourselves,
the necessary development of principles with the precision which becomes the
applications of analysis.

The subjects of these memoirs will be, the theory of radiant heat, the prob-
lem of the terrestrial temperatures, that of the temperature of dwellings, the
comparison of theoretic results with those which we have observed in different
experiments, lastly the demonstrations of the differential equations of the
movement of heat in fluids.

The work which we now publish has been written a long time since; different
circumstances have delayed and often interrupted the printing of it. In this
interval, science has been enriched by important observations; the principles
of our analysis, which had not at first been grasped, have become better
known ; the results which we had deduced from them have been discussed and
confirmed. We ourselves have applied these principles to new problems, and
have changed the form of some of the proofs. The delays of publication will
have contributed to make the work clearer and more complete.

The subject of our first analytical investigations on the transfer of heat was
its distribution amongst separated masses; these have been preserved in Chap-
ter IV, Section II. The problems relative to continuous bodies, which form the
theory rightly so called, were solved many years afterwards; this theory was
explained for the first time in a manuscript work forwarded to the Institute of
France at the end of the year 1807, an extract from which was published in the
Bulletin des Sciences (Socit6 Philomatique, year 1808, page 112). We added to
this memoir, and successively forwarded very extensive notes, concerning the
convergence of series, the diffusion of heat in an infinite prism, its emission in
spaces void of air, the constructions suitable for exhibiting the chief theorems,
and the analysis of the periodic movement at the surface of the earth. Our sec-
ond memoir, on the propagation of heat, was deposited in the archives of the
Institute, on the 28th of September, 1811. It was formed out of the preceding
memoir and the notes already sent in; the geometrical constructions and those
details of analysis which had no necessary relation to the physical problem
were omitted, and to it was added the general equation which expresses the
state of the surface. This second work was sent to press in the course of 1821,
to be inserted inthecoilectionjof the Academy of Sciences. It is printed without
any change or addition; the text agrees literally with the deposited manu-
script, which forms part of the archives of the Institute.

In this memoir, and in the writings which preceded it, will be found a first
explanation of applications which our actual work does not contain : they will

PRELIMINARY DISCOURSE 175

be treated in the subsequent memoirs at greater length, and, if it be in our
power, with greater clearness. The results of our labours concerning the same
problems are also indicated in several articles already published. The extract
inserted in the Annales de Chimie et de Physique shews the aggregate of our
researches (Vol. in, page 350, year 1816). We published in the Annales two
separate notes, concerning radiant heat (Vol. iv, page 128, year 1817, and
Vol. vi, page 259, year 1817).

Several other articles of the same collection present the most constant
results of theory and observation; the utility and the extent of thermological
knowledge could not be better appreciated than by the celebrated editors of
the Annales. 1

In the Bulletin des Sciences (Societe philomatique year 1818, page 1, and year
1820, page 60) will be found an extract from a memoir on the constant or vari-
able temperature of dwellings, and an explanation of the chief consequences of
our analysis of the terrestrial temperatures.

M. Alexandre de Humboldt, whose researches embrace all the great prob-
lems of natural philosophy, has considered the observations of the tempera-
tures proper to the different climates from a novel and very important point
of view (Memoir on Isothermal lines, Soci6t6 d'Arcueil, Vol. in, page 462) ;
(Memoir on the inferior limit of perpetual snow, Annales de Chimie et de
Physique, Vol. v, page 102, year 1817).

As to the differential equations of the movement of heat in fluids mention
has been made of them in the annual history of the Academy of Sciences. The
extract from our memoir shews clearly its object and principle. (Analyse des
travaux de VAcad&mie des Sciences, by M. De Lambre, year 1820.)

The examination of the repulsive forces produced by heat, which determine
the statical properties of gases, does not belong to the analytical subject which
we have considered. This question connected with the theory of radiant heat
has just been discussed by the illustrious author of the Mtcanique ctleste, to
whom all the chief branches of mathematical analysis owe important discov-
eries. (Connaissance des Temps, years 1824-5.)

The new theories explained in our work are united for ever to the mathe-
matical sciences, and rest like them on invariable foundations; all the elements
which they at present possess they will preserve, and will continually acquire
greater extent. Instruments will be perfected and experiments multiplied. The
analysis which we have formed will be deduced from more general, that is to
say, more simple and more fertile methods common to many classes of phe-
nomena. For all substances, solid or liquid, for vapours and permanent gases,
determinations will be made of all the specific qualities relating to heat, and
of the variations of the coefficients which express them. At different stations on
the earth observations will be made, of the temperatures of the ground at dif-
ferent depths, of the intensity of the solar heat and its effects, constant or vari-
able, in the atmosphere, in the ocean and in lakes; and the constant tempera-
ture of the heavens proper to the planetary regions will become known. The
theory itself will direct all these measures, and assign their precision. No con-
siderable progress can hereafter be made which is not founded on experiments
such as these; for mathematical analysis can deduce from general and simple
phenomena the expression of the laws of nature; but the special application of
these laws to very complex effects demands a long series of exact observations.

1 Gay-Lussac and Arago.

FIRST CHAPTER

INTRODUCTION

SECTION I. Statement of the Object of the Work

1. THE effects of heat are subject to constant laws which cannot be discovered
without the aid of mathematical analysis. The object of the theory which we
are about to explain is to demonstrate these laws; it reduces all physical re-
searches on the propagation of heat, to problems of the integral calculus whose
elements are given by experiment. No subject has more extensive relations
with the progress of industry and the natural sciences; for the action of heat
is always present, it penetrates all bodies and spaces, it influences the processes
of the arts, and occurs in all the phenomena of the universe.

When heat is unequally distributed among the different parts of a solid mass,
it tends to attain equilibrium, and passes slowly from the parts which are
more heated to those which are less; and at the same time it is dissipated at
the surface, and lost in the medium or in the void. The tendency to uniform
distribution and the spontaneous emission which acts at the surface of bodies,
change continually the temperature at their different points. The problem
of the propagation of heat consists in determining what is the temperature at
each point of a body at a given instant, supposing that the initial temperatures
are known. The following examples will more clearly make known the nature
of these problems.

2. If we expose to the continued and uniform action of a source of heat, the
same part of a metallic ring, whose diameter is large, the molecules nearest to
the source will be first heated, and, after a certain time, every point of the
solid will have acquired very nearly the highest temperature which it can at-
tain. This limit or greatest temperature is not the same at different points; it
becomes less and less according as they become more distant from that point
at which the source of heat is directly applied.

When the temperatures have become permanent, the source of heat sup-
plies, at each instant, a quantity of heat which exactly compensates for that
which is dissipated at all the points of the external surface of the ring.

If now the source be suppressed, heat will continue to be propagated in the
interior of the solid, but that which is lost in the medium or the void, will no
longer be compensated as formerly by the supply from the source, so that all
the temperatures will vary and diminish incessantly until they have become
equal to the temperatures of the surrounding medium.

3. Whilst the temperatures are permanent and the source remains, if at
every point of the mean circumference of the ring an ordinate be raised per-
pendicular to the plane of the ring, whose length is proportional to the fixed
temperature at that point, the curved line which passes through the ends of
these ordinates will represent the permanent state of the temperatures, and it
is very easy to determine by analysis the nature of this line. It is to be remarked

177

178 FOURIER CHAP. I

that the thickness of the ring is supposed to be sufficiently small for the tem-
perature to be sensibly equal at all points of the same section perpendicular
to the mean circumference. When the source is removed, the line which bounds
the ordinates proportional to the temperatures at the different points will
change its form continually. The problem consists in expressing, by one equa-
tion, the variable form of this curve, and in thus including in a single formula
all the successive states of the solid.

4. Let 2 be the constant temperature at a point m of the mean circumference,
x the distance of this point from the source, that is to say the length of the arc
of the mean circumference, included between the point m and the point o
which corresponds to the position of the source; z is the highest temperature
which the point m can attain by virtue of the constant action of the source,
and this permanent temperature z is a function f(x) of the distance x. The
first part of the problem consists in determining the function f(x) which rep-
resents the permanent state of the solid.

Consider next the variable state which succeeds to the former state as soon
as the source has been removed ; denote by t the time which has passed since
the suppression of the source, and by v the value of the temperature at the
point m after the time t. The quantity v will be a certain function F (x, t) of
the distance x and the time t] the object of the problem is to discover this func-
tion F (x, i), of which we only know as yet that the initial value is / (x), so
that we ought to have the equation / (x) = F (x, O).

5. If we place a solid homogeneous mass, having the form of a sphere or
cube, in a medium maintained at a constant temperature, and if it remains
immersed for a very long time, it will acquire at all its points a temperature
differing very little from that of the fluid. Suppose the mass to be withdrawn
in order to transfer it to a cooler medium, heat will begin to be dissipated at
its surface ; the temperatures at different points of the mass will not be sensi-
bly the same, and if we suppose it divided into an infinity of layers by surfaces
parallel to its external surface, each of those layers will transmit, at each in-
stant, a certain quantity of heat to the layer which surrounds it. If it be imag-
ined that each molecule carries a separate thermometer, which indicates its
temperature at every instant, the state of the solid will from time to time be
represented by the variable system of all these thermometric heights. It is re-
quired to express the successive states by analytical formulae, so that we may
know at any given instant the temperatures indicated by each thermometer,
and compare the quantities of heat which flow during the same instant, be-
tween two adjacent layers, or into the surrounding medium.

6. If the mass is spherical, and we denote by x the distance of a point of this
mass from the centre of the sphere, by t the time which has elapsed since the
commencement of the cooling, and by v the variable temperature of the point
m, it is easy to see that all points situated at the same distance x from the
centre of the sphere have the same temperature v. This quantity v is a certain
function F (x, f) of the radius x and of the time t; it must be such that it be-
comes constant whatever be the value of x, when we suppose t to be nothing;
for by hypothesis, the temperature at all points is the same at the moment of
emersion. The problem consists in determining that function of x and t which
expresses the value of v .

7. In the next place it is to be remarked, that during the cooling, a certain
quantity of heat escapes, at each instant, through the external surface, and

SECT. I THEORY OF HEAT 179

passes into the medium. The value of this quantity is not constant; it is great-
est at the beginning of the cooling. If however we consider the variable state
of the internal spherical surface whose radius is x, we easily see that there
must be at each instant a certain quantity of heat which traverses that sur-
face, and passes through that part of the mass which is more distant from the
centre. This continuous flow of heat is variable like that through the external
surface, and both are quantities comparable with each other; their ratios are
numbers whose varying values are functions of the distance x, and of the time
t which has elapsed. It is required to determine these functions.

8. If the mass, which has been heated by a long immersion in a medium, and
whose rate of cooling we wish to calculate, is of cubical form, and if we deter-
mine the position of each point m by three rectangular co-ordinates x, y, z,
taking for origin the centre of the cube, and for axes lines perpendicular to the
faces, we see that the temperature v of the point m after the time t, is a func-
tion of the four variables x t y t z, and t. The quantities of heat which flow out
at each instant through the whole external surface of the solid, are variable
and comparable with each other; their ratios are analytical functions depend-
ing on the time t, the expression of which must be assigned.

9. Let us examine also the case in which a rectangular prism of sufficiently
great thickness and of infinite length, being submitted at its extremity to a
constant temperature, whilst the air which surrounds it is maintained at a
less temperature, has at last arrived at a fixed state which it is required to
determine. All the points of the extreme section at the base of the prism have,
by hypothesis, a common and permanent temperature. It is not the same with
a section distant from the source of heat; each of the points of this rectangular
surface parallel to the base has acquired a fixed temperature, but this is not
the same at different points of the same section, and must be less at points
nearer to the surface exposed to the air. We see also that, at each instant,
there flows across a given section a certain quantity of heat, which always
remains the same, since the state of the solid has become constant. The prob-
lem consists in determining the permanent temperature at any given point of
the solid, and the whole quantity of heat which, in a definite time, flows across
a section whose position is given.

10. Take as origin of co-ordinates x, y, z, the centre of the base of the prism,
and as rectangular axes, the axis of the prism itself, and the two perpendicu-
lars on the sides: the permanent temperature v of the point m, whose co-ordi-
nates are x, y, 2, is a function of three variables F(x> y, z) : it has by hypothesis
a constant value, when we suppose x nothing, whatever be the values of y
and z. Suppose we take for the unit of heat that quantity which in the unit
of time would emerge from an area equal to a unit of surface, if the heated
mass which that area bounds, and which is formed of the same substance
as the prism, were continually maintained at the temperature of boiling
water, and immersed in atmospheric air maintained at the temperature of
melting ice.

We see that the quantity of heat which, in the permanent state of the rec-
tangular prism, flows, during a unit of time, across a certain section perpen-
dicular to the axis, has a determinate ratio to the quantity of heat taken as
unit. This ratio is not the same for all sections: it is a function <t>(x) of the dis-
tance x, at which the section is situated. It is required to find an analytical
expression of the function <f>(x).

180 FOURIER CHAP. I

11. The foregoing examples suffice to give an exact idea of the different prob-
lems which we have discussed.

The solution of these problems has made us understand that the effects of
the propagation of heat depend in the case of every solid substance, on three
elementary qualities, which are, its capacity for heat, its own conductivity,
and the exterior conductivity.

It has been observed that if two bodies of the same volume and of different
nature have equal temperatures, and if the same quantity of heat be added to
them, the increments of temperature are not the same ; the ratio of these incre-
ments is the inverse ratio of their capacities for heat. In this manner, the first
of the three specific elements which regulate the action of heat is exactly de-
fined, and physicists have for a long time known several methods of determin-
ing its value. It is not the same with the two others; their effects have often
been observed, but there is but one exact theory which can fairly distinguish,
define, and measure them with precision.

The proper or interior conductivity of a body expresses the facility with
which heat is propagated in passing from one internal molecule to another.
The external or relative conductivity of a solid body depends on the facility
with which heat penetrates the surface, and passes from this body into a given
medium, or passes from the medium into the solid. The last property is modi-
fied by the more or less polished state of the surface ; it varies also according to
the medium in which the body is immersed ; but the interior conductivity can
change only with the nature of the solid.

These three elementary qualities are represented in our formulae by constant
numbers, and the theory itself indicates experiments suitable for measuring
their values. As soon as they are determined, all the problems relating to the
propagation of heat depend only on numerical analysis. The knowledge of
these specific properties may be directly useful in several applications of the
physical sciences; it is besides an element in the study and description of differ-
ent substances. It is a very imperfect knowledge of bodies which ignores the
relations which they have with one of the chief agents of nature. In general,
there is no mathematical theory which has a closer relation than this with pub-
lic economy, since it serves to give clearness and perfection to the practice of
the numerous arts which are founded on the employment of heat.

12. The problem of the terrestrial temperatures presents one of the most
beautiful applications of the theory of heat; the general idea to be formed of it
is this. Different parts of the surface of the globe are unequally exposed to the
influence of the solar rays ; the intensity of their action depends on the latitude
of the place; it changes also in the course of the day and in the course of the
year, and is subject to other less perceptible inequalities. It is evident that,
between the variable state of the surface and that of the internal temperatures,
a necessary relation exists, which may be derived from theory. We know that,
at a certain depth below the surface of the earth, the temperature at a given
place experiences no annual variation : this permanent underground tempera-
ture becomes less and less according as the place is more and more distant
from the equator. We may then leave out of consideration the exterior enve-
lope, the thickness of which is incomparably small with respect to the earth's
radius, and regard our planet as a nearly spherical mass, whose surface is sub-
ject to a temperature which remains constant at all points on a given parallel,
but is not the same on another parallel. It follows from this that every internal

SECT. I THEORY OF HEAT 181

molecule has also a fixed temperature determined by its position. The mathe-
matical problem consists in discovering the fixed temperature at any given
point, and the law which the solar heat follows whilst penetrating the interior
of the earth.

This diversity of temperature interests us still more, if we consider the
changes which succeed each other in the envelope itself on the surface of which
we dwell. Those alternations of heat and cold which are reproduced every day
and in the course of every year, have been up to the present time the object of
repeated observations. These we can now submit to calculation, and from a
common theory derive all the particular facts which experience has taught us.
The problem is reducible to the hypothesis that every point of a vast sphere is
affected by periodic temperatures; analysis then tells us according to what law
the intensity of these variations decreases according as the depth increases,
what is the amount of the annual or diurnal changes at a given depth, the
epoch of the changes, and how the fixed value of the underground temperature
is deduced from the variable temperatures observed at the surface.

13. The general equations of the propagation of heat are partial differential
equations, and though their form is very simple the known methods do not
furnish any general mode of integrating them; we could not therefore deduce
from them the values of the temperatures after a definite time. The numerical
interpretation of the results of analysis is however necessary, and it is a degree
of perfection which it would be very important to give to every application of
analysis to the natural sciences. So long as it is not obtained, the solutions may
be said to remain incomplete and useless, and the truth which it is proposed to
discover is no less hidden in the formulae of analysis than it was in the physical
problem itself. We have applied ourselves with much care to this purpose, and
we have been able to overcome the difficulty in all the problems of which we
have treated, and which contain the chief elements of the theory of heat. There
is not one of the problems whose solution does not provide convenient and
exact means for discovering the numerical values of the temperatures acquired,
or those of the quantities of heat which have flowed through, when the values
of the time and of the variable coordinates are known. Thus will be given not
only the differential equations which the functions that express the values of
the temperatures must satisfy; but the functions themselves will be given
under a form which facilitates the numerical applications.

14. In order that these solutions might be general, and have an extent equal
to that of the problem, it was requisite that they should accord with the initial
state of the temperatures, which is arbitrary. The examination of this condition
shews that we may develop in convergent series, or express by definite integrals,
functions which are not subject to a constant law, and which represent the
ordinates or irregular or discontinuous lines. This property throws a new light
on the theory of partial differential equations, and extends the employment of
arbitrary functions by submitting them to the ordinary processes of analysis.

15. It still remained to compare the facts with theory. With this view, varied
and exact experiments were undertaken, whose results were in conformity
with those of analysis, and gave them an authority which one would have been
disposed to refuse to them in a new matter which seemed subject to so much
uncertainty. These experiments confirm the principle from which we started,
and which is adopted by all physicists in spite of the diversity of their hypo-
theses on the nature of heat.

182 FOURIER CHAP. I

16. Equilibrium of temperature is effected not only by way of contact, it is
established also between bodies separated from each other, which are situated
for a long time in the same region. This effect is independent of contact with a
medium; we have observed it in spaces wholly void of air. To complete our
theory it was necessary to examine the laws which radiant heat follows, on
leaving the surface of a body. It results from the observations of many physi-
cists and from our own experiments, that the intensities of the different rays,
which escape in all directions from any point in the surface of a heated body,
depend on the angles which their directions make with the surface at the same
point. We have proved that the intensity of a ray diminishes as the ray makes
a smaller angle with the element of surface, and that it is proportional to the sine
of that angle. This general law of emission of heat which different observations
had already indicated, is a necessary consequence of the principle of the equi-
librium of temperature and of the laws of propagation of heat in solid bodies.

Such are the chief problems which have been discussed in this work; they
are all directed to one object only, that is to establish clearly the mathematical
principles of the theory of heat, and to keep up in this way with the progress
of the useful arts, and of the study of nature.

17. From what precedes it is evident that a very extensive class of phenom-
ena exists, not produced by mechanical forces, but resulting simply from the
presence and accumulation of heat. This part of natural philosophy cannot be
connected with dynamical theories, it has principles peculiar to itself, and is
founded on a method similar to that of other exact sciences. The solar heat, for
example, which penetrates the interior of the globe, distributes itself therein
according to a regular law which does not depend on the laws of motion, and
cannot be determined by the principles of mechanics. The dilatations which
the repulsive force of heat produces, observation of which serves to measure
temperatures, are in truth dynamical effects; but it is not these dilatations
which we calculate, when we investigate the laws of the propagation of heat.

18. There are other more complex natural effects, which depend at the same
time on the influence of heat, and of attractive forces : thus, the variations of
temperatures which the movements of the sun occasion in the atmosphere and
in the ocean, change continually the density of the different parts of the air
and the waters. The effect of the forces which these masses obey is modified at
every instant by a new distribution of heat, and it cannot be doubted that this
cause produces the regular winds, and the chief currents of the sea; the solar
and lunar attractions occasioning in the atmosphere effects but slightly sensi-
ble, and not general displacements. It was therefore necessary, in order to sub-
mit these grand phenomena to calculation, to discover the mathematical laws
of the propagation of heat in the interior of masses.

19. It will be perceived, on reading this work, that heat attains in bodies a
regular disposition independent of the original distribution, which may be
regarded as arbitrary.

In whatever manner the heat was at first distributed, the system of tempera-
tures altering more and more, tends to coincide sensibly with a definite state
which depends only on the form of the solid. In the ultimate state the tempera-
tures of all the points are lowered in the same time, but preserve amongst each
other the same ratios: in order to express this property the analytical formulae
contain terms composed of exponentials and of quantities analogous to
trigonometric functions.

SECT. I THEORY OF HEAT 183

Several problems of mechanics present analogous results, such as the isoch-
ronism of oscillations, the multiple resonance of sonorous bodies. Common
experiments had made these results remarked, and analysis afterwards demon-
strated their true cause. As to those results which depend on changes of tem-
perature, they could not have been recognised except by very exact experi-
ments; but mathematical analysis has outrun observation, it has supplemented
our senses, and has made us in a manner witnesses of regular and harmonic
vibrations in the interior of bodies.

20. These considerations present a singular example of the relations which
exist between the abstract science of numbers and natural causes.

When a metal bar is exposed at one end to the constant action of a source of
heat, and every point of it has attained its highest temperature, the system of
fixed temperatures corresponds exactly to a table of logarithms; the numbers
are the elevations of thermometers placed at the different points, and the
logarithms are the distances of these points from the source. In general, heat
distributes itself in the interior of solids according to a simple law expressed by
a partial differential equation common to physical problems of different order.
The irradiation of heat has an evident relation to the tables of sines, for the
rays which depart from the same point of a heated surface, differ very much
from each other, and their intensity is rigorously proportional to the sine of the
angle which the direction of each ray makes with the element of surface.

If we could observe the changes of temperature for every instant at every
point of a solid homogeneous mass, we should discover in these series of ob-
servations the properties of recurring series, as of sines and logarithms; they
would be noticed for example in the diurnal or annual variations of tempera-
ture of different points of the earth near its surface.

We should recognise again the same results and all the chief elements of
general analysis in the vibrations of elastic media, in the properties of lines or
of curved surfaces, in the movements of the stars, and those of light or of
fluids. Thus the functions obtained by successive differentiations, which are
employed in the development of infinite series and in the solution of numerical
equations, correspond also to physical properties. The first of these functions,
or the fluxion properly so called, expresses in geometry the inclination of the
tangent of a curved line, and in dynamics the velocity of a moving body when
the motion varies ; in the theory of heat it measures the quantity of heat which
flows at each point of a body across a given surface. Mathematical analysis has
therefore necessary relations with sensible phenomena; its object is not created
by human intelligence; it is a pre-existent element of the universal order, and
is not in any way contingent or fortuitous; it is imprinted throughout all
nature.

21. Observations more exact and more varied will presently ascertain
whether the effects of heat are modified by causes which have not yet been
perceived, and the theory will acquire fresh perfection by the continued com-
parison of its results with the results of experiment; it will explain some im-
portant phenomena which we have not yet been able to submit to calculation;
it will shew how to determine all the thermometric effects of the solar rays, the
fixed or variable temperature which would be observed at different distances
from the equator, whether in the interior of the earth or beyond the limits of
the atmosphere, whether in the ocean or in different regions of the air. From it
will be derived the mathematical knowledge of the great movements which

184 FOURIER CHAP. I

result from the influence of heat combined with that of gravity. The same
principles will serve to measure the conductivities, proper or relative, of dif-
ferent bodies, and their specific capacities, to distinguish all the causes which
modify the emission of heat at the surface of solids, and to perfect thermomet-
ric instruments.

The theory of heat will always attract the attention of mathematicians, by
the rigorous exactness of its elements and the analytical difficulties peculiar to
it, and above all by the extent and usefulness of its applications; for all its
consequences concern at the same time general physics, the operations of the
arts, domestic uses and civil economy.

SECTION II. Preliminary Definitions and General Notions

22. Of the nature of heat uncertain hypotheses only could be formed, but the
knowledge of the mathematical laws to which its effects are subject is inde-
pendent of all hypothesis; it requires only an attentive examination of the
chief facts which common observations have indicated, and which have been
confirmed by exact experiments.

It is necessary then to set forth, in the first place, the general results of
observation, to give exact definitions of all the elements of the analysis, and to
establish the principles upon which this analysis ought to be founded.

The action of heat tends to expand all bodies, solid, liquid or gaseous; this is
the property which gives evidence of its presence. Solids and liquids increase in
volume, in most cases, if the quantity of heat which they contain increases;
they contract if it diminishes.

When all the parts of a solid homogeneous body, for example those of a mass
of metal, are equally heated, and preserve without any change the same quan-
tity of heat, they have also and retain the same density. This state is expressed
by saying that throughout the whole extent of the mass the molecules have a
common and permanent temperature.

23. The thermometer is a body whose smallest changes of volume can be
appreciated; it serves to measure temperatures by the dilatation of a fluid or
of air. We assume the construction, use and properties of this instrument to be
accurately known. The temperature of a body equally heated in every part,
and which keeps its heat, is that which the thermometer indicates when it is
and remains in perfect contact with the body in question.

Perfect contact is when the thermometer is completely immersed in a fluid
mass, and, in general, when there is no point of the external surface of the
instrument which is not touched by one of the points of the solid or liquid mass
whose temperature is to be measured. In experiments it is not always necessary
that this condition should be rigorously observed; but it ought to be assumed
in order to make the definition exact.

24. Two fixed temperatures are determined on, namely: the temperature of
melting ice which is denoted by 0, and the temperature of boiling water which
we will denote by 1 : the water is supposed to be boiling under an atmospheric
pressure represented by a certain height of the barometer (76 centimetres), the
mercury of the barometer being at the temperature 0.

25. Different quantities of heat are measured by determining how many
times they contain a fixed quantity which is taken as the unit. Suppose a mass
of ice having a definite weight (a kilogramme) to be at temperature 0, and to

SECT. II THEORY OF HEAT 185

be converted into water at the same temperature by the addition of a certain
quantity of heat: the quantity of heat thus added is taken as the unit of
measure. Hence the quantity of heat expressed by a number C contains C
times the quantity required to melt a kilogramme of ice at the temperature
zero into a mass of water at the same zero temperature.

26. To raise a metallic mass having a certain weight, a kilogramme of iron
for example, from the temperature to the temperature 1, a new quantity of
heat must be added to that which is already contained in the mass. The num-
ber C which denotes this additional quantity of heat, is the specific capacity of
iron for heat; the number C has very different values for different substances.

27. If a body of definite nature and weight (a kilogramme of mercury)
occupies a volume V at temperature 0, it will occupy a greater volume V+ A,
when it has acquired the temperature 1, that is to say, when the heat which it
contained at the temperature has been increased by a new quantity C, equal
to the specific capacity of the body for heat. But if, instead of adding this
quantity C, a quantity zC is added (z being a number positive or negative) the
new volume will be V+5 instead of F+A. Now experiments shew that if z is
equal to J, the increase of volume 5 is only half the total increment A, and that
in general the value of 6 is zA, when the quantity of heat added is zC.

28. The ratio z of the two quantities zC and C of heat added, which is the
same as the ratio of the two increments of volume 6 and A, is that which is
called the temperature, hence the quantity which expresses the actual tempera-
ture of a body represents the excess of its actual volume over the volume which
it would occupy at the temperature of melting ice, unity representing the
whole excess of volume which corresponds to the boiling point of water, over
the volume which corresponds to the melting point of ice.

29. The increments of volume of bodies are in general proportional to the
increments of the quantities of heat which produce the dilatations, but it must
be remarked that this proportion is exact only in the case where the bodies in
question are subjected to temperatures remote from those which determine
their change of state. The application of these results to all liquids must not be
relied on; and with respect to water in particular, dilatations do not always
follow augmentations of heat.

In general the temperatures are numbers proportional to the quantities of
heat added, and in the cases considered by us, these numbers are proportional
also to the increments of volume.

30. Suppose that a body bounded by a plane surface having a certain area
(a square metre) is maintained in any manner whatever at constant tempera-
ture 1, common to all its points, and that the surface in question is in contact
with air maintained at temperature : the heat which escapes continuously at
the surface and passes into the surrounding medium will be replaced always
by the heat which proceeds from the constant cause to whose action the body
is exposed ; thus, a certain quantity of heat denoted by h will flow through the
surface in a definite time (a minute).

This amount ft, of a flow continuous and always similar to itself, which takes
place at a unit of surface at a fixed temperature, is the measure of the external
conducibility of the body, that is to say, of the facility with which its surface
transmits heat to the atmospheric air.

The air is supposed to be continually displaced with a given uniform veloc-
ity : but if the velocity of the current increased, the quantity of heat communi-

186 FOURIER CHAP, I

cated to the medium would vary also : the same would happen if the density of
the medium were increased.

31. If the excess of the constant temperature of the body over the tempera-
ture of surrounding bodies, instead of being equal to 1, as has been supposed,
had a less value, the quantity of heat dissipated would be less than h. The
result of observation is, as we shall see presently, that this quantity of heat
lost may be regarded as sensibly proportional to the excess of the temperature
of the body over that of the air and surrounding bodies. Hence the quantity h
having been determined by one experiment in which the surface heated is at
temperature 1, and the medium at temperature 0; we conclude that hz would
be the quantity, if the temperature of the surface were z, all the other circum-
stances remaining the same. This result must be admitted when z is a small
fraction.

32. The value h of the quantity of heat which is dispersed across a heated
surface is different for different bodies; and it varies for the same body accord-
ing to the different states of the surface. The effect of irradiation diminishes as
the surface becomes more polished; so that by destroying the polish of the
surface the value of h is considerably increased. A heated metallic body will be
more quickly cooled if its external surface is covered with a black coating such
as will entirely tarnish its metallic lustre.

33. The rays of heat which escape from the surface of a body pass freely
through spaces void of air; they are propagated also in atmospheric air: their
directions are not disturbed by agitations in the intervening air : they can be
reflected by metal mirrors and collected at their foci. Bodies at a high tempera-
ture, when plunged into a liquid, heat directly only those parts of the mass
with which their surface is in contact. The molecules whose distance from this
surface is not extremely small, receive no direct heat; it is not the same with
aeriform fluids; in these the rays of heat are borne with extreme rapidity to
considerable distances, whether it be that part of these rays traverses freely
the layers of air, or whether these layers transmit the rays suddenly without
altering their direction.

34. When the heated body is placed in air which is maintained at a sensibly
constant temperature, the heat communicated to the air makes the layer of the
fluid nearest to the surface of the body lighter; this layer rises more quickly
the more intensely it is heated, and is replaced by another mass of cool air. A
current is thus established in the air whose direction is vertical, and whose
velocity is greater as the temperature of the body is higher. For this reason if
the body cooled itself gradually the velocity of the current would diminish
with the temperature, and the law of cooling would not be exactly the same as
if the body were exposed to a current of air at a constant velocity.

35. When bodies are sufficiently heated to diffuse a vivid light, part of their
radiant heat mixed with that light can traverse transparent solids or liquids,
and is subject to the force which produces refraction. The quantity of heat
which possesses this faculty becomes less as the bodies are less inflamed; it is,
we may say, insensible for very opaque bodies however highly they may be
heated. A thin transparent plate intercepts almost all the direct heat which
proceeds from an ardent mass of metal; but it becomes heated in proportion
as the intercepted rays are accumulated in it; whence, if it is formed of ice, it
becomes liquid; but if this plate of ice is exposed to the rays of a torch it
allows a sensible amount of heat to pass through with the light.

SECT. II THEORY OF HEAT 187

36. We have taken as the measure of the external conductivity of a solid
body a coefficient h, which denotes the quantity of heat which would pass, in a
definite time (a minute), from the surface of this body, into atmospheric air,
supposing that the surface had a definite extent (a square metre), that the
constant temperature of the body was 1, and that of the air 0, and that the
heated surface was exposed to a current of air of a given invariable velocity.
This value of h is determined by observation. The quantity of heat expressed
by the coefficient is composed of two distinct parts which cannot be measured
except by very exact experiments. One is the heat communicated by way of
contact to the surrounding air: the other, much less than the first, is the radi-
ant heat emitted. We must assume, in our first investigations, that the quan-
tity of heat lost does not change when the temperatures of the body and of the
medium are augmented by the same sufficiently small quantity.

37. Solid substances differ again, as we have already remarked, by their
property of being more or less permeable to heat; this quality is their conduc-
tivity proper: we shall give its definition and exact measure, after having
treated of the uniform and linear propagation of heat. Liquid substances
possess also the property of transmitting heat from molecule to molecule, and
the numerical value of their conductivity varies according to the nature of the
substances: but this effect is observed with difficulty in liquids, since their
molecules change places on change of temperature. The propagation of heat in
them depends chiefly on this continual displacement, in all cases where the
lower parts of the mass are most exposed to the action of the source of heat.
If, on the contrary, the source of heat be applied to that part of the mass
which is highest, as was the case in several of our experiments, the transfer of
heat, which is very slow, does not produce any displacement, at least when the
increase of temperature does not diminish the volume, as is indeed noticed in
singular cases bordering on changes of state.

38. To this explanation of the chief results of observation, a general remark
must be added on equilibrium of temperatures; which consists in this, that
different bodies placed in the same region, all of whose parts are and remain
equally heated, acquire also a common and permanent temperature.

Suppose that all the parts of a mass M have a common and constant tem-
perature a, which is maintained by any cause whatever: if a smaller body ra
be placed in perfect contact with the mass M, it will assume the common
temperature a.

In reality this result would not strictly occur except after an infinite time :
but the exact meaning of the proposition is that if the body m had the tempera-
ture a before being placed in contact, it would keep it without any change.
The same would be the case with a multitude of other bodies n, p y q, r each
of which was placed separately in perfect contact with the mass M : all
would acquire the constant temperature a. Thus a thermometer if succes-
sively applied to the different bodies m, n, p, q, r would indicate the same tem-
perature.

39. The effect in question is independent of contact, and would still occur, if
every part of the body m were enclosed in the solid M, as in an enclosure,
without touching any of its parts. For example, if the solid were a spherical
envelope of a certain thickness, maintained by some external cause at a tem-
perature a, and containing a space entirely deprived of air, and if the body m
could be placed in any part whatever of this spherical space, without touching

188 FOURIER CHAP. I

any point of the internal surface of the enclosure, it would acquire the common
temperature a, or rather, it would preserve it if it had it already. The result
would be the same for all the other bodies n, p, q y r, whether they were placed
separately or all together in the same enclosure, and whatever also their
substance and form might be.

40. Of all modes of presenting to ourselves the action of heat, that which
seems simplest and most conformable to observation, consists in comparing
this action to that of light. Molecules separated from one another reciprocally
communicate, across empty space, their rays of heat, just as shining bodies
transmit their light.

If within an enclosure closed in all directions, and maintained by some
external cause at a fixed temperature a, we suppose different bodies to be
placed without touching any part of the boundary, different effects will be
observed according as the bodies, introduced into this space free from air, are
more or less heated. If, in the first instance, we insert only one of these bodies,
at the same temperature as the enclosure, it will send from all points of its
surface as much heat as it receives from the solid which surrounds it, and is
maintained in its original state by this exchange of equal quantities.

If we insert a second body whose temperature b is less than a, it will at first
receive from the surfaces which surround it on all sides without touching it, a
quantity of heat greater than that which it gives out : it will be heated more
and more and will absorb through its surface more heat than in the first
instance.

The initial temperature 6 continually rising, will approach without ceasing
the fixed temperature a, so that after a certain time the difference will be
almost insensible. The effect would be opposite if we placed within the same
enclosure a third body whose temperature was greater than a.

41. All bodies have the property of emitting heat through their surface; the
hotter they are the more they emit; the intensity of the emitted rays changes
very considerably with the state of the surface.

42. Every surface which receives rays of heat from surrounding bodies
reflects part and admits the rest: the heat which is not reflected, but intro-
duced through the surface, accumulates within the solid; and so long as it
exceeds the quantity dissipated by irradiation, the temperature rises.

43. The rays which tend to go out of heated bodies are arrested at the sur-
face by a force which reflects part of them into the interior of the mass. The
cause which hinders the incident rays from traversing the surface, and which
divides these rays into two parts, of which one is reflected and the other
admitted, acts in the same manner on the rays which are directed from the
interior of the body towards external space.

If by modifying the state of the surface we increase the force by which it
reflects the incident rays, we increase at the same time the power which it has
of reflecting towards the interior of the body rays which are tending to go out.
The incident rays introduced into the mass, and the rays emitted through the
surface, are equally diminished in quantity.

44. If within the enclosure above mentioned a number of bodies were placed
at the same time, separate from each other and unequally heated, they would
receive and transmit rays of heat so that at each exchange their temperatures
would continually vary, and would all tend to become equal to the fixed
temperature of the enclosure.

SECT. II THEORY OF HEAT 189

This effect is precisely the same as that which occurs when heat is propa-
gated within solid bodies; for the molecules which compose these bodies are
separated by spaces void of air, and have the property of receiving, accumulat-
ing and emitting heat. Each of them sends out rays on all sides, and at the
same time receives other rays from the molecules which surround it.

45. The heat given out by a point situated in the interior of a solid mass can
pass directly to an extremely small distance only; it is, we may say, intercepted
by the nearest particles; these particles only receive the heat directly and act
on more distant points. It is different with gaseous fluids ; the direct effects of
radiation become sensible in them at very considerable distances.

46. Thus the heat which escapes in all directions from a part of the surface
of a solid, passes on in air to very distant points; but is emitted only by those
molecules of the body which are extremely near the surface. A point of a
heated mass situated at a very small distance from the plane superficies which
separates the mass from external space, sends to that space an infinity of rays,
but they do not all arrive there; they are diminished by all that quantity of
heat which is arrested by the intermediate molecules of the solid. The part of
the ray actually dispersed into space becomes less according as it traverses a
longer path within the mass. Thus the ray which escapes perpendicular to the
surface has greater intensity than that which, departing from the same point,
follows an oblique direction, and the most oblique rays are wholly intercepted.

The same consequences apply to all the points which are near enough to the
surface to take part in the emission of heat, from which it necessarily follows
that the whole quantity of heat which escapes from the surface in the normal
direction is very much greater than that whose direction is oblique. We have
submitted this question to calculation, and our analysis proves that the inten-
sity of the ray is proportional to the sine of the angle which the ray makes with
the element of surface. Experiments had already indicated a similar result.

47. This theorem expresses a general law which has a necessary connection
with the equilibrium and mode of action of heat. If the rays which escape from
a heated surface had the same intensity in all directions, a thermometer placed
at one of the points of a space bounded on all sides by an enclosure maintained
at a constant temperature would indicate a temperature incomparably greater
than that of the enclosure. Bodies placed within this enclosure would not take
a common temperature, as is always noticed; the temperature acquired by
them would depend on the place which they occupied, or on their form, or on
the forms of neighbouring bodies.

The same results would be observed, or other effects equally opposed to
common experience, if between the rays which escape from the same point any
other relations were admitted different from those which we have enunciated.
We have recognised this law as the only one compatible with the general fact
of the equilibrium of radiant heat.

48. If a space free from air is bounded on all sides by a solid enclosure whose
parts are maintained at a common and constant temperature a, and if a ther-
mometer, having the actual temperature a, is placed at any point whatever of
the space, its temperature will continue without any change. It will receive
therefore at each instant from the inner surface of the enclosure as much heat
as it gives out to it. This effect of the rays of heat in a given space is, properly
speaking, the measure of the temperature: but this consideration presupposes
the mathematical theory of radiant heat.

190 FOURIER CHAP. I

If now between the thermometer and a part of the surface of the enclosure a
body M be placed whose temperature is a, the thermometer will cease to
receive rays from one part of the inner surface, but the rays will be replaced by
those which it will receive from the interposed body M . An easy calculation
proves that the compensation is exact, so that the state of the thermometer
will be unchanged. It is not the same if the temperature of the body M is
different from that of the enclosure. When it is greater, the rays which the
interposed body M sends to the thermometer and which replace the inter-
cepted rays convey more heat than the latter; the temperature of the ther-
mometer must therefore rise.

If, on the contrary, the intervening body has a temperature less than a, that
of the thermometer must fall; for the rays which this body intercepts are
replaced by those which it gives out, that is to say, by rays cooler than those
of the enclosure; thus the thermometer does not receive all the heat necessary
to maintain its temperature a.

49. Up to this point abstraction has been made of the power which all sur-
faces have of reflecting part of the rays which are sent to them. If this property
were disregarded we should have only a very incomplete idea of the equilib-
rium of radiant heat.

Suppose then that on the inner surface of the enclosure, maintained at a
constant temperature, there is a portion which enjoys, in a certain degree, the
power in question ; each point of the reflecting surface will send into space two
kinds of rays; the one go out from the very interior of the substance of which
the enclosure is formed, the others are merely reflected by the same surface
against which they had been sent. But at the same time that the surface repels
on the outside part of the incident rays, it retains in the inside part of its own
rays. In this respect an exact compensation is established, that is to say, every
one of its own rays which the surface hinders from going out is replaced by a
reflected ray of equal intensity.

The same result would happen, if the power of reflecting rays affected in any
degree whatever other parts of the enclosure, or the surface of bodies placed
within the same space and already at the common temperature.

Thus the reflection of heat does not disturb the equilibrium of temperatures,
and does not introduce, whilst that equilibrium exists, any change in the law
according to which the intensity of rays which leave the same point decreases
proportionally to the sine of the angle of emission.

50. Suppose that in the same enclosure, all of whose parts maintain the
temperature a, we place an isolated body M, and a polished metal surface R,
which, turning its concavity towards the body, reflects great part of the rays
which it received from the body; if we place a thermometer between the body
M and the reflecting surface R, at the focus of this mirror, three different
effects will be observed according as the temperature of the body M is equal to
the common temperature a, or is greater or less.

In the first case, the thermometer preserves the temperature a; it receives
1, rays of heat from all parts of the enclosure not hidden from it by the body
M or by the mirror; 2, rays given out by the body; 3, those which the surface
R sends out to the focus, whether they come from the mass of the mirror
itself, or whether its surface has simply reflected them ; and amongst the last
we may distinguish between those which have been sent to the mirror by the
mass M , and those which it has received from the enclosure. All the rays in

SECT. II THEORY OF HEAT 191

question proceed from surfaces which, by hypothesis, have a common temper-
ature a, so that the thermometer is precisely in the same state as if the space
bounded by the enclosure contained no other body but itself.

In the second case, the thermometer placed between the heated body M and
the mirror, must acquire a temperature greater than a. In reality, it receives
the same rays as in the first hypothesis; but with two remarkable differences:
one arises from the fact that the rays sent by the body M to the mirror, and
reflected upon the thermometer, contain more heat than in the first case. The
other difference depends on the fact that the rays sent directly by the body M
to the thermometer contain more heat than formerly. Both causes, and chiefly
the first, assist in raising the temperature of the thermometer.

In the third case, that is to say, when the temperature of the mass M is less
than a, the temperature must assume also a temperature less than a. In fact, it
receives again all the varieties of rays which we distinguished in the first case:
but there are two kinds of them which contain less heat than in this first
hypothesis, that is to say, those which, being sent out by the body M, are
reflected by the mirror upon the thermometer, and those which the same body
M sends to it directly. Thus the thermometer does not receive all the heat
which it requires to preserve its original temperature a. It gives out more heat
than it receives. It is inevitable then that its temperature must fall to the
point at which the rays which it receives suffice to compensate those which it
loses. This last effect is what is called the reflection of cold, and which, prop-
erly speaking, consists in the reflection of too feeble heat. The mirror inter-
cepts a certain quantity of heat, and replaces it by a less quantity.

51. If in the enclosure, maintained at a constant temperature a, a body M
be placed, whose temperature a' is less than a, the presence of this body will
lower the thermometer exposed to its rays, and we may remark that the rays
sent to the thermometer from the surface of the body M 9 are in general of two
kinds, namely, those which come from inside the mass M , and those which,
coming from different parts of the enclosure, meet the surface M and are
reflected upon the thermometer. The latter rays have the common tempera-
ture a, but those which belong to the body M contain less heat, and these are
the rays which cool the thermometer. If now, by changing the state of the
surface of the body M, for example, by destroying the polish, we diminish the
power which it has of reflecting the incident rays, the thermometer will fall
still lower, and will assume a temperature a 11 less than a. In fact all the condi-
tions would be the same as in the preceding case, if it were not that the body
M gives out a greater quantity of its own rays and reflects a less quantity of
the rays which it receives from the enclosure; that is to say, these last rays,
which have the common temperature, are in part replaced by cooler rays.
Hence the thermometer no longer receives so much heat as formerly.

If, independently of the change in the surface of the body M , we place a
metal mirror adapted to reflect upon the thermometer the rays which have
left M f the temperature will assume a value a'" less than a". The mirror, in
fact, intercepts from the thermometer part of the rays of the enclosure which
all have the temperature a, and replaces them by three kinds of rays; namely,
1, those which come from the interior of the mirror itself, and which have the
common temperature; 2, those which the different parts of the enclosure send
to the mirror with the same temperature, and which are reflected to the focus ;
3, those which, coming from the interior of the body M , fall upon the mirror,

192 FOURIER CHAP. I

and are reflected upon the thermometer. The last rays have a temperature less
than a; hence the thermometer no longer receives so much heat as it received
before the mirror was set up.

Lastly, if we proceed to change also the state of the surface of the mirror,
and by giving it a more perfect polish, increase its power of reflecting heat, the
thermometer will fall still lower. In fact, all the conditions exist which occurred
in the preceding case. Only, it happens that the mirror gives out a less quan-
tity of its own rays, and replaces them by those which it reflects. Now,
amongst these last rays, all those which proceed from the interior of the mass
M are less intense than if they had come from the interior of the metal mirror;
hence the thermometer receives still less heat than formerly: it will assume
therefore a temperature a"" less than a'" .

By the same principles all the known facts of the radiation of heat or of cold
are easily explained.

52. The effects of heat can by no means be compared with those of an elastic
fluid whose molecules are at rest.

It would be useless to attempt to deduce from this hypothesis the laws of
propagation which we have explained in this work, and which all experience
has confirmed. The free state of heat is the same as that of light; the active
state of this element is then entirely different from that of gaseous substances.
Heat acts in the same manner in a vacuum, in elastic fluids, and in liquid or
solid masses, it is propagated only by way of radiation, but its sensible effects
differ according to the nature of bodies.

53. Heat is the origin of all elasticity; it is the repulsive force which pre-
serves the form of solid masses, and the volume of liquids. In solid masses,
neighbouring molecules would yield to their mutual attraction, if its effect
were not destroyed by the heat which separates them.

This elastic force is greater according as the temperature is higher ; which is the
reason why bodies dilate or contract when their temperature is raised or lowered.

54. The equilibrium which exists, in the interior of a solid mass, between the
repulsive force of heat and the molecular attraction, is stable; that is to say, it
re-establishes itself when disturbed by an accidental cause. If the molecules
are arranged at distances proper for equilibrium, and if an external force
begins to increase this distance without any change of temperature, the effect
of attraction begins by surpassing that of heat, and brings back the molecules
to their original position, after a multitude of oscillations which become less
and less sensible.

A similar effect is exerted in the opposite sense when a mechanical cause
diminishes the primitive distance of the molecules; such is the origin of the
vibrations of sonorous or flexible bodies, and of all the effects of their elasticity.

55. In the liquid or gaseous state of matter, the external pressure is addi-
tional or supplementary to the molecular attraction, and, acting on the sur-
face, does not oppose change of form, but only change of the volume occupied.
Analytical investigation will best shew how the repulsive force of heat, opposed
to the attraction of the molecules or to the external pressure, assists in the
composition of bodies, solid or liquid, formed of one or more elements, and
determines the elastic properties of gaseous fluids; but these researches do not
belong to the object before us, and appear in dynamic theories.

56. It cannot be doubted that the mode of action of heat always consists,
like that of light, in the reciprocal communication of rays, and this explana-

SECT. Ill THEORY OF HEAT 193

tion is at the present time adopted by the majority of physicists; but it is not
necessary to consider the phenomena under this aspect in order to establish
the theory of heat. In the course of this work it will be seen how the laws of
equilibrium and propagation of radiant heat, in solid or liquid masses, can
be rigorously demonstrated, independently of any physical explanation, as the
necessary consequences of common observations.

SECTION III. Principle of the Communication of Heat

57. We now proceed to examine what experiments teach us concerning the
communication of heat.

If two equal molecules are formed of the same substance and have the same
temperature, each of them receives from the other as much heat as it gives up
to it; their mutual action may then be regarded as null, since the result of this
action can bring about no change in the state of the molecules. If, on the con-
trary, the first is hotter than the second, it sends to it more heat than it re-
ceives from it; the result of the mutual action is the difference of these two
quantities of heat. In all cases we make abstraction of the two equal quantities
of heat which any two material points reciprocally give up; we conceive that
the point most heated acts only on the other, and that, in virtue of this action,
the first loses a certain quantity of heat which is acquired by the second. Thus
the action of the two molecules, or the quantity of heat which the hottest
communicates to the other, is the difference of the two quantities which they
give up to each other.

58. Suppose that we place in air a solid homogeneous body, whose different
points have unequal actual temperatures; each of the molecules of which the
body is composed will begin to receive heat from those which are at extremely
small distances, or will communicate it to them. This action exerted during
the same instant between all points of the mass, will produce an infinitesimal
resultant change in all the temperatures: the solid will experience at each
instant similar effects, so that the variations of temperature will become more
and more sensible.

Consider only the system of two molecules, m and n, equal and extremely
near, and let us ascertain what quantity of heat the first can receive from the
second during one instant: we may then apply the same reasoning to all the
other points which are near enough to the point m, to act directly on it during
the first instant.

The quantity of heat communicated by the point n to the point m depends
on the duration of the instant, on the very small distance between these
points, on the actual temperature of each point, and on the nature of the solid
substance; that is to say, if one of these elements happened to vary, all the
other remaining the same, the quantity of heat transmitted would vary also.
Now experiments have disclosed, in this respect, a general result : it consists in
this, that all the other circumstances being the same, the quantity of heat
which one of the molecules receives from the other is proportional to the dif-
ference of temperature of the two molecules. Thus the quantity would be
double, triple, quadruple, if everything else remaining the same, the difference
of the temperature of the point n from that of the point m became double,
triple, or quadruple. To account for this result, we must consider that the
action of n on m is always just as much greater as there is a greater difference

194 FOURIER CHAP. I

between the temperatures of the two points : it is null, if the temperatures are
equal, but if the molecule n contains more heat than the equal molecule m,
that is to say, if the temperature of m being t>, that of n is v+A, a portion of
the exceeding heat will pass from n to m. Now, if the excess of heat were dou-
ble, or, which is the same thing, if the temperature of n were e;+2A, the exceed-
ing heat would be composed of two equal parts corresponding to the two
halves of the whole difference of temperature 2A; each of these parts would
have its proper effect as if it alone existed: thus the quantity of heat com-
municated by n torn would be twice as great as when the difference of temper-
ature is onlyA. This simultaneous action of the different parts of the exceeding
heat is that which constitutes the principle of the communication of heat. It
follows from it that the sum of the partial actions, or the total quantity of heat
which m receives from n is porportional to the difference of the two tempera-
tures.

59. Denoting by v and e/ the temperatures of two equal molecules m and n,
by p, their extremely small distance, and by dt, the infinitely small duration of
the instant, the quantity of heat which m receives from n during this instant
will be expressed by (v' v)<f>(p) -dt. We denote by <t>(p) a certain function of
the distance p which, in solid bodies and in liquids, becomes nothing when p
has a sensible magnitude. The function is the same for every point of the same
given substance; it varies with the nature of the substance.

60. The quantity of heat which bodies lose through their surface is subject
to the same principle. If we denote by a the area, finite or infinitely small, of
the surface, all of whose points have the temperature v, and if a represents the
temperature of the atmospheric air, the coefficient h being the measure of the
external conducibility, we shall have ah(v a)dt as the expression for the
quantity of heat which this surface a transmits to the air during the instant dt.

When the two molecules, one of which transmits to the other a certain quan-
tity of heat, belong to the same solid, the exact expression for the heat com-
municated is that which we have given in the preceding article; and since the
molecules are extremely near, the difference of the temperatures is extremely
small. It is not the same when heat passes from a solid body into a gaseous
medium. But the experiments teach us that if the difference is a quantity
sufficiently small, the heat transmitted is sensibly proportional to that differ-
ence, and that the number h may, in these first researches, be considered as
having a constant value, proper to each state of the surface, but independent
of the temperature.

61. These propositions relative to the quantity of heat communicated have
been derived from different observations. We see first, as an evident conse-
quence of the expressions in question, that if we increased by a common quan-
tity all the initial temperatures of the solid mass, and that of the medium in
which it is placed, the successive changes of temperature would be exactly the
same as if this increase had not been made. Now this result is sensibly in
accordance with experiment; it has been admitted by the physicists who first
have observed the effects of heat.

62. If the medium is maintained at a constant temperature, and if the
heated body which is placed in that medium has dimensions sufficiently small
for the temperature, whilst falling more and more, to remain sensibly the same
at all points of the body, it follows from the same propositions, that a quantity
of heat will escape at each instant through the surface of the body proportional

SECT. Ill THEORY OF HEAT 195

to the excess of its actual temperature over that of the medium. Whence it is
easy to conclude, as will be seen in the course of this work, that the line whose
abscissae represent the times elapsed, and whose ordinates represent the tem-
peratures corresponding to those times, is a logarithmic curve : now, observa-
tions also furnish the same result, when the excess of the temperature of the
solid over that of the medium is a sufficiently small quantity.

63. Suppose the medium to be maintained at the constant temperature 0,
and that the initial temperatures of different points a, 6, c, d &c. of the same
mass are a, 0, 7, d &c., that at the end of the first instant they have become
a', 0', 7', d' &c., that at the end of the second instant they have become a n ', ",
7", d" &G.J and so on. We may easily conclude from the propositions enun-
ciated, that if the initial temperatures of the same points had been got, g(3, gy,
gd &c. (g being any number whatever), they would have become, at the end of
the first instant, by virtue of the action of the different points, ga', gP', gy',
gd' &c., and at the end of the second instant, got!' , g($", gy", gd" &c., and so on.
For instance, let us compare the case when the initial temperatures of the
points, a, 6, c, d &c. were a, /3, 7, 6 &c. with that in which they are 2a, 2/3, 27,
25 &c., the medium preserving in both cases the temperature 0. In the second
hypothesis, the difference of the temperatures of any two points whatever is
double what it was in the first, and the excess of the temperature of each point,
over that of each molecule of the medium, is also double; consequently the
quantity of heat which any molecule whatever sends to any other, or that
which it receives, is, in the second hypothesis, double of that which it was in
the first. The change of temperature which each point suffers being propor-
tional to the quantity of heat acquired, it follows that, in the second case, this
change is double what it was in the first case. Now we have supposed that the
initial temperature of the first point, which was or, became of at the end of the
first instant ; hence if this initial temperature had been 2a, and if all the other
temperatures had been doubled, it would have become 2a'. The same would
be the case with all the other molecules fr, c, d, and a similar result would be
derived, if the ratio instead of being 2, were any number whatever g. It follows
then, from the principle of the communication of heat, that if we increase or
diminish in any given ratio all the initial temperatures, we increase or diminish
in the same ratio all the successive temperatures.

This, like the two preceding results, is confirmed by observation. It could
not have existed if the quantity of heat which passes from one molecule to
another had not been, actually, proportional to the difference of the tem-
peratures.

64. Observations have been made with accurate instruments, on the perma-
nent temperatures at different points of a bar or of a metallic ring, and on the
propagation of heat in the same bodies and in several other solids of the form
of spheres or cubes. The results of these experiments agree with those which
are derived from the preceding propositions. They would be entirely different
if the quantity of heat transmitted from one solid molecule to another, or to a
molecule of air, were not proportional to the excess of temperature. It is
necessary first to know all the rigorous consequences of this proposition; by it
we determine the chief part of the quantities which are the object of the
problem. By comparing then the calculated values with those given by numer-
ous and very exact experiments, we can easily measure the variations of the
coefficients, and perfect our first researches.

196 FOURIER CHAP. I

SECTION IV. On the Uniform and Linear Movement of Heat

65. We shall consider, in the first place, the uniform movement of heat in the
simplest case, which is that of an infinite solid enclosed between two parallel
planes.

We suppose a solid body formed of some homogeneous substance to be
enclosed between two parallel and infinite planes ; the lower plane A is main-
tained, by any cause whatever, at a constant temperature a; we may imagine
for example that the mass is prolonged, and that the plane A is a section
common to the solid and to the enclosed mass, and is heated at all its points by
a constant source of heat; the upper plane B is also maintained by a similar
cause at a fixed temperature b, whose value is less than that of a; the problem
is to determine what would be the result of this hypothesis if it were continued
for an infinite time.

If we suppose the initial temperature of all parts of this body to be 6, it is
evident that the heat which leaves the source A will be propagated farther and
farther and will raise the temperature of the molecules included between the
two planes : but the temperature of the upper plane being unable, according to
hypothesis to rise above 6, the heat will be dispersed within the cooler mass,
contact with which keeps the plane B at the constant temperature b. The sys-
tem of temperatures will tend more and more to a final state, which it will
never attain, but which would have the property, as we shall proceed to shew,
of existing and keeping itself up without any change if it were once formed.

In the final and fixed state, which we are considering, the permanent tem-
perature of a point of the solid is evidently the same at all points of the same
section parallel to the base; and we shall prove that this fixed temperature,
common to all the points of an intermediate section, decreases in arithmetic
progression from the base to the upper plane, that is to say, if we represent the
constant temperatures a and 6 by the ordinates A a and Bp (see Fig. 1), raised

Fig. 1

perpendicularly to the distance A B between the two planes, the fixed tempera-
tures of the intermediate layers will be represented by the ordinates of the
straight line a/3 which joins the extremities a. and /3; thus, denoting by z the
height of an intermediate section or its perpendicular distance from the plane
A, by e the whole height or distance AB, and by v the temperature of the

6 a
section whose height is z, we must have the equation #

In fact, if the temperatures were at first established in accordance with this

SECT. IV THEORY OF HEAT 197

law, and if the extreme surfaces A and B were always kept at the temperatures
a and 6, no change would happen in the state of the solid. To convince our-
selves of this, it will be sufficient to compare the quantity of heat which would
traverse an intermediate section A' with that which, during the same time,
would traverse another section B'.

Bearing in mind that the final state of the solid is formed and continues, we
see that the part of the mass which is below and plane A' must communicate
heat to the part which is above that plane, since this second part is cooler than
the first.

Imagine two points of the solid, m and m', very near to each other, and
placed in any manner whatever, the one m below the plane A / ', and the other
m f above this plane, to be exerting their action during an infinitely small
instant : m the hottest point will communicate to m' a certain quantity of heat
which will cross the plane A'. Let x, y, z be the rectangular coordinates of the
point m, and x' , y', z f the coordinates of the point m': consider also two other
points n and n' very near to each other, and situated with respect to the plane
B' y in the same manner in which m and m' are placed with respect to the plane
A ' : that is to say, denoting by f the perpendicular distance of the two sections
A' and B', the coordinates of the point n will be x, y, z+f and those of the
point n', x', y', z'+f; the two distances mm' and nn' will be equal: further, the
difference of the temperature v of the point m above the temperature v r of the
point m f will be the same as the difference of temperature of the two points
n and n'. In fact the former difference will be determined by substituting first
z and then z' in the general equation

, 6 a
= +__ z,

and subtracting the second equation from the first, whence the result vv'

= (z zf). We shall then find, by the substitution of z+f and z'+f, that

the excess of temperature of the point n over that of the point n' is also ex-
pressed by

b a, ..

(*-*').

It follows from this that the quantity of heat sent by the point m to the
point m' will be the same as the quantity of heat sent by the point n to the
point n'j for all the elements which concur in determining this quantity of
transmitted heat are the same.

It is manifest that we can apply the same reasoning to every system of two
molecules which communicate heat to each other across the section A' or the
section B f ; whence, if we could sum up the whole quantity of heat which
flows, during the same instant, across the section A' or the section B', we
should find this quantity to be the same for both sections.

From this it follows that the part of the solid included between A' and B'
receives always as much heat as it loses, and since this result is applicable to
any portion whatever of the mass included between two parallel sections, it is
evident that no part of the solid can acquire a temperature higher than that
which it has at present. Thus, it has been rigorously demonstrated that the
state of the prism will continue to exist just as it was at first.

Hence, the permanent temperatures of different sections of a solid enclosed
between two parallel infinite planes, are represented by the ordinate^ of a

198 FOURIER CHAP. I

straight line aj8, and satisfy the linear equation = aH z.

66. By what precedes we see distinctly what constitutes the propagation of
heat in a solid enclosed between two parallel and infinite planes, each of which
is maintained at a constant temperature. Heat penetrates the mass gradually
across the lower plane: the temperatures of the intermediate sections are
raised, but can never exceed nor even quite attain a certain limit which they
approach nearer and nearer: this limit or final temperature is different for
different intermediate layers, and decreases in arithmetic progression from the
fixed temperature of the lower plane to the fixed temperature of the upper
plane.

The final temperatures are those which would have to be given to the solid
in order that its state might be permanent; the variable state which precedes
it may also be submitted to analysis, as we shall see presently : but we are now
considering only the system of final and permanent temperatures. In the last
state, during each division of time, across a section parallel to the base, or a
definite portion of that section, a certain quantity of heat flows, which is
constant if the divisions of time are equal. This uniform flow is the same for all
the intermediate sections; it is equal to that which proceeds from the source,
and to that which is lost during the same time, at the upper surface of the
solid, by virtue of the cause which keeps the temperature constant.

67. The problem now is to measure that quantity of heat which is propa-
gated uniformly within the solid, during a given time, across a definite part of
a section parallel to the base : it depends, as we shall see, on the two extreme
temperatures a and 6, and on the distance e between the two sides of the solid ;
it would vary if any one of these elements began to change, the other remain-
ing the same. Suppose a second solid to be formed of the same substance as the
first, and enclosed between two infinite parallel planes, whose perpendicular

/*'

Fig. 2

distance is e' (see Fig. 2) : the lower side is maintained at a fixed temperature a',
and the upper side at the fixed temperature &' ; both solids are considered to be
in that final and permanent state which has the property of maintaining itself
as soon as it has been formed. Thus the law of the temperatures is expressed

for the first body by the equation v=a-\ z, and for the second, by the

equation u = a'H - t z, v in the first solid, and u in the second, being the

temperature of the section whose height is z.

SECT. IV THEORY OF HEAT 199

This arranged, we will compare the quantity of heat which, during the unit
of time traverses a unit of area taken on an intermediate section L of the first
solid, with that which during the same time traverses an equal area taken on
the section L' of the second, e being the height common to the two sections,
that is to say, the distance of each of them from their own base. We shall
consider two very near points n and n f in the first body, one of which n is be-
low the plane L and the other n' above this plane: x, y y z are the co-ordinates
of n: and x' 9 y', z r the co-ordinates of n', c being less than z', and greater
than z.

We shall consider also in the second solid the instantaneous action of two
points p and p', which are situated, with respect to the section L', in the same
manner as the points n and n' with respect to the section L of the first solid.
Thus the same co-ordinates x, y, z, and x', y', z' referred to three rectangular
axes in the second body, will fix also the position of the points p and p'.

Now, the distance from the point n to the point n' is equal to the distance
from the point p to the point p', and since the two bodies are formed of the
same substance, we conclude, according to the principle of the communication
of heat, that the action of n on n' y or the quantity of heat given by n to n', and
the action of p on p', are to each other in the same ratio as the differences of
the temperature v v' and u u f .

Substituting v and then v 1 in the equation which belongs to the first solid,

and subtracting, we find v v f (2 z')] we have also by means of the

second equation u u f = - f (2 2'), whence the ratio of the two actions in

x- xu * r a ~ fc x *'-*>'

question is that of to - f .

We may now imagine many other systems of two molecules, the first of
which sends to the second across the plane L, a certain quantity of heat, and
each of these systems, chosen in the first solid, may be compared with a
homologous system situated in the second, and whose action is exerted across
the section L'} we can then apply again the previous reasoning to prove that

the ratio of the two actions is always that of to - f .

c c

Now, the whole quantity of heat which, during one instant, crosses the sec-
tion L, results from the simultaneous action of a multitude of systems each of
which is formed of two points; hence this quantity of heat and that which, in
the second solid, crosses during the same instant the section Z/, are also to each

,, . ., ,. -a b^ a' b'

other in the ratio of to -, .

e e'

It is easy then to compare with each other the intensities of the constant
flows of heat which are propagated uniformly in the two solids, that is to say,
the quantities of heat which, during unit of time, cross unit of surface of each

of these bodies. The ratio of these intensities is that of the two quotients

and - f . If the two quotients are equal, the flows are the same, whatever in

other respects the values a, b, e, a', fc', e', may be; in general, denoting the first
flow by F and the second by F', we shall have - = 1 - r .

200 FOURIER CHAP. I

68. Suppose that in Uie seuuiid solid, the permanent temperature a' of the
lower plane is that of boiling water, 1 ; that the temperature e f of the upper
plane is that of melting ice, 0; that the distance &' of the two planes is the unit
of measure (a metre); let us denote by K the constant flow of heat which,
during unit of time (a minute) would cross unit of surface in this last solid, if it
were formed of a given substance ; K expressing a certain number of units of
heat, that is to say a certain number of times the heat necessary to convert a
kilogramme of ice into water: we shall have, in general, to determine the
constant flow F, in a solid formed of the same substance, the equation

F a b Tr a ~- b

= or F = K .

K e e

The value of F denotes the quantity of heat which, during the unit of time,
passes across a unit of area of the surf ace taken on a section parallel to the base.

Thus the thermometric state of a solid enclosed between two parallel
infinite plane sides whose perpendicular distance is e, and which are main-
tained at fixed temperatures a and 6, is represented by the two equations:

. b a jrr rr a ~b ^ r ~ dv

v = a H z, and F = K or F = K -=- .

e e dz

The first of these equations expresses the law according to which the tem-
peratures decrease from the lower side to the opposite side, the second indi-
cates the quantity of heat which, during a given time, crosses a definite part of
a section parallel to the base.

69. We have taken this coefficient K, which enters into the second equation,
to be the measure of the specific conducibility of each substance; this number
has very different values for different bodies.

It represents, in general, the quantity of heat which, in a homogeneous solid
formed of a given substance and enclosed between two infinite parallel planes,
flows, during one minute, across a surface of one square metre taken on a sec-
tion parallel to the extreme planes, supposing that these two planes are main-
tained, one at the temperature of boiling water, the other at the temperature
of melting ice, and that all the intermediate planes have acquired and retain a
permanent temperature.

We might employ another definition of conductivity, since we could esti-
mate the capacity for heat by referring it to unit of volume, instead of referring
it to unit of mass. All these definitions are equally good provided they are clear
and precise.

We shall shew presently how to determine by observation the value K of
the conducibility or conductibility in different substances.

70. In order to establish the equations which we have cited in Article 68, it
would not be necessary to suppose the points which exert their action across
the planes to be at extremely small distances.

The results would still be the same if the distances of these points had any
magnitude whatever; they would therefore apply also to the case where the
direct action of heat extended within the interior of the mass to very consider-
able distances, all the circumstances which constitute the hypothesis remain-
ing in other respects the same.

We need only suppose that the cause which maintains the temperatures at
the surface of the solid, affects not only that part of the mass which is ex-
tremely near to the surface, but that its action extends to a finite depth. The

SECT. IV THEORY OF HEAT 201

equation v=a z will still represent in this case the permanent temper-

atures of the solid. The true sense of this proposition is that, if we give to all
points of the mass the temperatures expressed by the equation, and if besides
any cause whatever, acting on the two extreme laminae, retained always every-
one of their molecules at the temperature which the same equation assigns to
them, the interior points of the solid would preserve without any change their
initial state.

If we supposed ttxat the action of a point of the mass could extend to a finite
distance e, it would be necessary that the thickness of the extreme laminae,
whose state is maintained by the external cause, should be at least equal to c.
But the quantity having in fact, in the natural state of solids, only an inap-
preciable value, we may make abstraction of this thickness; and it is sufficient
for the external cause to act on each of the two layers, extremely thin, which
bound the solid. This is always what must be understood by the expression, to
maintain the temperature of the surface constant.

71. We proceed further to examine the case in which the same solid would
be exposed, at one of its faces, to atmospheric air maintained at a constant
temperature.

Suppose then that the lower plane preserves the fixed temperature a, by
virtue of any external cause whatever, and that the upper plane, instead of
being maintained as formerly at a less temperature 6, is exposed to atmospheric
air maintained at that temperature 6, the perpendicular distance of the two
planes being denoted always by e : the problem is to determine the final tem-
peratures.

Assuming that in the initial state of the solid, the common temperature of
its molecules is 6 or less than 6, we can readily imagine that the heat which
proceeds incessantly from the source A penetrates the mass, and raises more
and more the temperatures of the intermediate sections; the upper surface is
gradually heated, and permits part of the heat which has penetrated the solid
to escape into the air. The system of temperatures continually approaches a
final state which would exist of itself if it were once formed ; in this final state,
which is that which we are considering, the temperature of the plane B has a
fixed but unknown value, which we will denote by 0, and since the lower plane
A preserves also a permanent temperature a, the system of temperatures is

represented by the general equation v = a-\ z, v denoting always the fixed

temperature of the section whose height is z. The quantity of heat which flows
during unit of time across a unit of surface taken on any section whatever is

K , k denoting the interior conducibility.

We must now consider that the upper surface B, whose temperature is 0,
permits the escape into the air of a certain quantity of heat which must be
exactly equal to that which crosses any section whatever L of the solid. If it
were not so, the part of the mass included between this section L and the plane
B would not receive a quantity of heat equal to that which it loses; hence it
would not maintain its state, which is contrary to hypothesis; the constant
flow at the surface is therefore equal to that which traverses the solid : now, the
quantity of heat which escapes, during unit of time, from unit of surface taken
on the plane B, is expressed by A(j3 6), 6 being the fixed temperature of the

202 FOURIER CHAP. I

air, and h the measure of the conducibility of the surface B\ we must therefore

have the equation K - - = h($ 6), which will determine the value of p.

From this may be derived a ft = h -\-K ' an e( l uat ^ on w ^ ose second mem-

ber is known; for the temperatures a and 6 are given, as are also the quantities
h, k, e.

Introducing this value of a ft into the general equation v~a-\ -- 2, we

shall have, to express the temperatures of any section of the solid, the equation
a v = ^ 9 in which known quantities only enter with the corresponding

"~"

variables v and z.

72. So far we have determined the final and permanent state of the temper-
atures in a solid enclosed between two infinite and parallel plane surfaces,
maintained at unequal temperatures. This first case is, properly speaking, the case
of the linear and uniform propagation of heat, for there is no transfer of heat in
the plane parallel to the sides of the solid ; that which traverses the solid flows uni-
formly, since the value of the flow is the same for all instants and for all sections.

We will now restate the three chief propositions which result from the
examination of this problem ; they are susceptible of a great number of applica-
tions, and form the first elements of our theory.

1st. If at the two extremities of the thickness e of the solid we erect perpen-
diculars to represent the temperatures a and b of the two sides, and if we draw
the straight line which joins the extremities of these two first ordinates, all the
intermediate temperatures will be proportional to the ordinates of this straight

line; they are expressed by the general equation a v= - z, v denoting the

temperature of the section whose height is z.

2nd. The quantity of heat which flows uniformly, during unit of time, across
unit of surface taken on any section whatever parallel to the sides, all other
things being equal, is directly proportional to the difference a b of the ex-
treme temperatures, and inversely proportional to the distance e which

separates these sides. The quantity of heat is expressed by K - , or -K -r- ,

if we derive from the general equation the value of -7- which is constant; this

uniform flow may always be represented, for a given substance and in the solid
under examination, by the tangent of the angle included between the perpen-
dicular e and the straight line whose ordinates represent the temperatures.

3rd. One of the extreme surfaces of the solid being submitted always to the
temperature a, if the other plane is exposed to air maintained at a fixed
temperature b; the plane in contact with the air acquires, as in the preceding
case, a fixed temperature /3, greater than 6, and it permits a quantity of heat
to escape into the air across unit of surface, during unit of time, which is
expressed by h(0 6), h denoting the external conducibility of the plane.

The same flow of heat h(($ b) is equal to that which traverses the prism and

whose value is K(a ff)\ we have therefore the equation h((3--b)=K - - ,

which gives the value of /3.

SECT. V THEORY OF HEAT 203

SECTION V. Law of the Permanent Temperatures in
a Prism of Small Thickness

73. We shall easily apply the principles which have just been explained to the
following problem, very simple in itself, but one whose solution it is important
to base on exact theory.

A metal bar, whose form is that of a rectangular parallelepiped infinite in
length, is exposed to the action of a source of heat which produces a constant
temperature at all points of its extremity A. It is required to determine the
fixed temperatures at the different sections of the bar.

The section perpendicular to the axis is supposed to be a square whose side
21 is so small that we may without sensible error consider the temperatures to
be equal at different points of the same section. The air in which the bar is
placed is maintained at a constant temperature 0, and carried away by a
current with uniform velocity.

Inside the solid, heat will pass successively all parts situated to the right or
left (pro re nata) of the source, and not exposed directly to its action; they
will be heated more and more, but the temperature of each point will not
increase beyond a certain limit. This maximum temperature is not the same
for every section ; it in general decreases as the distance of the section from the
origin increases: we shall denote by v the fixed temperature of a section per-
pendicular to the axis, and situated at a distance x from the origin A .

Before every point of the solid has attained its highest degree of heat, the
system of temperatures varies continually, and approaches more and more to
a fixed state, which is that which we consider. This final state is kept up of
itself when it has once been formed. In order that the system of temperatures
may be permanent, it is necessary that the quantity of heat which, during unit
of time, crosses a section made at a distance x from the origin, should balance
exactly all the heat which, during the same time, escapes through that part of
the external surface of the prism which is situated to the right of the same
section. The lamina whose thickness is dx, and whose external surface is 8ldx,
allows the escape into the air, during unit of time, of a quantity of heat ex-
pressed by 8hlv-dx, h being the measure of the external conducibility of the
prism. Hence taking the integral f8hlv-dx from x = to x= >, we shall find
the quantity of heat which escapes from the whole surface of the bar during
unit of time; and if we take the same integral from x = to x = x, we shall have
the quantity of heat lost through the part of the surface included between the
source of heat and the section made at the distance x. Denoting the first
integral by C, whose value is constant, and the variable value of the second by
f&hlv-dx; the difference C fehlv-dx will express the whole quantity of heat
which escapes into the air across the part of the surface situated to the right of
the section. On the other hand, the lamina of the solid, enclosed between two
sections infinitely near at distances x and x+dx, must resemble an infinite
solid, bounded by two parallel planes, subject to fixed temperatures v and
v+dv, by hypothesis, the temperature does not vary throughout the whole
extent of the same section. The thickness of the solid is dx, and the area of the
section is 4Z 2 : hence the quantity of heat which flows uniformly, during unit of
time, across a section of this solid, is, according to the preceding principles,

~4PK -- , K being the specific internal conductivity: we must therefore have

204 FOURIER CHAP. I

the equation 4PjfiT -y- = C

whence Kl -T-T 2hv.

74. We should obtain the same result by considering the equilibrium of heat
in a single lamina infinitely thin, enclosed between two sections at distances
x and x+dx. In fact, the quantity of heat which, during unit of time, crosses

the first section situated at distances, is 4PK-T- . To find that which flows dur-

ing the same time across the successive section situated at distance x+dx,
we must in the preceding expression change x into x+dx, which gives

-T- + d ( -T- J . If

we subtract the second expression from the first we

shall find how much heat is acquired by the lamina bounded by these two sec-
tions during unit of time; and since the state of the lamina is permanent, it
follows that all the heat acquired is dispersed into the air across the external
surface SJdx of the same lamina: now the last quantity of heat is Shlvdx: we
shall obtain therefore the same equation

Shlvdx 4l 2 Kd ( -T- J, whence -7-7 = -7^ v.
\dxj' dx 2 Kl

75. In whatever manner this equation is formed, it is necessary to remark
that the quantity of heat which passes into the lamina whose thickness is dx,

has a finite value, and that its exact expression is 4l 2 K-r-. The lamina being

enclosed between two surfaces the first of which has a temperature v, and the
second a lower temperature v', we see that the quantity of heat which it
receives through the first surface depends on the difference v v', and is pro-
portional to it: but this remark is not sufficient to complete the calculation.
The quantity in question is not a differential : it has a finite value, since it is
equivalent to all the heat which escapes through that part of the external sur-
face of the prism which is situated to the right of the section. To form an exact
idea of it, we must compare the lamina whose thickness is dx, with a solid
terminated by two parallel planes whose distance is e, and which are main-
tained at unequal temperatures a and 6. The quantity of heat which passes
into such a prism across the hottest surface, is in fact proportional to the
difference a & of the extreme temperatures, but it does not depend only on
this difference: all other things being equal, it is less when the prism is thicker,

and in general it is proportional to - . This is why the quantity of heat

which passes through the first surface into the lamina, whose thickness is dx 9 is

,. . , v v'
proportional to -~-= .

We lay stress on this remark because the neglect of it has been the first
obstacle to the establishment of the theory. If we did not make a complete
analysis of the elements of the problem, we should obtain an equation not
homogeneous, and, a fortiori, we should not be able to form the equations
which express the movement of heat in more complex cases.

SECT.V THEORY OF HEAT 205

It was necessary also to introduce into the calculation the dimensions of the
prism, in order that we might not regard, as general, consequences which ob-
servation had furnished in a particular case. Thus, it was discovered by experi-
ment that a bar of iron, heated at one extremity, could not acquire, at a
distance of six feet from the source, a temperature -of one degree (octogesi-
mal 1 ) ; for to produce this effect, it would be necessary for the heat of the source
to surpass considerably the point of fusion of iron ; but this result depends on
the thickness of the prism employed. If it had been greater, the heat would
have been propagated to a greater distance, that is to say, the point of the
bar which acquires a fixed temperature of one degree is much more remote
from the source when the bar is thicker, all other conditions remaining the
same. We can always raise by one degree the temperature of one end of a bar
of iron, by heating the solid at the other end; we need only give the radius of
the base a sufficient length: which is, we may say, evident, and of which
besides a proof will be found in the solution of the problem (Art. 78).

76. The integral of the preceding equation is

A and B being two arbitrary constants; now, if we suppose the distance x
infinite, the value of the temperature v must be infinitely small; hence the term
B G+T \/KI does not exist in the integral : thus the equation v = Ae~ x \/^ t represents
the permanent state of the solid; the temperature at the origin is denoted by
the constant A, since that is the value of v when x is zero.

This law according to which the temperatures decrease is the same as that
given by experiment ; several physicists have observed the fixed temperatures
at different points of a metal bar exposed at its extremity to the constant
action of a source of heat, 2 and they have ascertained that the distances from the
origin represent logarithms, and the temperatures the corresponding numbers.

77. The numerical value of the constant quotient of two consecutive tem-
peratures being determined by observation, we easily deduce the value of the

ratio -T? ; for, denoting by v\, v% the temperatures corresponding to the distances
/v

xi, #2, we have

when ce

As for the separate values of h and K, they cannot be determined by experi-
ments of this kind : we must observe also the varying motion of heat.

78. Suppose two bars of the same material and different dimensions to be
submitted at their extremities to the same temperature A ; let li be the side of
a section in the first bar, and / 2 in the second, we shall have, to express the
temperatures of these two solids, the equations

/2h /2h

vi^Ae-^Vm and t> 2 = ^e~~* 2 v K*,,

Vi, in the first solid, denoting the temperature of a section made at distance x\,

and # 2 , in the second solid, the temperature of a section made at distance # 2 .

When these two bars have arrived at a fixed state, the temperature of a

section of the first, at a certain distance from the source, will not be equal to

1 Reaumer's scale of temperature.

2 The conducting power K is not constant, but diminishes as the temperature increases.

206 FOURIER CHAP. I

the temperature of a section of the second at the same distance from the focus;
in order that the fixed temperatures may be equal, the distances must be
different. If we wish to compare with each other the distances x\ and x 2 from
the origin up to the points which in the two bars attain the same temperature,
we must equate the second members of these equations, and from them we

x-f l\

conclude that 5 = 7-- Thus the distances in question are to each other as the
top fe ^

square roots Of the thicknesses.

79. If two metal bars of equal dimensions, but formed of different sub-
stances, are covered with the same coating, which gives them the same external
conducibility, and if they are submitted at their extremities to the same
temperature, heat will be propagated most easily and to the greatest distance
from the origin in that which has the greatest conductivity. To compare with
each other the distances x\ and x z from the common origin up to the points
which acquire the same fixed temperature, we must, after denoting the respec-
tive conducibilities of the two substances by K\ and Kij write the equation

e -*A/iS = e -**Vm , w hence ^ = ^.

a?2 A 2

Thus the ratio of the two conductivities is that of the squares of the
distances from the common origin to the points which attain the same fixed
temperature.

80. It is easy to ascertain how much heat flows during unit of time through a
section of the bar arrived at its fixed state: this quantity is expressed by

4K P -r- , or 4A \/2Khl 3 e" x \/^ and if we take its value at the origin, we shall

have 4A \/2Khl* as the measure of the quantity of heat which passes from the
source into the solid during unit of time; thus the expenditure of the source of
heat is, all other things being equal, proportional to the square root of the cube
of the thickness.

We should obtain the same result on taking the integral f8hlv-dx from x
nothing to x infinite.

SECTION VI. On the Heating of Closed Spaces

81. We shall again make use of the theorems of Article 72 in the following
problem, whose solution offers useful applications; it consists in determining
the extent of the heating of closed spaces.

Imagine a closed space, of any form whatever, to be filled with atmospheric
air and closed on all sides, and that all parts of the boundary are homogeneous
and have a common thickness e y so small that the ratio of the external surface
to the internal surface differs little from unity. The space which this boundary
terminates is heated by a source whose action is constant; for example, by
means of a surface whose area is <r maintained at a constant temperature a.

We consider here only the mean temperature of the air contained in the
space, without regard to the unequal distribution of heat in this mass of air;
thus we suppose that the existing causes incessantly mingle all the portions of
air, and make their temperatures uniform.

We see first that the heat which continually leaves the source spreads itself
in the surrounding air and penetrates the mass of which the boundary is

SECT. VI THEORY OF HEAT 207

formed, is partly dispersed at the surface, and passes into the external air,
which we suppose to be maintained at a lower and permanent temperature n.
The inner air is heated more and more: the same is the case with the solid
boundary : the system of temperatures steadily approaches a final state which
is the object of the problem, and has the property of existing by itself and of
being kept up unchanged, provided the surface of the source <r be maintained
at the temperature a, and the external air at the temperature n.

In the permanent state which we wish to determine the air preserves a fixed
temperature m ; the temperature of the inner surface s of the solid boundary
has also a fixed value a; lastly, the outer surface s, which terminates the enclos-
ure, preserves a fixed temperature 6 less than a, but greater than n. The quan-
tities <r, a, s, e and n are known, and the quantities m, a and 6 are unknown.

The degree of heating consists in the excess of the temperature m over n, the
temperature of the external air; this excess evidently depends on the area <r
of the heating surface and on its temperature a; it depends also on the thick-
ness e of the enclosure, on the area s of the surface which bounds it, on the
facility with which heat penetrates the inner surface or that which is opposite
to it; finally, on the specific conductivity of the solid mass which forms the
enclosure: for if any one of these elements were to be changed, the others
remaining the same, the degree of the heating would vary also. The problem is
to determine how all these quantities enter into the value of m n.

82. The solid boundary is terminated by two equal surfaces, each of which is
maintained at a fixed temperature; every prismatic element of the solid
enclosed between two opposite portions of these surfaces, and the normals
raised round the contour of the bases, is therefore in the same state as if it
belonged to an infinite solid enclosed between two parallel planes, maintained
at unequal temperatures. All the prismatic elements which compose the
boundary touch along their whole length. The points of the mass which are
equidistant from the inner surface have equal temperatures, to whatever
prism they belong; consequently there cannot be any transfer of heat in the
direction perpendicular to the length of these prisms. The case is, therefore,
the same as that of which we have already treated, and we must apply to it
the linear equations which have been stated in former articles.

83. Thus in the permanent state which we are considering, the flow of heat
which leaves the surface cr during a unit of time, is equal to that which, during
the same time, passes from the surrounding air into the inner surface of the
enclosure; it is equal also to that which, in a unit of time, crosses an inter-
mediate section made within the solid enclosure by a surface equal and parallel
to those which bound this enclosure; lastly, the same flow is again equal to
that which passes from the solid enclosure across its external surface, and is
dispersed into the air. If these four quantities of flow of heat were not equal,
some variation would necessarily occur in the state of the temperatures, which
is contrary to the hypothesis.

The first quantity is expressed by a (a m)g, denoting by g the external
conducibility of the surface <r, which belongs to the source of heat.

The second is s (m a) h, the coefficient h being the measure of the external con-
ducibility of the surface s, which is exposed to the action of the source of heat.

The third is s K 9 the coefficient K being the measure of the conduci-

bility proper to the homogeneous substance which forms the boundary.

208 FOURIER CHAP. I

The fourth is s(b ri)H, denoting by H the external conductivity of the
surface s, which the heat quits to be dispersed into the air. The coefficients h
and H may have very unequal values on account of the difference of the state
of the two surfaces which bound the enclosure; they are supposed to be known,
as also the coefficient K : we shall have then, to determine the three unknown
quantities m, a and ft, the three equations:

(a m)g s(m a)h,
(a m)g = s - K,

84. The value of m is the special object of the problem. It may be found by
writing the equations in the form

m a= ~ (a ra),

, a ge , N
a-b= - ^ (a-m),

b n = - jj ( m);

S Al

adding, we have m n = (a m) P,

denoting by P the known quantity H ~ + ~ + jj J ;
whence we conclude

s\h ' K ' H

85. The result shews how m ?z, the extent of the heating, depends on given
quantities which constitute the hypothesis. We will indicate the chief results
to be derived from it.

1st. The extent of the heating m n is directly proportional to the excess of
the temperature of the source over that of the external air.

2nd. The value ofm n does not depend on the form of the enclosure nor on

its volume, but only on the ratio - of the surface from which the heat proceeds

to the surface which receives it, and also on e the thickness of the boundary.

If we double a the surface of the source of heat, the extent of the heating
does not become double, but increases according to a certain law which the
equation expresses.

3rd. All the specific coefficients which regulate the action of the heat, that is
to say, g, K, H and h, compose, with the dimension e y in the value of m n a

single element | + ~ + T? > whose value may be determined by observation.

If we doubled e the thickness of the boundary, we should have the same
result if, in forming it, we employed a substance whose conductivity proper

SECT. VI THEORY OF HEAT 209

was twice as great. Thus the employment of substances which are bad con-
ductors of heat permits us to make the thickness of the boundary small ; the

effect which is obtained depends only on the ratio ^ .

4th. If the conducibility K is nothing, we find w = a; that is to say, the
inner air assumes the temperature of the source: the same is the case if H is
zero, or h zero. These consequences are otherwise evident, since the heat can-
not then be dispersed into the external air.

5th. The values of the quantities g, H, h, K and a, which we supposed
known, may be measured by direct experiments, as we shall shew in the
sequel; but in the actual problem, it will be sufficient to notice the value of
m n which corresponds to given values of v and of a, and this value may be

used to determine the whole coefficient T + j? + jf > by means of the equation
m n= (a ft) - p-r-llH p] in which p denotes the coefficient sought. We

must substitute in this equation, instead of and a ft, the values of those

quantities, which we suppose given, and that of m n which observation will
have made known. From it may be derived the value of p, and we may then
apply the formula to any number of other cases.

6th. The coefficient H enters into the value of m n in the same manner as
the coefficient A; consequently the state of the surface, or that of the envelope
which covers it, produces the same effect, whether it has reference to the inner
or outer surface.

We should have considered it useless to take notice of these different conse-
quences, if we were not treating here of entirely new problems, whose results
may be of direct use.

86. We know that animated bodies retain a temperature sensibly fixed,
which we may regard as independent of the temperature of the medium in
which they live. These bodies are, after some fashion, constant sources of heat,
just as inflamed substances are in which the combustion has become uniform.
We may then, by aid of the preceding remarks, foresee and regulate exactly
the rise of temperature in places where a great number of men are collected
together. If we there observe the height of the thermometer under given cir-
cumstances, we shall determine in advance what that height would be, if the
number of men assembled in the same space became very much greater.

In reality, there are several accessory circumstances which modify the
results, such as the unequal thickness of the parts of the enclosure, the
difference of their aspect, the effects which the outlets produce, the unequal
distribution of heat in the air. We cannot therefore rigorously apply the rules
given by analysis; nevertheless these rules are valuable in themselves, because
they contain the true principles of the matter: they prevent vague reasonings
and useless or confused attempts.

87. If the same space were heated by two or more sources of different kinds,
or if the first enclosure were itself contained in a second enclosure separated
from the first by a mass of air, we might easily determine in like manner the
degree of heating and the temperature of the surfaces.

If we suppose that, besides the first source <7, there is a second heated sur-
face TT, whose constant temperature is 0, and external conductivity j 9 we shall

210 FOURIER CHAP. I

find, all the other denominations being retained, the following equation:

, 1 ,

1 |

If we suppose only one source a, and if the first enclosure is itself contained
in a second, s', h', K ', H' , e', representing the elements of the second enclosure
which correspond to those of the first which were denoted by s y h, K, H, e] we
shall find, p denoting the temperature of the air which surrounds the external
surface of the second enclosure, the following equation :

The quantity P represents

* x

We should obtain a similar result if we had three or a greater number of suc-
cessive enclosures; and from this we conclude that these solid envelopes,
separated by air, assist very much in increasing the degree of heating, however
small their thickness may be.

88. To make this remark more evident, we will compare the quantity of heat
which escapes from the heated surface, with that which the same body would
lose, if the surface which envelopes it were separated from it by an interval
filled with air.

If the body A be heated by a constant cause, so that its surface preserves a
fixed temperature 6, the air being maintained at a less temperature a, the
quantity of heat which escapes into the air in the unit of time across a unit of
surface will be expressed by h (b a), h being the measure of the external con-
ductivity. Hence in order that the mass may preserve a fixed temperature 6,
it is necessary that the source, whatever it may be, should furnish a quantity
of heat equal to hS(b d) f S denoting the area of the surface of the solid.

Suppose an extremely thin shell to be detached from the body A and
separated from the solid by an interval filled with air; and suppose the surface
of the same solid A to be still maintained at the temperature 6. We see that the
air contained between the shell and the body will be heated and will take a
temperature a' greater than a. The shell itself will attain a permanent state
and will transmit to the external air whose fixed temperature is a all the heat
which the body loses. It follows that the quantity of heat escaping from the
solid will be hS(b a'), instead of being hS(b a), for we suppose that the new
surface of the solid and the surfaces which bound the shell have likewise the
same external conducibility h. It is evident that the expenditure of the source
of heat will be less than it was at first. The problem is to determine the exact
ratio of these quantities.

89. Let e be the thickness of the shell, m the fixed temperature of its inner
surface, n that of its outer surface, and K its internal conductivity. We shall
have, as the expression of the quantity of heat which leaves the solid through
its surface, hS(ba').

SECT. VI THEORY OF HEAT 211

As that of the quantity which penetrates the inner surface of the shell,
hS(a'-m).

As that of the quantity which crosses any section whatever of the same

i_ 11 Trn m ~~ ' n
shell, KS - .

Lastly, as the expression of the quantity which passes through the outer
surface into the air, hS(na).

All these quantities must be equal, we have therefore the following equa-
tions:

h(n d) (ra n),

Tf moreover we write down the identical equation

h(na) =h(n a),
and arrange them all under the forms

n a = n a,

he , N
m n= -T? (n a),

we find, on addition,

The quantity of heat lost by the solid was hS(b a), when its surface com-
municated freely with the air, it is now hS(b a') or hS(n-a), which is equiva-
lent to hS r-

he
The first quantity is greater than the second in the ratio of 3+ j? to 1.

In order therefore to maintain at temperature 6 a solid whose surface com-
municates directly to the air, more than three times as much heat is necessary
than would be required to maintain it at temperature 6, when its extreme
surface is not adherent but separated from the solid by any small interval
whatever filled with air.

If we suppose the thickness e to be infinitely small, the ratio of the quantities
of heat lost will be 3, which would also be the value if K were infinitely great.

We can easily account for this result, for the heat being unable to escape
into the external air, without penetrating several surfaces, the quantity which
flows out must diminish as the number of interposed surfaces increases; but
we should have been unable to arrive at any exact judgment in this case, if the
problem had not been submitted to analysis.

90. We have not considered, in the preceding article, the effect of radiation
across the layer of air which separates the two surfaces; nevertheless this
circumstance modifies the problem, since there is a portion of heat which

212 FOURIER CHAP. I

passes directly across the intervening air. We shall suppose then, to make the
object of the analysis more distinct, that the interval between the surfaces is
free from air, and that the heated body is covered by any number whatever of
parallel laminae separated from each other.

If the heat which escapes from the solid through its plane superficies main-
tained at a temperature 6 expanded itself freely in vacuo and was received by a
parallel surface maintained at a less temperature a, the quantity which would
be dispersed in unit of time across unit of surface would be proportional to
(b a), the difference of the two constant temperatures: this quantity would
be represented by H(b a), H being the value of the relative conducibility
which is not the same as h.

The source which maintains the solid in its original state must therefore
furnish, in every unit of time, a quantity of heat equal to HS(b a).

We must now determine the new value of this expenditure in the case where
the surface of the body is covered by several successive laminae separated by
intervals free from air, supposing always that the solid is subject to the action
of any external cause whatever which maintains its surface at the temperature b.

Imagine the whole system of temperatures to have become fixed; let mi be
the temperature of the under surface of the first lamina which is consequently
opposite to that of the solid, let n\ be the temperature of the upper surface of
the same lamina, e its thickness, and K its specific conductivity; denote also
by mi, n\, m 2 , ?i 2 , m 3 , n 3 , m 4 , n 4 , &c. the temperatures of the under and upper
surfaces of the different laminae, and by K, e, the conductivity and thickness
of the same laminae; lastly suppose all these surfaces to be in a state similiar to
the surface of the solid, so that the value of the coefficient H is common to them.

The quantity of heat which penetrates the under surface of a lamina cor-
responding to any suffix i is #/S(n;_i m*), that which crosses this lamina is

ii rii), and the quantity which escapes from its upper surface is

mi+i). These three quantities, and all those which refer to the other
laminae are equal; we may therefore form the equation by comparing all these
quantities in question with the first of them, which is //S(6 mi); we shall
thus have, denoting the number of laminae by j :

bmi = b m\,

He ,, ^
mini = -g- (6 mi),

ni m 2 = & Wi,

He ^ ^
m 2 n 2 = -- (6 mi),

He ,

Adding these equations, we find

The expenditure of the source of heat necessary to maintain the surface of
the body A at the temperature 6 is HS(b a), when this surface sends its rays
to a fixed surface maintained at the temperature a. The expenditure is

SECT. VII THEORY OF HEAT 213

HS(b mi) when we place between the surface of the body A, and the fixed
surface maintained at temperature a, a number j of isolated laminae; thus the
quantity of heat which the source must furnish is very much less in the second

hypotheses than in the first, and the ratio of the two quantities is

If we suppose the thickness e of the laminae to be infinitely small, the ratio
is .-- Y . The expenditure of the source is then inversely as the number of

laminae which cover the surface of the solid.

91. The examination of these results and of those which we obtained when
the intervals between successive enclosures were occupied by atmospheric air
explain clearly why the separation of surfaces and the intervention of air
assist very much in retaining heat.

Analysis furnishes in addition analogous consequences when we suppose the
source to be external, and that the heat which emanates from it crosses suc-
cessively different diathermanous envelopes and the air which they enclose.
This is what has happened when experimenters have exposed to the rays of the
sun thermometers covered by several sheets of glass within which different
layers of air have been enclosed.

For similar reasons the temperature of the higher regions of the atmosphere
is very much less than at the surface of the earth.

In general the theorems concerning the heating of air in closed spaces extend
to a great variety of problems. It would be useful to revert to them when we
wish to foresee and regulate temperature with precision, as in the case of
green-houses, drying-houses, sheep-folds, work-shops, or in many civil estab-
lishments, such as hospitals, barracks, places of assembly.

In these different applications we must attend to accessory circumstances
which modify the results of analysis, such as the unequal thickness of different
parts of the enclosure, the introduction of air, &c.; but these details would
draw us away from our chief object, which is the exact demonstration of gen-
eral principles.

For the rest, we have considered only, in what has just been said, the per-
manent state of temperature in closed spaces. We can in addition express
analytically the variable state which precedes, or that which begins to take
place when the source of heat is withdrawn, and we can also ascertain in this
way, how the specific properties of the bodies which we employ, or their
dimensions affect the progress and duration of the heating; but these re-
searches require a different analysis, the principles of which will be explained
in the following chapters.

SECTION VII. On the Uniform Movement of Heat in Three Dimensions

92. Up to this time we have considered the uniform movement of heat in one
dimension only, but it is easy to apply the same principles to the case in which
heat is propagated uniformly in three directions at right angles.

Suppose the different points of a solid enclosed by six planes at right angles
to have unequal actual temperatures represented by the linear equation
v = A+ax+by-}-cz, x, y, z, being the rectangular co-ordinates of a molecule

214 FOURIER CHAP. I

whose temperature is v. Suppose further that any external causes whatever
acting on the six faces of the prism maintain every one of the molecules situ-
ated on the surface, at its actual temperature expressed by the general equa-
tion

v~A+ax+by+cz (a),

we shall prove that the same causes which, by hypothesis, keep the outer layers
of the solid in their initial state, are sufficient to preserve also the actual tem-
peratures of every one of the inner molecules, so that their temperatures do not
cease to be represented by the linear equation.

The examination of this question is an element of the general theory, it will
serve to determine the laws of the varied movement of heat in the interior of a
solid of any form whatever, for every one of the prismatic molecules of which
the body is composed is during an infinitely small time in a state similar to
that which the linear equation (a) expresses. We may then, by following the
ordinary principles of the differential calculus, easily deduce from the notion of
uniform movement the general equations of varied movement.

93. In order to prove that when the extreme layers of the solid preserve their
temperatures no change can happen in the interior of the mass, it is sufficient
to compare with each other the quantities of heat which, during the same
instant, cross two parallel planes.

Let b be the perpendicular distance of these two planes which we first sup-
pose parallel to the horizontal plane of x and y. Let m and m f be two infinitely
near molecules, one of which is above the first horizontal plane and the other
below it: let x, y, z be the co-ordinates of the first molecule, and x'j y', z f those
of the second. In like manner let M and M' denote two infinitely near mole-
cules, separated by the second horizontal plane and situated, relatively to that
plane, in the same manner as nt and m' are relatively to the first plane ; that is
to say, the co-ordinates of M are x, y, z-\-@, and those of M' are x', y' , z'+/B. It
is evident that the distance mm' of the two molecules m and m' is equal to the
distance MM' of the two molecules M and M' ; further, let v be the tempera-
ture of m, and v' that of w', also let V and V be the temperatures of M and M',
it is easy to see that the two differences v v' and V V are equal ; in fact,
substituting first the co-ordinates of m and m' in the general equation

v = A +ax+by+cz,
we find v v' = a(x x') +b(y y') -\-c(z z'),

and then substituting the co-ordinates of M and M', we find also V V
~a(x x')~{-b(y y')+c(z z'). Now the quantity of heat which m sends to m 1
depends on the distance mm', which separates these molecules, and it is
proportional to the difference v v f of their temperatures. This quantity of
heat transferred may be represented by

q(v v')dt\

the value of the coefficient q depends in some manner on the distance mm', and
on the nature of the substance of which the solid is formed, dt is the duration of
the instant. The quantity of heat transferred from M to M', or the action of
M on M' is expressed likewise by q(V V')dt y and the coefficient q is the same
as in the expression q(v v')dt y since the distance MM' is equal to mm' and the
two actions are effected in the same solid: furthermore V V is equal to t; t/,
hence the two actions are equal.

SECT. VII THEORY OF HEAT 215

If we choose two other points n and n', very near to each other, which
transfer heat across the first horizontal plane, we shall find in the same manner
that their action is equal to that of two homologous points N and N' which
communicate heat across the second horizontal plane. We conclude then that
the whole quantity of heat which crosses the first plane is equal to that which
crosses the second plane during the same instant. We should derive the same
result from the comparison of two planes parallel to the plane of x and z, or
from the comparison of two other planes parallel to the plane of y and z. Hence
any part whatever of the solid enclosed between six planes at right angles,
receives through each of its faces as much heat as it loses through the opposite
face; hence no portion of the solid can change temperature.

94. Thus, across one of these planes, a quantity of heat flows which is the
same at all instants, and which is also the same for all other parallel sections.

In order to determine the value of this constant flow we shall compare it
with the quantity of heat which flows uniformly in the most simple case,
which has been already discussed. The case is that of an infinite solid enclosed
between two infinite planes and maintained in a constant state. We have seen
that the temperatures of the different points of the mass are in this case
represented by the equation v = A+cz; we proceed to prove that the uniform
flow of heat per unit area propagated in the vertical direction in the infinite
solid is equal to that which flows in the same direction per unit area across the
prism enclosed by six planes at right angles. This equality necessarily exists if
the coefficient c in the equation v = A+cz, belonging to the first solid, is the
same as the coefficient c in the more general equation v A +ax+by+cz which
represents the state of the prism. In fact, denoting by H a plane in this prism
perpendicular to z, and by m and M two molecules very near to each other,
the first of which m is below the plane H, and the second above this plane,
let v be the temperature of m whose co-ordinates are x, y, z, and w the tem-
perature of M whose co-ordinates are x+a, y-\-&, z+y. Take a third molecule
M' whose co-ordinates are x a, y @, z+y, and whose temperature may be
denoted by w'. We see that M and M' are on the same horizontal plane, and that
the vertical drawn from the middle point of the line MM'? which joins these two
points, passes through the point m, so that the distances mp. and m^ f are equal.
The action of m on M? or the quantity of heat which the first of these molecules
sends to the other across the plane H, depends on the difference v w of their
temperatures. The action of m on y! depends in the same manner on the differ-
ence v w r of the temperatures of these molecules, since the distance of m from
M is the same as that of m from M'- Thus, expressing by q(vw) the action of
m on M during the unit of time, we shall have q(v w') to express the action of
m on M 7 , q being a common unknown factor, depending on the distance WM and
on the nature of the solid. Hence the sum of the two actions exerted during unit
of time is ^(v w+v w').

If instead of x, y, and z, in the general equation

v = A +ax+by+cz,
we substitute the co-ordinates of m and then those of M and M'> we shall find

The sum of the two actions of m on M and of m on M' is therefore -~2qcy.

216 FOURIER CHAP. I

Suppose then that the plane H belongs to the infinite solid whose tempera-
ture equation is v = A+cz, and that we denote also by m, M and M' those mole-
cules in this solid whose co-ordinates are x, y, z for the first, x+, t/+/3, z+y
for the second, and x a, y p, z+y for the third: we shall have, as in the
preceding case, v w-}-v w' = 2cy. Thus the sum of the two actions of m on
IJL and of m on //, is the same in the infinite solid as in the prism enclosed
between the six planes at right angles.

We should obtain a similar result, if we considered the action of another
point n below the plane H on two others v and v', situated at the same height
above the plane. Hence, the sum of all the actions of this kind, which are
exerted across the plane H, that is to say the whole quantity of heat which,
during unit of time, passes to the upper side of this surface, by virtue of the
action of very near molecules which it separates, is always the same in both
solids.

95. In the second of these two bodies, that which is bounded by two infinite
planes, and whose temperature equation is v = A+cz, we know that the quan-
tity of heat which flows during unit of time across unit of area taken on any
horizontal section whatever is cK y c being the coefficient of 2, and K the
specific conductivity; hence, the quantity of heat which, in the prism enclosed
between six planes at right angles, crosses during unit of time, unit of area
taken on any horizontal section whatever, is also cK, when the linear equa-
tion which represents the temperatures of the prism is

v = A +ax-{-by+cz.

In the same way it may be proved that the quantity of heat which, during
unit of time, flows uniformly across unit of area taken on any section whatever
perpendicular to x, is expressed by aK, and that the whole quantity which,
during unit of time, crosses unit of area taken on a section perpendicular to y,
is expressed by bK.

The theorems which we have demonstrated in this and the two preceding
articles, suppose the direct action of heat in the interior of the mass to be
limited to an extremely small distance, but they would still be true, if the rays
of heat sent out by each molecule could penetrate directly to a quite appreci-
able distance, but it would be necessary in this case, as we have remarked in
Article 70, to suppose that the cause which maintains the temperatures of the
faces of the solid affects a part extending within the mass to a finite depth.

SECTION VIII. Measure of the Movement of Heat at a Given Point

of a Solid Mass

96. It still remains for us to determine one of the principal elements of the
theory of heat, which consists in defining and in measuring exactly the quan-
tity of heat which passes through every point of a solid mass across a plane
whose direction is given.

If heat is unequally distributed amongst the molecules of the same body,
the temperatures at any point will vary every instant. Denoting by t the time
which has elapsed, and by v the temperature attained after a time t by an
infinitely small molecule whose co-ordinates are x, y, z; the variable state of the
solid will be expressed by an equation similar to the following v~F(x, y, z, t).
Suppose the function F to be given, and that consequently we can determine

SECT. VIII THEORY OF HEAT 217

at every instant the temperature of any point whatever; imagine that through
the point m we draw a horizontal plane parallel to that of x and y, and that on
this plane we trace an infinitely small circle co, whose centre is at ra; it is
required to determine what is the quantity of heat which during the instant dt
will pass across the circle co from the part of the solid which is below the plane
into the part above it.

All points extremely near to the point m and under the plane exert their
action during the infinitely small instant dt, on all those which are above the
plane and extremely near to the point m, that is to say, each of the points
situated on one side of this plane will send heat to each of those which are
situated on the other side.

We shall consider as positive an action whose effect is to transport a certain
quantity of heat above the plane, and as negative that which causes heat to
pass below the plane. The sum of all the partial actions which are exerted
across the circle co, that is to say, the sum of all the quantities of heat which,
crossing any point whatever of this circle, pass from the part of the solid below
the plane to the part above, compose the flow whose expression is to be found.

It is easy to imagine that this flow may not be the same throughout the
whole extent of the solid, and that if at another point m f we traced a horizontal
circle co' equal to the former, the two quantities of heat which rise above these
planes co and co' during the same instant might not be equal : these quantities
are comparable with each other and their ratios are numbers which may be
easily determined.

97. We know already the value of the constant flow for the case of linear and
uniform movement; thus in the solid enclosed between two infinite horizontal
planes, one of which is maintained at the temperature a and the other at the
temperature 6, the flow of heat is the same for every part of the mass; we may
regard it as taking place in the vertical direction only. The value corresponding

to unit of surface and to unit of time is K I 1, e denoting the perpendic-
ular distance of the two planes, and K the specific conducibility : the tempera-
tures at the different points of the solid are expressed by the equation

/a-6
v=a I

V e

When the problem is that of a solid comprised between six rectangular
planes, pairs of which are parallel, and the temperatures at the different points
are expressed by the equation

the propagation takes place at the same time along the directions of x, of y y
of z; the quantity of heat which flows across a definite portion of a plane
parallel to that of x and y is the same throughout the whole extent of the
prism; its value corresponding to unit of surface, and to unit of time is cK,
in the direction of z, it is -~bK, in the direction of y, and aK in that of x.
In general the value of the vertical flow in the two cases which we have just
cited, depends only on the coefficient of z and on the specific conductivity K\

this value is always equal to K -r

The expression of the quantity of heat which, during the instant dt, flows
across a horizontal circle infinitely small, whose area is co, and passes in this

218 FOURIER CHAP. I

manner from the part of the solid which is below the plane of the circle to the
part above, is, for the two cases in question, K j- udt.

98. It is easy now to generalise this result and to recognise that it exists in every
case of the varied movement of heat expressed by the equation v = F(x, y, z, t).

Let us in fact denote by z', y', z', the co-ordinates of this point ra, and its
actual temperature by v'. Let x'+, y'+y, z'+, be the co-ordinates of a
point /x infinitely near to the point w, and whose temperature is w; f, 77, f are
quantities infinitely small added to the co-ordinates x', i/, z f ; they determine
the position of molecules infinitely near to the point m, with respect to three
rectangular axes, whose origin is at w, parallel to the axes of x, y, and z.
Differentiating the equation

v = F(x, y,z,

and replacing the differentials by , 17, f , we shall have, to express the value of
w which is equivalent to v+dv, the linear equation w v'+ -r- + -T- 77+ -T- f ;

the coefficients v', -T- , -j- , -T- , are functions of x, y, z, t, in which the given and

constant values x', y', z', which belong to the point m, have been substituted
for Xj y, z.

Suppose that the same point m belongs also to a solid enclosed between six
rectangular planes, and that the actual temperatures of the points of this
prism, whose dimensions are finite, are expressed by the linear equation
w = A+a+bri+cf; and that the molecules situated on the faces which bound
the solid are maintained by some external cause at the temperature which is
assigned to them by the linear equation. , 17, f are the rectangular co-ordinates
of a molecule of the prism, whose temperature is w, referred to three axes
whose origin is at m.

This arranged, if we take as the values of the constant coefficients A, a, 6,

c, which enter into the equation for the prism, the quantities v', -T- , -7- , ~T- ,

which belong to the differential equation; the state of the prism expressed by

the equation

f dv'

will coincide as nearly as possible with the state of the solid; that is to say, all
the molecules infinitely near to the point m will have the same temperature,
whether we consider them to be in the solid or in the prism. This coincidence
of the solid and the prism is quite analogous to that of curved surfaces with the
planes which touch them.

It is evident, from this, that the quantity of heat which flows in the solid
across the circle o>, during the instant dt, is the same as that which flows in the
prism across the same circle; for all the molecules whose actions concur in one
effect or the other, have the same temperature in the two solids. Hence, the

flow in question, in one solid or the other, is expressed by K -r- wdt. It would
be K -T- o>dt, if the circle w, whose centre is m, were perpendicular to the axis
of y, and K -y- udt, if this circle were perpendicular to the axis of x.

SECT. VIII THEORY OF HEAT 219

The value of the flow which we have just determined varies in the solid from
one point to another, and it varies also with the time. We might imagine it to
have, at all the points of a unit of surface, the same value as at the point m,
and to preserve this value during unit of time; the flow would then be ex-

pressed by K -j- , it would be K -j- in the direction of y, and K -T- in that

of x. We shall ordinarily employ in calculation this value of the flow thus
referred to unit of time and to unit of surface.

99. This theorem serves in general to measure the velocity with which heat
tends to traverse a given point of a plane situated in any manner whatever in
the interior of a solid whose temperatures vary with the time. Through the
given point m, a perpendicular must be raised upon the plane, and at every
point of this perpendicular ordinates must be drawn to represent the actual
temperatures at its different points. A plane curve will thus be formed whose
axis of abscissae is the perpendicular. The fluxion of the ordinate of this curve,
answering to the point ra, taken with the opposite sign, expresses the velocity
with which heat is transferred across the plane. This fluxion of the ordinate is
known to be the tangent of the angle formed by the element of the curve with
a parallel to the abscissae.

The result which we have just explained is that of which the most frequent
applications have been made in the theory of heat. We cannot discuss the
different problems without forming a very exact idea of the value of the flow at
every point of a body whose temperatures are variable. It is necessary to insist
on this fundamental notion; an example which we are about to refer to will
indicate more clearly the use which has been made of it in analysis.

100. Suppose the different points of a cubic mass, an edge of which has the
length TT, to have unequal actual temperatures represented by the equation
v = cos x cos y cos z. The co-ordinates x, y, z are measured on three rectangular
axes, whose origin is at the centre of the cube, perpendicular to the faces. The
points of the external surface of the solid are at the actual temperature 0, and
it is supposed also that external causes maintain at all these points the actual
temperature 0. Ori this hypothesis the body will be cooled more and more, the
temperatures of all the points situated in the interior of the mass will vary,
and, after an infinite time, they will all attain the temperature of the surface.
Now, we shall prove in the sequel, that the variable state of this solid is
expressed by the equation

cos x cos y cos z,

o i-

the coefficient g is equal to 7T~~n > ^ * s ^ e specific conductivity of the sub-

stance of which the solid is formed, D is the density and C the specific heat;
t is the time elapsed.

We here suppose that the truth of this equation is admitted, and we proceed
to examine the use which may be made of it to find the quantity of heat which
crosses a given plane parallel to one of the three planes at the right angles.

If, through the point m, whose co-ordinates are x, y, z, we draw a plane
perpendicular to 2, we shall find, after the mode of the preceding article, that

the value of the flow, at this point and across the plane, is K -T- , or Ke~ at cos
#-cos y-sin z. The quantity of heat which, during the instant dt, crosses an

220 FOURIER CHAP. I

infinitely small rectangle, situated on this plane, and whose sides are dx and
dy, is

K e~ et cos x cos y sin z dx dy dL

Thus the whole heat which, during the instant dt, crosses the entire area of
the same plane, is

K e~<* sin z*dt JJ cos x cos y dx dy;

the double integral being taken from x= %-rr up to x = JTT, and from y = TT
up to y = iTT. We find then for the expression of this total heat,

4 K e~ at sin z-dt.

If then we take the integral with respect to t, from t = to t t, we shall find
the quantity of heat which has crossed the same plane since the cooling began

up to the actual moment. This integral is sin z(l e~ 0t ), its value at the sur-

face is

so that after an infinite time the quantity of heat lost through one of the faces
is - .The same reasoning being applicable to each of the six faces, we conclude

that the solid has lost by its complete cooling a total quantity of heat equal to

or 8CD, since g is equivalent to 77^ . The total heat which is dissipated

during the cooling must indeed be independent of the special conductivity K,
which can only influence more or less the velocity of cooling.

100. A. We may determine in another manner the quantity of heat which the
solid loses during a given time, and this will serve in some degree to verify the
preceding calculation. In fact, the mass of the rectangular molecule whose
dimensions are dx, dy, dz, is D dx dy dz, consequently the quantity of heat
which must be given to it to bring it from the temperature to that of boiling
water is CD dx dy dz, and if it were required to raise this molecule to the
temperature v, the expenditure of heat would be v CD dx dy dz.

It follows from this, that in order to find the quantity by which the heat of
the solid, after time t, exceeds that which it contained at the temperature 0,
we must take the multiple integral J/J v CD dx dy dz, between the limits

X= $w, X = $7r, y= TT, 2/ = ?7r, 2 = ^TT, 2 = ^.

We thus find, on substituting for v its value, that is to say

e~ ai cos x cos y cos 2,

that the excess of actual heat over that which belongs to the temperature is
8CDe~ ot ; or, at the start, 8CD, as we found before.

We have described, in this introduction, all the elements which it is neces-
sary to know in order to solve different problems relating to the movement of
heat in solid bodies, and we have given some applications of these principles,
in order to shew the mode of employing them in analysis; the most important
use which we have been able to make of them, is to deduce from them the
general equations of the propagation of heat, which is the subject of the next
chapter.

SECOND CHAPTER

EQUATIONS OF THE MOVEMENT OF HEAT

SECTION I. Equation of the Varied Movement of Heat in a Ring

101. We might form the general equations which represent the movement of
heat in solid bodies of any form whatever, and apply them to particular cases.
But this method would often involve very complicated calculations which
may easily be avoided. There are several problems which it is preferable to
treat in a special manner by expressing the conditions which are appropriate
to them; we proceed to adopt this course and examine separately the problems
which have been enunciated in the first section of the introduction; we will
limit ourselves at first to forming the differential equations, and shall give the
integrals of them in the following chapters.

102. We have already considered the uniform movement of heat in a pris-
matic bar of small thickness whose extremity is immersed in a constant source
of heat. This first case offered no difficulties, since there was no reference
except to the permanent state of the temperatures, and the equation which
expresses them is easily integrated. The following problem requires a more pro-
found investigation; its object is to determine the variable state of a solid ring
whose different points have received initial temperatures entirely arbitrary.

The solid ring or armlet is generated by the revolution of a rectangular sec-
tion about an axis perpendicular to the plane of the ring (see figure 3), / is the
perimeter of the section whose area is *S, the coefficient h
measures the external conductivity, K the internal con-
ductivity, C the specific capacity for heat, D the density.
The line oxx'x" represents the mean circumference of the
armlet, or that line which passes through the centres of
figure of all the sections; the distance of a section from
the origin o is measured by the arc whose length is x ; R
is the radius of the mean circumference.

p- ^ It is supposed that on account of the small dimensions

arid of the form of the section, we may consider the tem-
perature at the different points of the same section to be equal.

103. Imagine that initial arbitrary temperatures have been given to the
different sections of the armlet, and that the solid is then exposed to air main-
tained at the temperature 0, and displaced with a constant velocity ; the sys-
tem of temperatures will continually vary, heat will be transmitted within the
ring, and dispersed at the surface : it is required to determine what will be the
state of the solid at any given instant.

Let v be the temperature which the section situated at distance x will have
acquired after a lapse of time t ; v is a certain function of x and , into which all
the initial temperatures also must enter: this is the function which is to be
discovered.

221

222 FOURIER CHAP. II

104. We will consider the movement of heat in an infinitely small slice,
enclosed between a section made at distance x and another section made at
distance x-\-dx. The state of this slice for the duration of one instant is that of
an infinite solid terminated by two parallel planes maintained at unequal
temperatures; thus the quantity of heat which flows during this instant dt
across the first section, and passes in this way from the part of the solid which
precedes the slice into the slice itself, is measured according to the principles
established in the introduction, by the product of four factors, that is to say,

the conducibility K, the area of the section S, the ratio -7- , and the duration

of the instant; its expression is KS-j-dt. To determine the quantity of heat

ctx

which escapes from the same slice across the second section, and passes into
the contiguous part of the solid, it is only necessary to change x into x+dx in
the preceding expression, or, which is the same thing, to add to this expression
its differential taken with respect to x\ thus the slice receives through one of

its faces a quantity of heat equal to KS -r- dt, and loses through the opposite
face a quantity of heat expressed by

-KS^dt-KS^dxdt.
dx dx 2

It acquires therefore by reason of its position a quantity of heat equal to the
difference of the two preceding quantities, that is

rf 2 D

KS^dxdt.
dx 2

On the other hand, the same slice, whose external surface is Idx and whose
temperature differs infinitely little from v y allows a quantity of heat equivalent
to hlv dx dt to escape into the air during the instant dt] it follows from this that
this infinitely small part of the solid retains in reality a quantity of heat

d 2 v
represented by KS -= a dx dt hlv dx dt which makes its temperature vary. The

amount of this change must be examined.

105. The coefficient C expresses how much heat is required to raise unit of
weight of the substance in question from temperature up to temperature 1 ;
consequently, multiplying the volume Sdx of the infinitely small slice by the
density Z>, to obtain its weight, and by C the specific capacity for heat, we
shall have CDS dx as the quantity of heat which would raise the volume of the
slice from temperature up to temperature 1. Hence the increase of tempera-
ture which results from the addition of a quantity of heat equal to KS -j 2 dx dt

hlv dx dt will be found by dividing the last quantity by CDS dx. Denoting
therefore, according to custom, the increase of temperature which takes place

during the instant dt by -37 dt, we shall have the equation

dv _ K_ d*v M_

dt CD dx 2 CDS V ' " " W '

We shall explain in the sequel the use which may be made of this equation
to determine the complete solution, and what the difficulty of the problem

SECT. I THEORY OF HEAT 223

consists in ; we limit ourselves here to a remark concerning the permanent state
of the armlet.

106. Suppose that, the plane of the ring being horizontal, sources of heat,
each of which exerts a constant action, are placed below different points m, n,
p, q etc.; heat will be propagated in the solid, and that which is dissipated
through the surface being incessantly replaced by that which emanates from
the sources, the temperature of every section of the solid will approach more
and more to a stationary value which varies from one section to another. In
order to express by means of equation (6) the law of the latter temperatures,
which would exist of themselves if they were once established, we must sup-
pose that the quantity v does not vary with respect to t; which annuls the

term -r: . We thus have the equation

2 = U whence ,-

M and N being two constants.

107. Suppose a portion of the circumference of the ring, situated between
two successive sources of heat, to be divided into equal parts, and denote by
0i, 02, 03, 04, &c., the temperatures at the points of division whose distances
from the origin are Xi, x 2j x 3 , x 4 , &c. ; the relation between v and x will be given
by the preceding equation, after the two constants have been determined by
means of the two values_of v corresponding to the sources of heat. Denoting

by a. the quantity e~ v ra, and by X the distance x% x\ of two consecutive
points of division, we shall have the equations:

whence we derive the following relation - - = a x +a~ x .

We should find a similar result for the three points whose temperatures are
02, 03, 04? and in general for any three consecutive points. It follows from this
that if we observed the temperatures 01, 2 , 03, 04, 06 &c. of several successive
points, all situated between the same two sources m and n and separated by a
constant interval X, we should perceive that any three consecutive tempera-
tures are always such that the sum of the two extremes divided by the mean
gives a constant quotient a x +~ x .

108. If, in the space included between the next two sources of heat n and p,
the temperatures of other different points separated by the same interval X
were observed, it would still be found that for any three consecutive points,
the sum of the two extreme temperatures, divided by the mean, gives the same
quotient <* x +<*~ x . The value of this quotient depends neither on the position
nor on the intensity of the sources of heat.

109. Let q be this constant value, we have the equation

03 = 302 01;

we see by this that when the circumference is divided into equal parts, the
temperatures at the points of division, included between two consecutive
sources of heat, are represented by the terms of a recurring series whose scale
of relation is composed of two terms q and 1.

224 FOURIER CHAP. II

Experiments have fully confirmed this result. We have exposed a metallic
ring to the permanent and simultaneous action of different sources of heat,
and we have observed the stationary temperatures of several points separated
by constant intervals; we always found that the temperatures of any three
consecutive points, not separated by a source of heat, were connected by the
relation in question. Even if the sources of heat be multiplied, and in whatever
manner they be disposed, no change can be effected in the numerical value of

the quotient ; it depends only on the dimensions or on the nature of the

ring, and not on the manner in which that solid is heated.

110. When we have found, by observation, the value of the constant quo-
tient q or , the value of x may be derived from it by means of the equa-

V<2

tion a x +c*- x = <7. One of the roots is a x , and other root is a~ x . This quantity
being determined, we may derive from it the value of the ratio jz , which is

y (log a) 2 . Denoting a x by w, we shall have a? 2 qu+l =0. Thus the ratio of the

two conductivities is found by multiplying y by the square of the hyperbolic

logarithm of one of the roots of the equation co 2 qu+1 = 0, and dividing the
product by X 2 .

SECTION II. Equation of the Varied Movement of Heat in a Solid Sphere

111. A solid homogeneous mass, of the form of a sphere, having been im-
mersed for an infinite time in a medium maintained at a permanent tempera-
ture 1, is then exposed to air which is kept at temperature 0, and displaced
with constant velocity : it is required to determine the successive states of the
body during the whole time of the cooling.

Denote by x the distance of any point whatever from the centre of the
sphere, and by v the temperature of the same point, after a time t has elapsed ;
and suppose, to make the problem more general, that the initial temperature,
common to all points situated at the distance x from the centre, is different for
different values of x] which is what would have been the case if the immersion
had not lasted for an infinite time.

Points of the solid, equally distant from the centre, will not cease to have a
common temperature; v is thus a function of x and t. When we suppose Z = 0,
it is essential that the value of this function should agree with the initial state
which is given, and which is entirely arbitrary.

112. We shall consider the instantaneous movement of heat in an infinitely
thin shell, bounded by two spherical surfaces whose radii are x and x+dx: the
quantity of heat which, during an infinitely small instant dt, crosses the lesser
surface whose radius is x t and so passes from that part of the solid which is
nearest to the centre into the spherical shell, is equal to the product of four
factors which are the conductivity K, the duration dt y the extent 4wx 2 of

surface, and the ratio -T- , taken with the negative sign; it is expressed by

^dt.
dx

SECT. II THEORY OF HEAT 225

To determine the quantity of heat which flows during the same instant
through the second surface of the same shell, and passes from this shell into
the part of the solid which envelops it, x must be changed into x-\-dx, in the

preceding expression: that is to say, to the term 4K7rx* -p dt must be added
the differential of this term taken with respect to x. We thus find

\f~di

as the expression of the quantity of heat which leaves the spherical shell
across its second surface; and if we subtract this quantity from that which

enters through the first surface, we shall have 4Kird I x 2 -r~ \ dt. This difference

is evidently the quantity of heat which accumulates in the intervening shell,
and whose effect is to vary its temperature.

113. The coefficient C denotes the quantity of heat which is necessary to
raise, from temperature to temperature 1, a definite unit of weight; D is the
weight of unit of volume, 4-KX-dx is the volume of the intervening layer, differ-
ing from it only by a quantity which may be omitted : hence 4irCDx 2 dx is the
quantity of heat necessary to raise the intervening shell from temperature to
temperature 1. Hence it is requisite to divide the quantity of heat which
accumulates in this shell by 47rCDx 2 dx, and we shall then find the increase of
its temperature v during the time dt. We thus obtain the equation

^ = JL (^ 4. ? d"\ ( \

dt CD ' \dx* + x dx) ' (C) '

114. The preceding equation represents the law of the movement of heat in
the interior of the solid, but the temperatures of points in the surface are sub-
ject also to a special condition which must be expressed. This condition rela-
tive to the state of the surface may vary according to the nature of the prob-
lems discussed: we may suppose for example, that, after having heated the
sphere, and raised all its molecules to the temperature of boiling water, the
cooling is effected by giving to all points in the surface the temperature 0, and
by retaining them at this temperature by any external cause whatever. In this
case we may imagine the sphere, whose variable state it is desired to deter-
mine, to be covered by a very thin envelope on which the cooling agency exerts
its action. It may be supposed, 1, that this infinitely thin envelope adheres to
the solid, that it is of the same substance as the solid and that it forms a part
of it, like the other portions of the mass; 2, that all the molecules of the enve-
lope are subjected to temperature by a cause always in action which prevents
the temperature from ever being above or below zero. To express this condi-
tion theoretically, the function v, which contains x and t, must be made to
become nul, when we give to x its complete value X equal to the radius of the
sphere, whatever else the value of t may be. We should then have, on this

226 FOURIER CHAP. II

hypothesis, if we denote by <t>(x, t) the function of x and t, which expresses the
value of Vj the two equations

dv K Sd 2 v . 2 dv

Further, it is necessary that the initial state should be represented by the same
function 0(#, : we shall therefore have as a second condition <(#, 0) = 1. Thus
the variable state of a solid sphere on the hypothesis which we have first
described will be represented by a function v, which must satisfy the three
preceding equations. The first is general, and belongs at every instant to all
points of the mass; the second affects only the molecules at the surface, and
the third belongs only to the initial state.

115. If the solid is being cooled in air, the second equation is different; it
must then be imagined that the very thin envelope is maintained by some
external cause, in a state such as to produce the escape from the sphere, at
every instant, of a quantity of heat equal to that which the presence of the
medium can carry away from it.

Now the quantity of heat which, during an infinitely small instant dt, flows
within the interior of the solid across the spherical surface situate at distance

x, is equal to ^KTrx^-j-dt; and this general expression is applicable to all

values of x. Thus, by supposing x = X we shall ascertain the quantity of heat
which in the variable state of the sphere would pass across the very thin
envelope which bounds it; on the other hand, the external surface of the solid
having a variable temperature, which we shall denote by V, would permit the
escape into the air of a quantity of heat proportional to that temperature, and
to the extent of the surface, which is 4?rX 2 . The value of this quantity is
IhirXWdt.

To express, as is supposed, that the action of the envelope supplies the
place, at every instant, of that which would result from the presence of the
medium, it is sufficient to equate the quantity ^hirX 2 Vdt to the value which

the expression 4K7rX 2 -T- dt receives when we give to x its complete value X;
hence we obtain the equation -T- = -^ v, which must hold when in the func-
tions -j- and v we put instead of x its value X, which we shall denote by writing

it in the form K ^+hV = 0.
ax

116. The value of -5- taken when x X. must therefore have a constant ratio

ax J

j; to the value of v, which corresponds to the same point. Thus we shall
suppose that the external cause of the cooling determines always the state of
the very thin envelope, in such a manner that the value of -y- which results
from this state, is proportional to the value of i>, corresponding to x = X, and
that the constant ratio of these two quantities is -^ . This condition being
fulfilled by means of some cause always present, which prevents the extreme

SECT. Ill THEORY OF HEAT 227

value of -p from being anything else but -~ v, the action of the envelope will

take the place of that of the air.

It is not necessary to suppose the envelope to be extremely thin, and it will
be seen in the sequel that it may have an indefinite thickness. Here the thick-
ness is considered to be indefinitely small, so as to fix the attention on the state
of the surface only of the solid.

117. Hence it follows that the three equations which are required to deter-
mine the function <^(x y t) or v are the following,

dt K/d*v2dv

The first applies to all possible values of x and t] the second is satisfied when
x = X, whatever be the value of t ; and the third is satisfied when t = 0, whatever
be the value of x.

It might be supposed that in the initial state all the spherical layers have not
the same temperature: which is what would necessarily happen, if the immer-
sion were imagined not to have lasted for an indefinite time. In this case,
which is more general than the foregoing, the given function, which expresses
the initial temperature of the molecules situated at distance x from the centre
of the sphere, will be represented by F(x); the third equation will then be
replaced by the following, <t>(x y 0) =F(x).

Nothing more remains than a purely analytical problem, whose solution
will be given in one of the following chapters. It consists in finding the value
of v, by means of the general condition, and the two special conditions to
which it is subject.

SECTION III. Equations of the Varied Movement of Heat in a Solid Cylinder

118. A solid cylinder of infinite length, whose side is perpendicular to its
circular base, having been wholly immersed in a liquid whose temperature is
uniform, has been gradually heated, in such a manner that all points equally
distant from the axis have acquired the same temperature; it is then exposed
to a current of colder air; it is required to determine the temperatures of the
different layers, after a given time.

x denotes the radius of a cylindrical surface, all of whose points are equally
distant from the axis; X is the radius of the cylinder; v is the temperature
which points of the solid, situated at distance x from the axis, must have after
the lapse of a time denoted by , since the beginning of the cooling. Thus v is a
function of x and t, and if in it t be made equal to 0, the function of x which
arises from this must necessarily satisfy the initial state, which is arbitrary.

119. Consider the movement of heat in an infinitely thin portion of the
cylinder, included between the surface whose radius is x, and that whose
radius is x+dx. The quantity of heat which this portion receives during the
instant dt, from the part of the solid which it envelops, that is to say, the
quantity which during the same time crosses the cylindrical surface whose
radius is a?, and whose length is supposed to be equal to unity, is expressed
by

%-di.
dx

228 FOURIER CHAP. II

To find the quantity of heat which, crossing the second surface whose radius
is x+dx, passes from the infinitely thin shell into the part of the solid which
envelops it, we must, in the foregoing expression, change x into x+dx, or,
which is the same thing, add to the term

dx '

the differential of this term, taken with respect to x. Hence the difference of
the heat received and the heat lost, or the quantity of heat which accumulating
in the infinitely thin shell determines the changes of temperature, is the same
differential taken with the opposite sign, or

2K7r.dt-d(x^

on the other hand, the volume of this intervening shell is 2wxdx, and 2CDirxdx
expresses the quantity of heat required to raise it from the temperature to
the temperature 1, C being the specific heat, and D the density. Hence the
quotient

2Kir-dt'd[x~

2CDvxdx

is the increment which the temperature receives during the instant dt. Whence
we obtain the equation

dv K_ (d^ 1 dv\
dt CD\dx*^ x dx)'

120. The quantity of heat which, during the instant dt, crosses the cylin-
drical surface whose radius is x, being expressed in general by 2K irx -r- dt, we

shall find that quantity which escapes during the same time from the surface
of the solid, by making x = X in the foregoing value ; on the other hand, the
same quantity, dispersed into the air, is, by the principle of the communica-
tion of heat, equal to 2irXhvdt; we must therefore have at the surface the

definite equation K-r- = kv. The nature of these equations is explained

at greater length, either in the articles which refer to the sphere, or in
those wherein the general equations have been given for a body of any form
whatever. The function v which represents the movement of heat in
an infinite cylinder must therefore satisfy, 1st, the general equation

dv K /d*v , 1 dv\ ,. , .. , x _ . rt ,.,_, ^

jj = CD V 5^2 ^~x~dx)' wluch a PP lle s whatever x and t may be; 2nd, the defi-
nite equation j? v + ~T~ = 0> which is true, whatever the variable t may be,

when x = X; 3rd, the definite equation v = F(x). The last condition must be
satisfied by all values of v, when t is made equal to 0, whatever the variable x
may be. The arbitrary function F(x) is supposed to be known; it corresponds
to the initial state.

SECT. IV THEORY OF HEAT 229

SECTION IV. Equations of the Uniform Movement of Heat
in a Solid Prism of Infinite Length

121. A prismatic bar is immersed at one extremity in a constant source of heat
which maintains that extremity at the temperature A] the rest of the bar,
whose length is infinite, continues to be exposed to a uniform current of at-
mospheric air maintained at temperature 0; it is required to determine the
highest temperature which a given point of the bar can acquire.

The problem differs from that of Article 73, since we now take into consider-
ation all the dimensions of the solid, which is necessary in order to obtain an
exact solution.

We are led, indeed, to suppose that in a bar of very small thickness all points
of the same section would acquire sensibly equal temperatures; but some un-
certainty may rest on the results of this hypothesis. It is therefore preferable
to solve the problem rigorously, and then to examine, by analysis, up to what
point, and in what cases, we are justified in considering the temperatures of
different points of the same section to be equal.

122. The section made at right angles to the length of the bar, is a square
whose side is 21, the axis of the bar is the axis of x, and the origin is at the
extremity A. The three rectangular co-ordinates of a point of the bar are x,
y, z, and v denotes the fixed temperature at the same point.

The problem consists in determining the temperatures which must be
assigned to different points of the bar, in order that they may continue to
exist without any change, so long as the extreme surface A, which communi-
cates with the source of heat, remains subject, at all its points, to the perma-
nent temperature A ; thus v is a function of x, y, and z.

123. Consider the movement of heat in a prismatic molecule, enclosed
between six planes perpendicular to the three axes of x, y, and z. The first
three planes pass through the point m whose co-ordinates are x, y, z, and the
others pass through the point m' whose co-ordinates are x+dx, y-\-dy, z+dz.

To find what quantity of heat enters the molecule during unit of time across
the first plane passing through the point m and perpendicular to x, we must
remember that the extent of the surface of the molecule on this plane is dy dz,
and that the flow across this area is, according to the theorem of Article 98,

equal to K -r- ; thus the molecule receives across the rectangle dy dz passing

through the point m a quantity of heat expressed by K dy dz -7- . To find the

quantity of heat which crosses the opposite face, and escapes from the
molecule, we must substitute, in the preceding expression, x+dx for x, or,
which is the same thing, add to this expression its differential taken with
respect to x only; whence we conclude that the molecule loses, at its second
face perpendicular to x, a quantity of heat equal to

we must therefore subtract this from that which enters at the opposite face;
the differences of these two quantities is

K dy dz d I -r- j , or, K dx dy dz -j 2 ;

230 FOURIER CSAP. II

this expresses the quantity of heat accumulated in the molecule in consequence
of the propagation in direction of x; which accumulated heat would make the
temperature of the molecule vary, if it were not balanced by that which is lost

in some other direction.

It is found in the same manner that a quantity of heat equal to Kdzdx-j-

enters the molecule across the plane passing through the point m perpendicular
to y, and that the quantity which escapes at the opposite face is

-Kdzdx^- -Kdzdxd(^\ ,

the last differential being taken with respect to y only. Hence the difference of

d 2 v

the two quantities, or Kdxdydz -T-J , expresses the quantity of heat which the

molecule acquires, in consequence of the propagation in direction of y.

Lastly, it is proved in the same manner that the molecule acquires, in conse-
quence of the propagation in direction of z, a quantity of heat equal to

K dx dy dz -=-$ . Now, in order that there may be no change of temperature, it is

necessary for the molecule to retain as much heat as it contained at first, so
that the heat it acquires in one direction must balance that which it loses in
another. Hence the sum of the three quantities of heat acquired must be
nothing; thus we form the equation

d 2 v d 2 v d 2 v n
dx 2 + dy 2 + dz 2 '

124. It remains now to express the conditions relative to the surface. If we
suppose the point m to belong to one of the faces of the prismatic bar, and the
face to be perpendicular to 2, we see that the rectangle dxdy, during unit of
time, permits a quantity of heat equal to V h dx dy to escape into the air, V
denoting the temperature of the point m of the surface, namely what < (x, y, z)
the function sought becomes when z is made equal to Z, half the dimension of
the prism. On the other hand, the quantity of heat which, by virtue of the
action of the molecules, during unit of time, traverses an infinitely small

surface o>, situated within the prism, perpendicular to z, is equal to K(^~ ,

CLZ

according to the theorems quoted above. This expression is general, and ap-
plying it to points for which the co-ordinate z has its complete value Z, we
conclude from it that the quantity of heat which traverses the rectangle dx dy

taken at the surface is Kdxdy-j-, giving to z in the function -y- its complete

value Z. Hence the two quantities Kdxdy-j-, and h dx dy v, must be equal,
in order that the action of the molecules may agree with that of the medium.
This equality must also exist when we give to z in the functions -y- and v the

value Z, which it has at the face opposite to that first considered. Further,
the quantity of heat which crosses an infinitely small surface w, perpendicular

to the axis of y> being KOJ-J-, it follows that that which flows across a

SECT. V THEORY OF HEAT 231

rectangle dz dx taken on a face of the prism perpendicular to y is Kdzdx-r-,

giving to y in the function -T- its complete value I. Now this rectangle dz dx
permits a quantity of heat expressed by hvdx dz to escape into the air; the
equation hv = K -T- becomes therefore necessary, when y is made equal to I or

I in the functions v and -j- .

125. The value of the function v must by hypothesis be equal to A, when we
suppose x = 0, whatever be the values of y and z. Thus the required function v
is determined by the following conditions: 1st, for all values of x, y, z, it satis-
fies the general equation

d*v d 2 v d*v

dx 2 + dy* + dz* ~ U;

2nd, it satisfies the equation j* v+ -7- =0, when y is equal to I or I, whatever

x and z may be, or satisfies the equation j? v+ -j- = 0, when z is equal to Z or

Z, whatever x and i/ may be; 3rd, it satisfies the equation v = A, when x =
whatever y and z may be.

SECTION V. Equations of the Varied Movement of Heat in a Solid Cube

126. A solid in the form of a cube, all of whose points have acquired the same
temperature, is placed in a uniform current of atmospheric air, maintained at
temperature 0. It is required to determine the successive states of the body
during the whole time of the cooling.

The centre of the cube is taken as the origin of rectangular coordinates; the
three perpendiculars dropped from this point on the faces, are the axes of x,
y, and z; 21 is the side of the cube, v is the temperature to which a point whose
coordinates are x, y, z, is lowered after the time t has elapsed since the com-
mencement of the cooling : the problem consists in determining the function v,
which depends on x, y, z and t.

127. To form the general equation which v must satisfy, we must ascertain
what change of temperature an infinitely small portion of the solid must
experience during the instant dt y by virtue of the action of the molecules
which are extremely near to it. We consider then a prismatic molecule enclosed
between six planes at right angles; the first three pass through the point m,
whose co-ordinates are x, y, z, and the three others, through the point m',

whose co-ordinates are

x+dx 9 y+dy, z+dz.

The quantity of heat which during the instant dt passes into the molecule
across the first rectangle dy dz perpendicular to a:, is K dy dz -T- dt, and that

which escapes in the same time from the molecule, through the opposite
face, is found by writing x+dx in place of x in the preceding expression, it is

232 FOURIER CHAJV!!

the differential being taken with respect to x only. The quantity of heat
which during the instant dt enters the molecule, across the first rectangle

dz dx perpendicular to the axis of y, is K dz dx -r- dt, and that which escapes
from the molecule during the same instant, by the opposite face, is

-
dy \dy

the differential being taken with respect to y only. The quantity of heat which
the molecule receives during the instant dt, through its lower face, perpendicu-

lar to the axis of z, is Kdxdy-j-dt, and that which it loses through the
opposite face is

-A' dx dy ~ dt-K dx dy d (j\ dt,

the differential being taken with respect to z only.

The sum of all the quantities of heat which escape from the molecule must
now be deducted from the sum of the quantities which it receives, and the
difference is that which determines its increase of temperature during the
instant : this difference is

K dy dz d ( f- ) dt +K dz dx d ( %- ) dt + K dx dy d [ ^ ) dt,
\dfXj \dy/ \^/

TS j j j $d 2 v . d' 2 v . d 2 v\ ,.
or A dx dy dz < -=-= + -p-r + -r-^ > dt.
\dx* dy 2 dz 2 )

128. If the quantity which has just been found be divided by that which is
necessary to raise the molecule from the temperature to the temperature 1,
the increase of temperature which is effected during the instant dt will become
known. Now, the latter quantity is CD dx dy dz: for C denotes the capacity of
the substance for heat; D its density, and dx dy dz the volume of the molecule.
The movement of heat in the interior of the solid is therefore expressed by the
equation

dv A / d*v d*v d
dt = CD \dtf + dtf + d

129. It remains to form the equations which relate to the state of the surface,
which presents no difficulty, in accordance with the principles which we have
established. In fact, the quantity of heat which, during the instant dt, crosses

the rectangle dzdy, traced on a plane perpendicular to x, is Kdydz-r-dt.

This result, which applies to all points of the solid, ought to hold when the
value of x is equal to I, half the thickness of the prism. In this case, the rectan-
gle dy dz being situated at the surface, the quantity of heat which crosses it,
and is dispersed into the air during the instant dt, is expressed by hv dy dz dt, we

ought therefore to have, when # = Z, the equation hv= K -j- . This condition

must also be satisfied when x= I.

It will be found also that, the quantity of heat which crosses the rectangle

SECT. VI THEORY OF HEAT 233

dzdx situated on a plane perpendicular to the axis of y being in general
Kdzdx , and that which escapes at the surface into the air across the

same rectangle being hvdzdxdt, we must have the equation hv+K -T- = 0,
when y = I or I. Lastly, we obtain in like manner the definite equation

which is satisfied when z = l or I

130. The function sought, which expresses the varied movement of heat in
the interior of a solid of cubic form, must therefore be determined by the
following conditions:

1st. It satisfies the general equation

dv __ K /d 2 v d 2 v , d 2 v
Tt ~~ C^D\dx 2 + dy* + <T

2nd. It satisfies the three definite equations

hv+K = o, hv+K - 0, hv+K = 0,

dx ' dy ' dz '

which hold when x= 1, y=* 1, z= 1;

3rd. If in the function v which contains x, y, z, t, we make t = 0, whatever be
the values of x, y, and z, we ought to have, according to hypothesis, v=A,
which is the initial and common value of the temperature.

131. The equation arrived at in the preceding problem represents the move-
ment of heat in the interior of all solids. Whatever, in fact, the form of the
body may be, it is evident that, by decomposing it into prismatic molecules,
we shall obtain this result. We may therefore limit ourselves to demonstrating
in this manner the equation of the propagation of heat. But in order to make
the exhibition of principles more complete, and that we may collect into a
small number of consecutive articles the theorems which serve to establish the
general equation of the propagation of heat in the interior of solids, and the
equations which relate to the state of the surface, we shall proceed, in the two
following sections, to the investigation of these equations, independently of
any particular problem, and without reverting to the elementary propositions
which we have explained in the introduction.

SECTION VI. General equation of the Propagation of Heat
in the Interior of Solids

132. THEOREM I. // the different points of a homogeneous solid mass, enclosed
between six planes at right angles, have actual temperatures determined by the
linear equation

v=Aax bycz, , (a),

and if the molecules situated at the external surface on the six planes which bound
the prism are maintained, by any case whatever, at the temperature expressed by
the equation (a): all the molecules situated in the interior of the mass will of
themselves retain their actual temperatures, so that there will be no change in the
state of the prism.

234 FOURIER CHAP. II

. t> denotes the actual temperature of the point whose co-ordinates are x, y, z\
A, a, b, c, are constant coefficients.

To prove this proposition, consider in the solid any three points whatever
mM, situated on the same straight line mjj,, which the point M divides into
two equal parts; denote by x, y, z the co-ordinates of the point M, and its
temperature by v, the co-ordinates of the point ^ by x+<x, y+P> 2+7, and its
temperature by w, the co-ordinates of the point m by x a, y p } z y, and
its temperature by u, we shall have

v = Aax by cz,

whence we conclude that,

v w = a<x+b@+cy, and u v =
therefore v w = u v.

Now the quantity of heat which one point receives from another depends on
the distance between the two points and on the difference of their tempera-
tures. Hence the action of the point M on the point fj, is equal to the action of
m on M; thus the point M receives as much heat from m as it gives up to the
point ^.

We obtain the same result, whatever be the direction and magnitude of the
line which passes through the point M , and is divided into two equal parts.
Hence it is impossible for this point to change its temperature, for it receives
from all parts as much heat as it gives up.

The same reasoning applies to all other points; hence no change can happen
in the state of the solid.

133. COROLLARY I. A solid being enclosed between two infinite parallel
planes A and B, if the actual temperature of its different points is supposed to
be expressed by the equation v = lz, and the two planes which bound it are
maintained by any cause whatever, A at the temperature 1, and B at the
temperature 0; this particular case will then be included in the preceding
theorem, if we make A = 1, a = 0, 6 = 0, c = 1 .

134. COROLLARY II. If in the interior of the same solid we imagine a plane
M parallel to those which bound it, we see that a certain quantity of heat flows
across this plane during unit of time; for two very near points, such as m and n,
one of which is below the plane and the other above it, are unequally heated;
the first, whose temperature is highest, must therefore send to the second,
during each instant, a certain quantity of heat which, in some cases, may be
very small, and even insensible, according to the nature of the body and the
distance of the two molecules.

The same is true for any two other points whatever separated by the plane.
That which is most heated sends to the other a certain quantity of, heat, and
the sum of these partial actions, or of all the quantities of heat sent across the
plane, composes a continual flow whose value does not change, since all the
molecules preserve their temperatures. It is easy to prove that this flow, or the
quantity of heat which crosses the plane M during the unit of time, is equivalent
to that which crosses, during the same time, another plane N parallel to the first.
In fact, the part of the mass which is enclosed between the two surfaces M ajid
N will receive continually, across the plane M , as much heat as it loses across

SECT. VI THEORY OF HEAT 235

the plane N. If the quantity of heat, which in passing the plane M enters the
part of the mass which is considered, were not equal to that which escapes by
the opposite surface N, the solid enclosed between the two surfaces would acquire
fresh heat, or would lose a part of that which it has, and its temperatures would
not be constant; which is contrary to the preceding corollary.

135. The measure of the specific conducibility of a given substance is taken
to be the quantity of heat which, in an infinite solid, formed of this substance,
and enclosed between two parallel planes, flows during unit of time across unit
of surface, taken on any intermediate plane whatever, parallel to the external
planes, the distance between which is equal to unit of length, one of them
being maintained at temperature 1, and the other at temperature 0. This
constant flow of the heat which crosses the whole extent of the prism is denoted
by the coefficient K, and is the measure of the conductivity.

136. LEMMA. // we suppose all the temperatures of the solid in question under
the preceding article, to be multiplied by any number whatever g, so that the equa-
tion of temperatures is v = g gz, instead of being v=lz, and if the two external
planes are maintained, one at the temperature g, and the other at temperature 0,
the constant flow of heat, in this second hypothesis, or the quantity which during
unit of time crosses unit of surface taken on an intermediate plane parallel to the
bases, is equal to the product of the first flow multiplied by g.

In fact, since all the temperatures have been increased in the ratio of 1 to g,
the differences of the temperatures of any two points whatever m and ju, are
increased in the same ratio. Hence, according to the principle of the communi-
cation of heat, in order to ascertain the quantity of heat which m sends to ju,
on the second hypothesis, we must multiply by g the quantity which the same
point m sends to ^ on the first hypothesis. The same would be true for any two
other points whatever. Now, the quantity of heat which crosses a plane M
results from the sum of all the actions which the points m, m', m", m'", etc.,
situated on the same side of the plane, exert on the points v, p,', // ', M'"> etc.,
situated on the other side. Hence, if in the first hypothesis the constant flow is
denoted by K, it will be equal to gK, when we have multiplied all the tem-
peratures by g.

137. THEOREM II. In a prism whose constant temperatures are expressed by
the equation v = A ax by cz, and which is bounded by six planes at right
angles all of whose points a/re maintained at constant temperatures determined by
the preceding equation, the quantity of heat which, during unit of time, crosses
unit of surface taken on any intermediate plane whatever perpendicular to z, is the
same as the constant flow in a solid of the same substance would be, if enclosed
between two infinite parallel planes, and for which the equation of constant tem-
peratures is v = c cz.

To prove this, let us consider in the prism, and also in the infinite solid, two
extremely near points m and /u, separated by the plane M perpendicular to the
axis of 2; M being above the plane, and m below it (see Fig. 4), and below the

m h' m'
Fig. 4

236 FOURIER CHAP. II

same plane let us take a point m' such that the perpendicular dropped from the
point M on the plane may also be perpendicular to the distance mm' at its
middle point h'. Denote by x, y, z+h, the co-ordinates of the point /*, whose
temperature is w, by a? a, y , 2, the co-ordinates of m, whose temperature
is v, and by x+a, y+P, z, the co-ordinates of ra', whose temperature is v f .
The action of m on n, or the quantity of heat which m sends to M during a
certain time, may be expressed by q(v w). The factor q depends on the dis-
tance m/jij and on the nature of the mass. The action of m' on ju will therefore
be expressed by q(v' w)', and the factor q is the same as in the preceding
expression ; hence the sum of the two actions of m on /*, and of m f on JJL, or the
quantity of heat which n receives from m and from m', is expressed by

q(vw+v' w).
Now, if the points m, v, m' belong to the prism, we have

and t/ = A

and if the same points belonged to an infinite solid, we should have, by

hypothesis,

w = cc(z+h), v = ccz, and t/ = c cz.

In the first case, we find

q(v w+v'w) = 2qch,

and, in the second case, we still have the same result. Hence the quantity of
heat which /z receives from m and from m f on the first hypothesis, when the
equation of constant temperatures is v = A -ax by cz, is equivalent to the
quantity of heat which ju receives from m and from m' when the equation of con-
stant temperatures is v = c cz.

The same conclusion might be drawn with respect to any three other points
whatever m', yt ', m", provided that the second v! be placed at equal distances
from the other two, and the altitude of the isosceles triangle m'// m" be parallel
to z. Now, the quantity of heat which crosses any plane whatever M , results
from the sum of the actions which all the points m, m', m", m" r etc., situated
on one side of this plane, exert on all the points M> M', M"> M"', etc., situated on
the other side : hence the constant flow, which, during unit of time, crosses a
definite part of the plane M in the infinite solid, is equal to the quantity of
heat which flows in the same time across the same portion of the plane M in
the prism, all of whose temperatures are expressed by the equation

v = Aax bycz.

138. COROLLARY. The flow has the value cK in the infinite solid, when the
part of the plane which it crosses has unit of surface. In the prism also it has

the same value cK or K-j-. It is proved in the same manner, that the constant

flow which takes place, during unit of time, in the same prism across unit of
surface, on any plane whatever perpendicular to y, is equal to

bKor -K^.

dy '

and that which crosses a plane perpendicular to x has the value

or -K^-.
dx

SECT. VI THEORY OF HEAT 237

139. The propositions which we have proved in the preceding articles apply
also to the case in which the instantaneous action of a molecule is exerted in
the interior of the mass up to an appreciable distance. In this case, we must
suppose that the cause which maintains the external layers of the body in the
state expressed by the linear equation, affects the mass up to a finite depth.
All observation concurs to prove that in solids and liquids the distance in
question is extremely small.

140. THEOREM III. If the temperatures at the points of a solid are expressed
by the equation v=f(x, y, z, t), in which x y y, z are the co-ordinates of a mole-
cule whose temperature is equal to v after the lapse of a time t] the flow of heat
which crosses part of a plane traced in the solid, perpendicular to one of the
three axes, is no longer constant; its value is different for different parts of the
plane, and it varies also with the time. This variable quantity may be deter-
mined by analysis.

Let co be an infinitely small circle whose centre coincides with the point m
of the solid, and whose plane is perpendicular to the vertical co-ordinate z,
during the instant dt there will flow across this circle a certain quantity of heat
which will pass from the part of the circle below the plane of the solid into the
upper part. This flow is composed of all the rays of heat which depart from a
lower point and arrive at an upper point, by crossing a point of the small
surface co. We proceed to shew that the expression of the value of the fioio is

Let us denote by #', t/', z f the co-ordinates of the point m whose temperature
is v'; and suppose all the other molecules to be referred to this point m chosen
as the origin of new axes parallel to the former axes: let , 77, f, be the three
co-ordinates of a point referred to the origin ?n; in order to express the actual
temperature w of a molecule infinitely near to m, we shall have the linear
equation

dv f . dv f . to dv'

The coefficients v', -j , -r- , -j- are the values which are found by sub-

stituting in the functions v, -7- , -T- , -j- , for the variables x, y, z, the constant

quantities x', y', z' , which measure the distances of the point m from the first
three axes of x, t/, and z.

Suppose now that the point m is also an internal molecule of a rectangular
prism, enclosed between six planes perpendicular to the three axes whose
origin is m] that w the actual temperature of each molecule of this prism,
whose dimensions are finite, is expressed by the linear equation w = A+a%
+6?7+cf, and that the six faces which bound the prism are maintained at the
fixed temperatures which the last equation assigns to them. The state of the
internal molecules will also be permanent, and a quantity of heat measured by
the expression K c wdt will flow during the instant dt across the circle co.

This arranged, if we take as the values of the constants A, a, fr, c, the quan-

tities v f , -T- , -T- , -T- , the fixed state of the prism will be expressed by the

equation w _, & & &

ax ay az

238 FOURIER CHAP. II

Thus the molecules infinitely near to the point m will have, during the
instant dt, the same actual temperature in the solid whose state is variable,
and in the prism whose state is constant. Hence the flow which exists at the
point m, during the instant dt, across the infinitely small circle w, is the same

in either solid; it is therefore expressed by K -^ udt.

From this we derive the following proposition

// in a solid whose internal temperatures vary with the time, by virtue of the
action of the molecules, we trace any straight line whatever, and erect (see Fig. 5),
at the different points of this line, the ordinates pm of a plane curve equal to the
temperatures of these points taken at the same moment; the flow of heat, at each
point p of the straight line, will be proportional to the tangent of the angle a which
the element of the curve makes with the parallel to the abscissae; that is to say, if
at the point p we place the centre of an infinitely small circle o> perpendicular

Fig. 5

to the line, the quantity of heat which has flowed during the instant dt,
across this circle, in the direction in which the abscissae op increase, will be
measured by the product of four factors, which are, the tangent of the angle a,
a constant coefficient K, the area c*> of the circle, and the duration dt of the
instant.

141. COROLLARY. If we represent by the abscissa of this curve or the dis-
tance of a point p of the straight line from a fixed point o, and by v the ordinate
which represents the temperature of the point p, v will vary with the distance e
and will be a certain f unction /(c) of that distance; the quantity of heat which
would flow across the circle o>, placed at the point p perpendicular to the line,

will be K -r &dt, or

denoting the function ,

We may express this result in the following manner, which facilitates its
application.

To obtain the actual flow of heat at a point p of a straight line drawn in a solid
whose temperatures vary by action of the molecules, we must divide the difference
of the temperatures at two points infinitely near to the point p by the distance
between these points. The flow is proportional to the quotient.

SECT, VI THEORY OF HEAT 239

142. THEOREM IV. From the preceding Theorems it is easy to deduce the
general equations of the propagation of heat.

Suppose the different points of a homogeneous solid of any form whatever, to
have received initial temperatures which vary successively by the effect of the mutual
action of the molecules, and suppose the equation v =/(#, y, z, t) to represent the
successive states of the solid, it may now be shewn that v a function of four vari-
ables necessarily satisfies the equation

dv K_ (d?v_ d?y_ d?v\
dt CD \dx 2 + dy 2 "*" dz 2 )

In fact, let us consider the movement of heat in a molecule enclosed between
six planes at right angles to the axes of x, y, and z; the first three of these
planes pass through the point m whose coordinates are x, y, z, the other three
pass through the point m', whose coordinates are x+dx, y+dy, z+dz.

During the instant dt, the molecule receives, across the lower rectangle dxdy,

which passes through the point m, a quantity of heat equal to K dxdy -3- dt.

To obtain the quantity which escapes from the molecule by the opposite face,
it is sufficient to change z into z+dz in the preceding expression, that is to say,
to add to this expression its own differential taken with respect to z only; we
then have

K dxdy-rdtK dxdy V / dz dt
az az

as the value of the quantity which escapes across the upper rectangle. The
same molecule receives also across the first rectangle dzdx which passes

through the point m, a quantity of heat equal to K-r-dzdx dt', and if we add

cty

to this expression its own differential taken with respect to y only, we find that
the quantity which escapes across the opposite face dz dx is expressed by

d \ir

K-r-dzdxdtK -~ dydzdxdt.
dy dy

Lastly, the molecule receives through the first rectangle dy dz a quantity of
heat equal to K -T- dy dz dt, and that which it loses across the opposite
rectangle which passes through m f is expressed by

-K^dydzdt-K -^-dxdydzdt.
ax ax

We must now take the sum of the quantities of heat which the molecule
receives and subtract from it the sum of those which it loses. Hence it appears
that during the instant dt, a total quantity of heat equal to

accumulates in the interior of the molecule. It remains only to obtain the
increase of temperature which must result from this addition of heat.

240 FOURIER CHAP. II

D being the density of the solid, or the weight of unit of volume, and C the
specific capacity, 01 the quantity of heat which raises the unit of weight from
the temperature to the temperature 1 ; the product CD dx dy dz expresses the
quantity of heat required to raise from to 1 the molecule whose volume is
dx dy dz. Hence dividing by this product the quantity of heat which the mole-
cule has just acquired, we shall have its increase of temperature. Thus we
obtain the general equation

~dt = CD \ch? + dy 2 + d

which is the equation of the propagation of heat in the interior of all solid bodies.

143. Independently of this equation the system of temperatures is often
subject to several definite conditions, of which no general expression can be
given, since they depend on the nature of the problem.

If the dimensions of the mass in which heat is propagated are finite, and if
the surface is maintained by some special cause in a given state; for example,
if all its points retain, by virtue of that cause, the constant temperature 0, we
shall have, denoting the unknown function v by <t> (x, y, z, ), the equation of
condition </>(#, ?/, z, t) = 0; which must be satisfied by all values of x, y, z which
belong to points of the external surface, whatever be the value of t. Further, if
we suppose the initial temperatures of the body to be expressed by the known
function F(x, y, z), we have also the equation <(#, 2/, 2, Q)=F(x, y, 2); the
condition expressed by this equation must be fulfilled by all values of the
co-ordinates x, y, z which belong to any point whatever of the solid.

144. Instead of submitting the surface of the body to a constant tempera-
ture, we may suppose the temperature not to be the same at different points
of the surface, and that it varies with the time according to a given law; which
is what takes place in the problem of terrestrial temperature. In this case the
equation relative to the surface contains the variable t.

145. In order to examine by itself, and from a very general point of view,
the problem of the propagation of heat, the solid whose initial state is given
must be supposed to have all its dimensions infinite; no special condition
disturbs then the diffusion of heat, and the law to which this principle is
submitted becomes more manifest ; it is expressed by the general equation

dv _ J{_ /d 2 v d 2 ^ dv 2 \
dt ~~ CD \dx 2 + dy 2 + dz 2 ) '

to which must be added that which relates to the initial arbitrary state of the solid.
Suppose the initial temperature of a molecule, whose co-ordinates are x, y, z,
to be a known function F(x, y, 2), and denote the unknown value v by
0(x, y> 2, t), we shall have the definite equation <f>(x, y, z, Q)=F(x, y, 2); thus
the problem is reduced to the integration of the general equation (A) in such a
manner that it may agree, when the time is zero, with the equation which
contains the arbitrary function F.

SECTION VII. General Equation Relative to the Surface

146. If the solid has a definite form, and if its original heat is dispersed grad-
ually into atmospheric air maintained at a constant temperature, a third
condition relative to the state of the surface must be added to the general
equation (A) and to that which represents the initial state.

SECT. VII THEORY OF HEAT 241

We proceed to examine, in the following articles, the nature of the equation
which expresses this third condition.

Consider the variable state of a solid whose heat is dispersed into air, main-
tained at the fixed temperature 0. Let w be an infinitely small part of the
external surface, and M a point of w, through which a normal to the surface is
drawn; different points of this line have at the same instant different tempera-
tures.

Let v be the actual temperature of the point M, taken at a definite instant,
and w the corresponding temperature of a point v of the solid taken on the
normal, and distant from /* by an infinitely small quantity a. Denote by x, y :
z the co-ordinates of the point M> and those of the point v by x+dx, y+dy,
z+dz; let f(x, y, z) =0 be the known equation to the surface of the solid, and
t> = </>(x, y, z, t) the general equation which ought to give the value of v as a
function of the four variables x, y, z, t. Differentiating the equation f(x, y, z)
= 0, we shall have

mdx+ndy -\-pdz = ;

m, n, p being functions of x, y, z.

It follows from the corollary enunciated in Article 141, that the flow in
direction of the normal, or the quantity of heat which during the instant dt
would cross the surface w, if it were placed at any point whatever of this line,
at right angles to its direction, is proportional to the quotient which is obtained
by dividing the difference of temperature of two points infinitely near by their
distance. Hence the expression for the flow at the end of the normal is

.fiT - -udt:
a.

K denoting the specific conducibility of the mass. On the other hand, the sur-
face w permits a quantity of heat to escape into the air, during the time dt,
equal to hv&dt; h being the conductivity relative to atmospheric air. Thus the
flow of heat at the end of the normal has two different expressions, that is to
say:

hvvdt and K udt:

hence these two quantities are equal; and it is by the expression of this equal-
ity that the condition relative to the surface is introduced into the analysis.
147. We have

dv dv dv

w = v-\-dv = v-\ r-dx-] 7- oy-\ 7- dz.
dx dy dz

Now it follows from the principles of geometry, that the co-ordinates dx, dy,
dz, which fix the position of the point v of the normal relative to the point /A
satisfy the following conditions :

pdx = mdz, pdy = ndz.
We have therefore

w
we have also

1 / dv dv . dv\

v- I m -3 hft -5 hp-j- I

p\ dx dy ^ dz)

242 FOURIER CHAP. II

or ot -dz, denoting by q the quantity (m 2 +n 2 +p 2 ) 1 ,

, w~ v / "dv , dv . dv\ 1

hence - = I m -7- +^ -y- +p -y- I - ;

a \ cte d|/ ^ dz/ g

consequently the equation

becomes the following :

dv . dv , dv . h

This equation is definite and applies only to points at the surface ; it is that
which must be added to the general equation of the propagation of heat (A),
and to the condition which determines the initial state of the solid; m, n, p> q>
are known functions of the co-ordinates of the points on the surface.

148. The equation (B) signifies in general that the decrease of the tempera-
ture, in the direction of the normal, at the boundary of the solid, is such that
the quantity of heat which tends to escape by virtue of the action of the mole-
cules, is equivalent always to that which the body must lose in the medium.

The mass of the solid might be imagined to be prolonged, in such a manner
that the surface, instead of being exposed to the air, belonged at the same time
to the body which it bounds, and to the mass of a solid envelope which con-
tained it. If, on this hypothesis, any cause whatever regulated at every instant
the decrease of the temperatures in the solid envelope, and determined it in
such a manner that the condition expressed by the equation (B) was always
satisfied, the action of the envelope would take the place of that of the air, and
the movement of heat would be the same in either case : we can suppose then
that this cause exists, and determine on this hypothesis the variable state of
the solid; which is what is done in the employment of the two equations (A)
and (B).

By this it is seen how the interruption of the mass and the action of the
medium, disturb the diffusion of heat by submitting it to an accidental condi-
tion.

149. We may also consider the equation (B), which relates to the state pf the
surface, under another point of view: but we must first derive a remarkable
consequence from Theorem III. (Art. 140). We retain the construction re-
ferred to in the corollary of the same theorem (Art. 141). Let x, y, z be the
co-ordinates of the point p, and

x+8x, y+dy, z+dz

those of a point q infinitely near to p, and taken on the straight line in ques-
tion : if we denote by v and w the temperatures of the two points p and q taken
at the same instant, we have

dv - , dv _ , dv .

v+ - Sx+ - Sy+ - Sz .

hence the quotient

dv dv 3x . dv dy , dv 8z .

7- = ;r 7~ + T" * + T~ r > and fe=

oc ax 06 ay de dz 3e

SECT. VII THEORY OF HEAT 243

thus the quantity of heat which flows across the surface w placed at the point
p, perpendicular to the straight line, is

TJT jAdv 8x . dv dy . dv &z\
A coat < j- -r r ~r~" 7 r~ T~ r '
\dx de dy de dz 8e)

The first term is the product of K-j-bydt and by co . The latter quan-
tity is, according to the principles of geometry, the area of the projection of w
on the plane of y and z; thus the product represents the quantity of heat which
would flow across the area of the projection, if it were placed at the point p
perpendicular to the axis of x.

The second term K -y- w ~- dt represents the quantity of heat which would

cross the projection of co, made on the plane of x and z, if this projection were
placed parallel to itself at the point p.

Lastly, the third term K-r u-r-dt represents the quantity of heat which

would flow during the instant dt, across the projection of a; on the plane of x
and y> if this projection were placed at the point p, perpendicular to the co-
ordinate z.

By this it is seen that the quantity of heat which flows across every infinitely
small part of a surface drawn in the interior of the solid, can always be decomposed
into three other quantities of flow, which penetrate the three orthogonal projections
of the surface, along the directions perpendicular to the planes of the projections.
The result gives rise to properties analogous to those which have been noticed
in the theory of forces.

150. The quantity of heat which flows across a plane surface w, infinitely
small, given in form and position, being equivalent to that which would cross
its three orthogonal projections, it follows that, if in the interior of the solid
an element be imagined of any form whatever, the quantities of heat which
pass into this polyhedron by its different faces, compensate each other recipro-
cally : or more exa'ctly, the sum of the terms of the first order, which enter into
the expression of the quantities of heat received by the molecule, is zero; so
that the heat which is in fact accumulated in it, and makes its temperature
vary, cannot be expressed except by terms infinitely smaller than those of the
first order.

This result is distinctly seen when the general equation (A) has been estab-
lished, by considering the movement of heat in a prismatic molecule (Articles
127 and 142); the demonstration may be extended to a molecule of any form
whatever, by substituting for the heat received through each face, that which
its three projections would receive.

In other respects it is necessary that this should be so: for, if one of the
molecules of the solid acquired during each instant a quantity of heat expressed
by a term of the first order, the variation of its temperature would be infinitely
greater than that of other molecules, that is to say, during each infinitely small
instant its temperature would increase or decrease by a finite quantity, which
is contrary to experience.

151. We proceed to apply this remark to a molecule situated at the external
surface of the solid.

244 FOURIER CHAP. II

Through a point a (see Fig. 6), taken on the plane of x and t/, draw two planes
perpendicular, one to the axis of x the other to the axis of y. Through a point 6
of the same plane, infinitely near to a, draw two other planes parallel to the
two preceding planes; the ordinates z, raised at the points a, 6, c, d, up to the

Fig. 6

external surface of the solid, will mark on this surface four points a', 6', c', d',
and will be the edges of a truncated prism, whose base is the rectangle abed. If
through the point of which denotes the least elevated of the four points a', &',
c', d', a plane be drawn parallel to that of x and y, it will cut off from the trun-
cated prism a molecule, one of whose faces, that is to say a'b'c'd* ', coincides
with the surface of the solid. The values of the four ordinates aa', cc', dd', bb'
are the following :

T,, dz , dz j

bb' = z+ -j- dx+ -j- dy.
ax ay

152, One of the faces perpendicular to x is a triangle, and the opposite face
is a trapezium. The area of the triangle is

dz j

and the flow of heat in the direction perpendicular to this surface being
K-- we have, omitting the factor dt

as the expression of the quantity of heat which in one instant passes into the
molecule, across the triangle in question.
The area of the opposite face is

u fdz j , dz , dz , \

* dy \Tx dx+ Tx dx+ Ty dy )>

and the flow perpendicular to this face is also K-r-, suppressing terms of the

SECT. VII THEORY OF HEAT 245

second order infinitely smaller than those of the first; subtracting the quantity
of heat which escapes by the second face from that which enters by the first
we find

dv dz , ,

K Txdx dxdy -

This term expresses the quantity of heat the molecule receives through the
faces perpendicular to x.

It will be found, by a similar process, that the same molecule receives,

through the faces perpendicular to y, a quantity of heat equal to K -y- -r dx dy.

&y dy

The quantity of heat which the molecule receives through the rectangular
base is K-rdx dy. Lastly, across the upper surface a'b'c'd', a certain quan-

tity of heat is permitted to escape, equal to the product of hv into the extent <o
of that surface. The value of cu is, according to known principles, the same as

that of dx dy multiplied by the ratio - ; e denoting the length of the normal
between the external surface and the plane of x and y, and

hence the molecule loses across its surface a'Vc'd' a quantity of heat equal to
hv dx dy - .

Now, the terms of the first order which enter into the expression of the total
quantity of heat acquired by the molecule, must cancel each other, iri order
that the variation of temperature may not be at each instant a finite quantity;
we must then have the equation

dv dz , .. . dv dz , , dv
te dx dxdy+ dy ^dxdy- Tz

IL e dv dz dv dz dv
K z dx dx dy dy dz

153. Substituting for -r- and -7- their values derived from the equation

mdx + ndy + pdz = 0,
and denoting by q the quantity

we have

dv , dv . dv
die +n Ty +P dz

r , , . \

K m +n +P )

thus we know distinctly what is represented by each of the terms of this
equation.

Taking them all with contrary signs and multiplying them by dx dy y the first
expresses how much heat the molecule receives through the two faces perpen-
dicular to x, the second how much it receives through its two faces perpen-

246 FOURIER CHAP. II

dioular to y, the third how much it receives through the face perpendicular to
3, and the fourth how much it receives from the medium. The equation there-
fore expresses that the sum of all the terms of the first order is zero, and that
the heat acquired cannot be represented except by terms of the second order.

154. To arrive at equation (B), we in fact consider one of the molecules
whose base is in the surface of the solid, as a vessel which receives or loses heat
through its different faces. The equation signifies that all the terms of the first
order which enter into the expression of the heat acquired cancel each other;
so that the gain of heat cannot be expressed except by terms of the second
order. We may give to the molecule the form, either of a right prism whose axis
is normal to the surface of the solid, or that of a truncated prism, or any form
whatever.

The general equation (A), (Art. 142) supposes that all the terms of the first
order cancel each other in the interior of the mass, which is evident for pris-
matic molecules enclosed in the solid. The equation (B), (Art. 147) expresses
the same result for molecules situated at the boundaries of bodies.

Such are the general points of view from which we may look at this part of
the theory of heat.

* dv K /d*v . d*v . d*v\ . ,, , .

The equation j- = -^ I -7-5 + jri + jrs ) represents the movement of heat

in the interior of bodies. It enables us to ascertain the distribution from instant
to instant in all substances solid or liquid ; from it we may derive the equation
which belongs to each particular case.

In the two following articles we shall make this application to the problem
of the cylinder, and to that of the sphere.

SECTION VIII. Application of the General Equations

155. Let us denote the variable radius of any cylindrical envelope by r, and
suppose, as formerly, in Article 118, that all the molecules equally distant from
the axis have at each instant a common temperature; v will be a function of r
and t' y r is a function of y y z, given by the equation r 2 = y 2 +z 2 . It is evident in

the first place that the variation of v with respect to x is nul; thus the term -7-5

must be omitted. We shall have then, according to the principles of the differ-
ential calculus, the equations

dv __ dv dr d*v _ d*v (dr\ dv /dV\

dy ~ dr dy and dy 2 ~ dr 2 \dy) + dr \dy 2 ) '

dv __ dv dr d?v _ d 2 ^ (dr\ dv /d 2 r

dz ~~ dr dz and dz 2 " dr 2 dz + dr

whence

d*v d*v _ d*v f/drV /drV\ , dv /d*r d*r
dtf + dz 2 - dr~* \\dyj + \Tz) / + dr \dtf + d

In the second member of the equation, the quantities

dr dr d*r dV
dy 9 dz 9 dy 2 ' dz* '

SECT. VIII THEORY OF HEAT 247

must be replaced by their respective values; for which purpose we derive from
the equation

dr _ , /dr\ 2 . d 2 r
y = r -T- and 1= I -T- I +r -J-T ,
dy \dyj dy 2 '

dr A 1 fdr\, d*r
z = r -T- and 1 = I -j- 1 +r 3-5 >
dz \dz/ dz 2 '

and consequently

__ , , ,

w + w +r \^ + a?/

The first equation, whose first member is equal to r 2 , gives

the second gives, when we substitute for
its value 1,

dz 2 r '

If the values given by equations (6) and (c) be now substituted in (a), we
have

d^v.cPvdfv.l dv
~dy* + dz 2 ~ dr 2 + r dr *

Hence the equation which expresses the movement of heat in the cylinder, is

*!? j. 1 *!

dr 2 + r dr

as was found formerly, Art. 119.

We might also suppose that particles equally distant from the centre have
not received a common initial temperature; in this case we should arrive at a
much more general equation.

156. To determine, by means of equation (A), the movement of heat in a
sphere which has been immersed in a liquid, we shall regard v as a function of
r and t] r is a function of x, y, z, given by the equation

r being the variable radius of an envelope. We have then

dv _ dv dr jd 2 ^^^ /dr\ 2 _, dv dV
dx ~ dr dx an(1 dz 2 ~ dr 2 \dx) + dr dx* '

dv _ dv dr .d^^d 2 ^ /dr\ 2 , dv
dy "" dr dy aml dy 2 ~ dr 2 \dy) + dr

248 FOURIER CHAP. II

^_ A d 2v f^!\ 2 i ^ d* T

"dz ~ dr ~dz ancl dz 2 ~~ d7 2 \^5/ + dr 5F 2 *
Making these substitutions in the equation

dv = _K_ {d? , d^; d 2 ^)
dt CD Idz 2 + dy 2 + d2 2 J f

we shall have

dv K_ rd 2 v (/dr\ 2 , /dr\ 2 , /dr\ 2 l , dv (d 2 r , d 2 r
dt ~~ CD

(dr\\ dv
\dz) ] + Tr

The equation x*+y 2 +z 2 = r 2 gives the following results:

dr , , (dr\ , cPr
x = r -j- and 1 = 1 3- I +r ~r- 9 ,
dx \dx/ dx 2 '

dr . t fdr\ , d 2 r
y = r -r- and 1 = ( -r- 1 +r ^-^ ,
% \rft// dy 2>

dr , , /dr\ 2 . d*r
z = r -7- and 1 = I -5- I +r -7-^ .
d-e \d^/ dz 2

The three equations of the first order give :

The three equations of the second order give :

dr\ fdr\ (dr\ (d*r d*r d*r\

dlc) + V*// + W W 2 W d^) :

and substituting for

/drV /drV /

Vrfxy + Vw \

its value 1, we have

dV dV dV = 2

dx 2 + dy 2 ~*~ dz 2 r '

Making these substitutions in the equation (a) we have the equation

dv K (d 2 v 2 dv\
dt CD (dr 2 ^ r dr} '

which is the same as that of Art. 114.

The equation would contain a greater number of terms, if we supposed
molecules equally distant from the centre not to have received the same initial
temperature.

We might also deduce from the definite equation (B), the equations which
express the state of the surface in particular cases, in which we suppose solids
of given form to communicate their heat to the atmospheric air; but in most
cases these equations present themselves at once, and their form is very
simple, when the co-ordinates are suitably chosen.

SECT. IX THEORY OF HEAT 249

SECTION IX. General Remarks

157. The investigation of the laws of movement of heat in solids now consists
in the integration of the equations which we have constructed; this is the
object of the following chapters. We conclude this chapter with general re-
marks on the nature of the quantities which enter into our analysis.

In order to measure these quantities and express them numerically, they
must be compared with different kinds of units, five in number, namely, the
unit of length, the unit of time, that of temperature, that of weight, and finally
the unit which serves to measure quantities of heat. For the last unit, we might
have chosen the quantity of heat which raises a given volume of a certain
substance from the temperature to the temperature 1. The choice of this
unit would have been preferable in many respects to that of the quantity of
heat required to convert a mass of ice of a given weight, into an equal mass of
water at 0, without raising its temperature. We have adopted the last unit
only because it had been in a manner fixed beforehand in several works on
physics; besides this supposition would introduce no change into the results of
analysis.

158. The specific elements which in every body determine the measurable
effects of heat are three in number, namely, the conductivity proper to the
body, the conductivity relative to the atmospheric air, and the capacity for
heat. The numbers which express these quantities are, like the specific
gravity, so many natural characters proper to different substances.

We have already remarked, Art. 36, that the conductivity of the surface
would be measured in a more exact manner, if we had sufficient observations
on the effects of radiant heat in spaces deprived of air.

It may be seen, as has been mentioned in the first section of Chapter I, Art.
11, that only three specific coefficients, K, h, C, enter into the investigation;
they must be determined by observation; and we shall point out in the sequel
the experiments adapted to make them known with precision.

159. The number C which enters into the analysis, is always multiplied by
the density Z), that is to say, by the number of units of weight which are equiv-
alent to the weight of unit of volume; thus the product CD may be replaced by
the coefficient c. In this case we must understand by the specific capacity for
heat, the quantity required to raise from temperature to temperature 1 unit
of volume of a given substance, and not unit of weight of that substance.

With the view of not departing from the common definition, we have re-
ferred the capacity for heat to the weight and not to the volume; but it would
be preferable to employ the coefficient c which we have just defined; magni-
tudes measured by the unit of weight would not then enter into the analytical
expressions: we should have to consider only, 1st, the linear dimension x, the
temperature v, and the time t\ 2nd, the coefficients c, h, and K. The three first
quantities are undetermined, and the three others are, for each substance,
constant elements which experiment determines. As to the unit of surface and
the unit of volume, they are not absolute, but depend on the unit of length.

160. It must now be remarked that every undetermined magnitude or
constant has one dimension proper to itself, and that the terms of one and the
same equation could not be compared, if they had not the same exponent of
dimension. We have introduced this consideration into the theory of heat, in
order to make our definitions more exact, and to serve to verify the analysis*

250 FOURIER CHAP. II

it is derived from primary notions on quantities; for which reason, in geometry
and mechanics, it is the equivalent of the fundamental lemmas which the
Greeks have left us without proof.

161. In the analytical theory of heat, every equation (E) expresses a neces-
sary relation between the existing magnitudes x, t, v, c, h, K. This relation
depends in no respect on the choice of the unit of length, which from its very
nature is contingent, that is to say, if we took a different unit to measure the
linear dimensions, the equation (E) would still be the same. Suppose then the
unit of length to be changed, and its second value to be equal to the first
divided by m. Any quantity whatever x which in the equation (E) represents a
certain line a&, and which, consequently, denotes a certain number of times
the unit of length, becomes mx y corresponding to the same length ab; the value
t of the time, and the value v of the temperature will not be changed; the same

is not the case with the specific elements h,K,c: the first, h y becomes -5 ; for it

expresses the quantity of heat which escapes, during the unit of time, from the
unit of surface at the temperature 1. If we examine attentively the nature of
the coefficient K, as we have defined it in Articles 68 and 135, we perceive that

it becomes ; for the flow of heat varies directly as the area of the surface, and

iiL

inversely as the distance between two infinite planes (Art. 72). As to the co-
efficient c which represents the product CD, it also depends on the unit of

^
length and becomes 5 ; hence equation (E) must undergo no change when we

write mx instead of x, and at the same time , ^ , ^ , instead of K,h, c; the

' m ' m 2 ' m 3 > > >

number m disappears after these substitutions: thus the dimension of x with
respect to the unit of length is 1, that of K is 1, that of h is 2, and that of t
is 3. If we attribute to each quantity its own exponent o/ dimension, the
equation will be homogeneous, since every term will have the same total
exponent. Numbers such as S, which represent surfaces or solids, are of two
dimensions in the first case, and of three dimensions in the second. Angles,
sines, and other trigonometrical functions, logarithms or exponents of powers,
are, according to the principles of analysis, absolute numbers which do not
change with the unit of length; their dimensions must therefore be taken equal
to 0, which is the dimension of all abstract numbers.

If the unit of time, which was at first 1, becomes - , the number t will become

' n '

nt, and the numbers x and v will not change. The coefficients K, h. c will be-

JC 7i

come , - , c. Thus the dimensions of x t t } v with respect to the unit of time are
i\ n>

0, 1, 0, and those of K, h, c are 1, 1, 0.

If the unit of temperature be changed, so that the temperature 1 becomes
that which corresponds to an effect other than the boiling of water; and if that
effect requires a less temperature, which is to that of boiling water in the ratio
of 1 to the number p; v will become vp, x and t will keep their values, and the

coefficients K . h , c will become , -. -.

P'PP

The following table indicates the dimensions of the three undetermihed
quantities and the three constants, with respect to each kind of unit.

SECT. IX THEORY OF HEAT 251

Quantity or Constant Length Duration Temperature

Exponent of dimension of x

t( a a ft *

it tt tt tt ..

The specific conducibility, K

-1

The surface conducibility, h

-2

-1

The canacitv for heat. c

-1

162. If we retained the coefficients C and Z), whose product has been
represented by c, we should have to consider the unit of weight, and we should
find that the exponent of dimension, with respect to the unit of length, is 3
for the density Z), and for C.

On applying the preceding rule to the different equations and their trans-
formations, it will be found that they are homogeneous with respect to each
kind of unit, and that the dimension of every angular or exponential quantity
is nothing. If this were not the case, some error must have been committed in
the analysis, or abridged expressions must have been introduced.

If, for example, we take equation (6) of Art. 105,

dv J<_ d?v _ hi
dt " CD dx* CDS V '

we find that, with respect to the unit of length, the dimension of each of the
three terms is 0; it is 1 for the unit of temperature, and 1 for the unit of time.

In the equation v = Ae~ x '\/m of Art. 76, the linear dimension of each term

/o~jT

is 0, and it is evident that the dimension of the exponent x\-f7j is always noth-
ing, whatever be the units of length, time, or temperature.

EXPERIMENTAL RESEARCHES
IN ELECTRICITY

BIOGRAPHICAL NOTE

MICHAEL FARADAY, 1791-1867

FARADAY was born September 22, 1791, in
Newington, Surrey, the son of a blacksmith.
When he was five, the family moved to Lon-
don, and he grew up in such poverty that, as
he later recalled, the loaf of bread his mother
gave him had to last a week. "My education/'
he wrote, "was of the most ordinary descrip-
tion, consisting of little more than the rudi-
ments of reading, writing, and arithmetic at a
common day school. My hours out of school
were passed at home and in the streets."

At the age of twelve he became an errand-
boy for a bookseller and bookbinder, and a year
later he was accepted because of exemplary
conduct as an apprentice without fee. His sci-
entific education began while he was engaged
in binding books. As he later wrote to a friend:
"It was in those books, in the hours after work,
that I found the beginning of my philosophy.
There were two that especially helped me, the
Encyclopaedia Britannica, from which I gained
my first notions of electricity, and Mrs. Mar-
cet's Conversations on Chemistry, which gave
me my foundation in that science." With what
money he could spare he bought materials for
experiments, and by 1812 was conducting in-
vestigations in electrolytic decomposition. In
the spring of that year, through the generosity
of a customer, he was able to attend a series of
four lectures by Sir Humphry Davy at the
Royal Institution. He took careful notes, wrote
them out in fuller form, and bound them into
a book. He sent the notes to Davy with a re-
quest for employment at the Royal Institution
in any capacity connected with science. Davy
advised him not to give up a skilled trade for
something in which there was neither security,
money, nor opportunity for advancement, but
a few months later, on the dismissal of a lab-
oratory assistant, he offered the post to Fara-
day. He became Davy's assistant in March,
1813, and in October of that year accompanied
him on a tour of the universities and labora-
tories of France, Italy, and Switzerland, which
lasted until April, 1815.

Upon his return to England and the Institu-

tion, Faraday continued as Davy's assistant
and began research of his own. In 1816 he made
his first contribution in the form of an analysis
of caustic lime from Tuscany, which was pub-
lished in the Quarterly Journal of Science. From
that time he wrote an increasing number of
notes and memoirs. In 1821 he began work
upon electro magnetism ; he first collected and
repeated all the known experiments, published
an account of them in the Annals of Philoso-
phy, and proceeded to make his own investiga-
tions. His experiments were meticulously re-
corded in numbered paragraphs, and in 1831
he started the first section of his Experimental
Researches in Electricity y which was to occupy
him intermittently for the next twenty-three
years. First published in the form of mono-
graphs in the "Transactions of the Royal So-
ciety," they were later brought out in three
volumes (1844, 1847, 1855).

Faraday was occupied during these years
with many things in addition to research in
electricity. Pursuing the chemical investiga-
tions he had begun as Davy's assistant, he
made a special study of chlorine, discovered
two new chlorides of carbon, initiated experi-
ments on the diffusion of gases, and was among
the first to succeed in their liquefaction. Many
of his discoveries had industrial applications,
some of which he investigated, such as the al-
loys of steel and the manufacture of glass. He
was also called upon to act as a consultant on
many works of public concern, and for thirty
years he was adviser to Trinity House on the
supervision of the lighthouses of England. In
1823 he was elected to the Royal Society over
Davy's strong opposition, which, however, Far-
aday did not permit to interfere with their
friendship. In 1833 he was made the Fullerian
professor of chemistry for life, and although he
was not obliged to lecture, he frequently did so
in order to increase the stability and influence
of the Institution. His celebrated Chemical His-
tory of a Candle was one of the series of Christ-
mas lectures for children which he had started
at the Institution. He received honorary de-

255

256

BIOGRAPHICAL NOTE

grees and scientific tributes from all parts of
the world, and both the Royal Society and the
Royal Institution tried in vain to persuade him
to accept the presidency. As he told his friend
Tyndali in refusing the Royal Society's offer,
"I must remain plain Michael Faraday to the
last."

After he had become famous for his discov-
eries, Faraday's services were eagerly sought
by industry and commerce. For a few years he
did a little "professional business," as he called
it, and in 1830 received more than a thousand
pounds in return. It is estimated that this work
might easily have yielded five thousand pounds
in 1832, but he then felt, as he later told Tyn-
dali, that he had to decide whether to make
wealth or science the pursuit of his life. He
chose science and lived and died a poor man.

Faraday married in 1821, "an event," he
wrote, "which more than any other contributed
to my earthly happiness and healthful state of
mind." The marriage was childless, but Fara-
day's lodgings in the Royal Institution were
always full of his wife's nieces and nephews, for
he enjoyed the company of children and liked

to take part in their games. Faraday's parents
belonged to the small dissident Presbyterian
sect known as Sandemanians, and Faraday
himself attended their meetings from child-
hood; he made a formal declaration of faith at
thirty and for two different periods discharged
the office of elder.

Faraday's last years were spent in seriously
declining health. As early as 1841, as a result
of overwork, he had suffered a serious break-
down and was compelled to take a complete
rest for a period of several years. Although he
was back in the laboratory by 1845 and for fif-
teen years engaged in some of his most impor-
tant research, his health was never completely
restored. When at length he found his memory
failing and his powers declining, he yielded to
others whatever parts of his work he could no
longer accomplish according to his own stand-
ard of efficiency. Queen Victoria, in 1858, pro-
vided him with a house at Hampton Court
which had rooms so arranged that he had no
stairs to climb. In 1862 he delivered his last
lecture and performed his last experiment. He
died August 25, 1867.

CONTENTS

BIOGRAPHICAL NOTE, 255; PREFACES TO VOLUMES I, II and III, 261

SERIES PAR.

I. I. On the Induction of Electric Currents 6
5 2. On the Evolution of Electricity

from Magnetism 27

3. New Electrical State or Con-
dition of Matter 60
{ 4. Explication of Arago's Magnetic

Phenomena 81

II. { 6. Terrestrial Magneto-electric

Induction 140

6. General Remarks and Illustra-
tions of the Force and Direc-
tion of Magneto-electric
Induction 193

III. 5 7. Identity of Electricities Derived

from Different Sources 265

I. Voltaic Electricity 268

II. Ordinary Electricity 284

III. Magneto-electricity 343

IV. Thermo-electricity 349
V. Animal Electricity 351

8. Relation by Measure of Common

and Voltaic Electricity 361

IV. ( 9. On a New Law of Electric

Conduction 380

10. On Conducting Power

Generally 418

V. 11. On Electro-chemical Decom-
position 450

f i. New Conditions of Electro-
chemical Decomposition 453

*J ii. Influence of Water in
Electro-chemical Decomposition 472

1f iii. Theory of Electro-chem-
ical Decomposition 477
VI. 12. On the Power of Metals and
Other Solids to Induce the
Combination of Gaseous
Bodies 564
VII. Jll. On Electro-chemical Decom-
position, continued 661

% iv. On Some General Condi-
tions of Electro-chemical
Decomposition 669

^ v. On a New Measurer of

Volta-electridty 704

f vi. On the Primary or
Secondary Character of the
Bodies Evolved at the
Electrodes 742

1T vii. On the Definite Nature
and Extent of Electro-
chemical Decompositions 783
{ 13., On the Absolute Quantity of
Electricity Associated with
the Particles or Atoms of
Matter 852

SERIES PAR.

VIII. 5 14. On the Electricity of the Voltaic
Pile; its Source, Quantity,
Intensity and General
Characters 875

If i. On Simple Voltaic

Circles 875

If ii. On the Intensity

Necessary for Electrolyzalion 966
U iii. On Associated Voltaic

Circles, or the Voltaic Battery 989
If iv. On the Resistance of an
Electrolyte to Electrolytic
Action, and on Interpositions 1007
1f v. General Remarks on the

Active Voltaic Battery 1034

IX. 15. On the Influence by Induction

of an Electric Current on itself:
and on the Inductive Action
of Electric Currents
Generally 1048

X. 16. On an Improved Form of the

Voltaic Battery 1119

17. Some Practical Results Respect-
ing the Construction and Use
of the Voltaic Battery 1136

XI. 18. On Induction 1161

1f i. Induction an Action

of Contiguous Particles 1161

1f ii. On the Absolute Charge

of Matter 1169

f iii. Electrometer and In-
ductive Apparatus Employed 1179
Tf iv. Induction in Curved

Lines 1215

If v. On Specific Induction,
or Specific Inductive
Capacity 1252

1f vi. General Results as to
Induction 1295

Supplementary Note 1307

XII. If vii. Conduction, or Con-

ductive Discharge 1320

f viii. Electrolytic Discharge 1343
1f ix. Disruptive Discharge
Insulation Spark Brush
Difference of Discharge at the
Positive and Negative Surfaces
of Conductors 1359

Disruptive Discharge
and Insulation 1359

The Electric Spark or
Flash . 1406

The Electric Brush 1425

Difference of Discharge
at the Positive and Negative
Conducting Surfaces 1465

257

XXI.

258 FARADAY

SERIES PAR. SERIES

XIII. U ix. Disruptive Discharge XX.

(continued) Peculiarities of
Positive and Negative Dis-
charge either as Spark or
Brush Glow Discharge
Dark Discharge 1480

Glow Discharge 1526

Dark Discharge 1544

If x. Convection, or Carrying

Discharge 1662

1f xi. Relation of a Vacuum

to Electrical Phenomena 1613

19. Nature of the Electrical

Current 1617

XIV. 20. Nature of the Electric Force

or Forces 1667

21. Relation of the Electric and

Magnetic Forces 1709

22. Note on Electrical Excitation 1737
XV. 5 23. Notice of the Character and Di-
rection of the Electric Force
of the Gymnotus 1749

XVI. 24. On the Source of Power in the

Voltaic Pile 1796

H i. Exciting Electrolytes,
<fcc., Being Conductors of
Thermo and Feeble
Currents 1812

1f ii. Inactive Conducting
Circles Containing a Fluid
or Electrolyte 1823

f iii. Active Circles Excited
by Solution of Sulphuret of
Potassium, &c. 1877

XVII. f iv. The Exciting Chemical

Force Affected by Tem-
perature 1913 XXIII

Cases of One Metal
and One Electrolyte; One
Junction Being Heated 1942

Cases of Two Metals
and One Electrolyte; One
Junction Being Heated 1960

1 v. The Exciting Chemical

Force Affected by Dilution 1969
Tf vi. Differences in the order
of the Metallic Elements of
Voltaic Circles 2010

f vii. Active Voltaic Circles
and Batteries without Metal-
lic Contact 2017
1f viii. Considerations of the
Sufficiency of Chemical
Action 2029
1f ix. Thermo-electric

Evidence 2054

1f x. Improbable Nature of

the Assumed Contact Force 2065
XVIII. 5 25. On the Electricity Evolved by
the Friction of Water and
Steam against Other Bodies 2075
XIX. 26. On the Magnetization of Light
and the Illumination of
Magnetic Lines of Force 2146

1f i. Action of Magnets on

Light 2146

1f ii. Action of Electric Cur-
rent* on Light 2189
1f iii. General Considerations 2221

5 27. On New Magnetic Actions, and
on the Magnetic Condition of

PAR.

all Matter 2243

i. Apparatus Required 2245
ii. Action of Magnets on
Heavy Glass 2253

iii. Action of Magnets on
Other Substances Acting
Magnetically on Light 2275

iv. Action of Magnets on
Metals Generally 2287

v. Action of Magnets on
the Magnetic Metals and
their Compounds 2343

1f vi. Action of Magnets on
Air and Gases 2400

f vii. General Considera-

tions 2417

XXII. 28. On the Crystalline Polarity of
Bismuth (and Other Bodies) ,
and on its Relation' to the
Magnetic Form of Force 2454

11 i. Crystalline Polarity
of Bismuth 2457

1f ii. Crystalline Polarity
of Antimony 2508

If iii. Crystalline Polarity

of Arsenic 2532

1f iv. Crystalline Condition
of Various Bodies 2535

Tf v. Nature of the Magne-
crystallic Force, and General
Observations 2550

1f vi. On the Position of a
Crystal of Sulphate of Iron
in the Magnetic Field 2615

29. On the Polar or Other

Condition of Diamagnetic
Bodies 2640

30. On the Possible Relation of

Gravity to Electricity 2702

31. On the Magnetic and

diamagnetic Condition of

Bodies 2718

1f i. Non-expansion of
Gaseous Bodies by Magnetic
Force 2718

f ii. Differential Magnetic
Action 2757

^ iii. Magnetic Characters of
Oxygen, Nitrogen , and
Space 2770

XXVI. 32. Magnetic Conducting Power 2797

f i. Magnetic Conduction 2797

If ii. Conduction Polarity 2818

1f iii. Magnecrystallic Con-

duction 2836

33. Atmospheric Magnetism 2847

If i. General Principles 2847

f ii. Experimental Inquiry
into the Laws of Atmospheric
Magnetic Action,' and their
Application to Particular
Cases 2969

i 34. On Lines of Magnetic Force;
their Definite Character;
and their Distribution
within a Magnet and through
Space 3070

XXIV.
XXV.

XXVII.

xxvni.

CONTENTS

259

SERIES PAR.

XXIX. 35. On the Employment of the
Induced Magneto-electric
Current as a Test and
Measure of Magnetic
Forces 3177

1[ i. Galvanometer 3178

^f ii. Revolving Rectangles

and Rings 3192

36. On the Amount and General

Disposition of the Forces of a
Magnet when Associated with
Other Magnets 3215

37. Delineation of Lines of
Magnetic Force by Iron
Filings 3234

PAPERS

PAGE
On Some New Electro- mag netical Motions, and

on the Theory of Magnetism 795
Electro-magnetic Rotation Apparatus 807
Description of an Electro-mag netical Appara-
tus for the Exhibition of Rotary Motion 807
Note on New Electro-magnetical Motions 809
Effect of Cold on Magnetic Needles 812

PAGE

Electro-magnetic Current (under the Influence of

a Magnet) 812
Electric Powers (and Place) of Oxalate of Lime 813
On the General Magnetic Relations and Charac-
ters of the Metals 813
On the General Magnetic Relations and Charac-
ters of the Metals: Additional Facts 815
On the Physical Lines of Magnetic Force . 816
Observations on the Magnetic Force 819
On Electric Induction Associated Cases of

Current and Static Effects 824

On Some Points of Magnetic Philosophy 830

Magnetic Polarity 832

Media 834

Time 836

Curved Lines of Magnetic Force 837

Places of No Magnetic Action 842

The Moving Conductor 845

LETTERS

On Static Electrical Inductive Action 848
A Speculation^ Touching Electric Conduction and

the Nature of Matter 850
On the Diamagnetic Conditions of Flame and

Gases 855

INDEX, p. 867

PREFACES FROM ORIGINAL THREE-VOLUME EDITION

Preface to Volume I

I HAVE been induced by various circumstances to collect in one volume the
Fourteen Series of Experimental Researches in Electricity, which have appeared
in the Philosophical Transactions during the last seven years : the chief reason
has been the desire to supply at a moderate price the whole of these papers,
with an index, to those who may desire to have them.

The readers of the volume will, I hope, do me the justice to remember that
it was not written as a whole, but in parts; the earlier portions rarely having
any known relation at the time to those which might follow. If I had rewritten
the work, I perhaps might have considerably varied the form, but should not
have altered much of the real matter: it would not, however, then have been
considered a faithful reprint or statement of the course and results of the whole
investigation, which only I desired to supply.

I may be allowed to express my great satisfaction at finding, that the differ-
ent parts, written at intervals during seven years, harmonize so well as they do.
There would have been nothing particular in this, if the parts had related only
to matters well-ascertained before any of them were written: but as each
professes to contain something of original discovery, or of correction of re-
ceived views, it does surprise even my partiality, that they should have the
degree of consistency and apparent general accuracy which they seem to me
to present.

I have made some alterations in the text, but they have been altogether of a
typographical or grammatical character; and even where greatest, have been
intended to explain the sense, not to alter it. I have often added Notes at the
bottom of the page, as to paragraphs 59, 360, 439, 521, 552, 555, 598, 657, 883,
for the correction of errors, and also the purpose of illustration : but these are
all distinguished from the Original Notes of the Researches by the date of
Dec, 1838.

The date of a scientific paper containing any pretensions to discovery is fre-
quently a matter of serious importance, and it is a great misfortune that there
are many most valuable communications, essential to the history and progress
of science, with respect to which this point cannot now be ascertained. This
arises from the circumstance of the papers having no dates attached to them
individually, and of the journals in which they appear having such as are inac-
curate, i.e. dates of a period earlier than that of publication. I may refer to the
note at the end of the First Series, as an illustration of the kind of confusion
thus produced. These circumstances have induced me to affix a date at the top
of every other page, and I have thought myself justified in using that placed by
the Secretary of the Royal Society on each paper as it was received. An author
has no right, perhaps, to claim an earlier one, unless it has received confirma-
tion by some public act or officer.

261

262 FARADAY

Before concluding these lines I would beg leave to make a reference or two;
first, to my own "Papers on Electro-magnetic Rotations" in the Quarterly
Journal of Science, 1822. XII, 74, 186, 283, 416, and also to my "Letter on Mag-
neto-electric Induction" in the Annales de Chimie, LI, p. 404. These might, as
to the matter, very properly have appeared in this volume, but they would have
interfered with it as a simple reprint of the Experimental Researches of the Phil-
osophical Transactions.

Then I wish to refer, in relation to the Fourth Series on a new law of Electric
Conduction, to Franklin's experiments on the non-conduction of ice, which
have been very properly separated and set forth by Professor Bache (Journal
of the Franklin Institute, 1836. XVII, 183). These, which I did not at all re-
member as to the extent of the effect, though they in no way anticipate the ex-
pression of the law I state as to the general effect of liquefaction on electrolytes,
still should never be forgotten when speaking of that law as applicable to the
case of water.

There are two papers which I am anxious to refer to, as corrections or criti-
cisms of parts of the Experimental Researches. The first of these is one by Jacobi
(Philosophical Magazine, 1838. XIII, 401), relative to the possible production
of a spark on completing the junction of the two metals of a single pair of plates
(915). It is an excellent paper, and though I have not repeated the experiments,
the description of them convinces me that I must have been in error. The sec-
ond is by that excellent philosopher Marianini (Memoria della Societa Italiana
di Modena, XXI, 205), and is a critical and experimental examination of Series
VIII, and of ttie question whether metallic contact is or is not productive of a
part of the electricity of the voltaic pile. I see no reason as yet to alter the opin-
ion I have given; but the paper is so very valuable, comes to the question so
directly, and the point itself is of such great importance, that I intend at the
first opportunity renewing the inquiry, and, if I can, rendering the proofs either
on the one side or the other undeniable to all.

Other parts of these researches have received the honour of critical attention
from various philosophers, to all of whom I am obliged, and some of whose cor-
rections I have acknowledged in the foot notes. There are, no doubt, occasions
on which I have not felt the force of the remarks, but time and the progress of
science will best settle such cases; and, although I cannot honestly say that I
wish to be found in error, yet I do fervently hope that the progress of science
in the hands of its many zealous present cultivators will be such, as by giving
us new and other developments, and laws more and more general in their ap-
plications, will even make me think that what is written and illustrated in
these experimental researches, belongs to the by-gone parts of science.

MICHAEL FARADAY

Royal Institution, March, 1839

Preface to Volume II

FOB reasons stated in the former volume of Experimental Researches in Elec-
tricity, I have been induced to gather the remaining Series together, and to add
to them certain other papers devoted to Electrical research.

To the prefatory remarks containing these reasons, I would recall the recol-
lection of those who may honour these Researches with any further attention.

PREFACES 263

I have printed the papers in this volume, as before, with little or no alteration,
except that I have placed the fair and just date of each at the top of the pages.

I regret the presence of those papers which partake of a controversial charac-
ter, but could not help it; some of them contain much new, important and ex-
planatory matter. The introduction of matter due to other parties than myself,
as Nobili and Antinori, or Hare, was essential to the comprehension of the fur-
ther development given in the replies.

I owe many thanks to the Royal Society, to Mr. Murray, and to Mr. Taylor,
for the great kindness I have received in the loan of plates, &c., and in other
facilities granted to me for the printing of the volume.

As the Index belongs both to the Experimental Researches and to the miscel-
laneous papers, its references are of necessity made in two ways; those to the
Researches are, as before, to the numbers of the Paragraphs, and are easily
recognised by the greatness of the numbers: the other references are to the
pages, and being always preceded by p. or pp., are known by that mark.

MICHAEL, FARADAY

Preface to Volume III

FOR reasons stated in the First Volume of these Experimental Researches, I have
been induced to gather the remaining Series together, and to add to them cer-
tain other papers devoted to Electrical and Magnetic Research.

To the prefatory remarks containing these reasons, I would recall the recol-
lection of those who may honour these Researches with any further attention.
I have printed the papers in this volume, as before, with little or no alteration,
except that I have placed the fair and just date of each at the top of the pages.

As regards magnecry stall ic action, which commences at paragraph 2454, the
reader will see the gradual change and enlargement of view respecting its na-
ture in the course of long investigations at the following places, 2550, 2562,
2576, 2584, &c., 2591, 2639, 2797, 2818, 2836, &c. I would refer readers to the
paper by Tyndall and Knoblauch in the Philosophical Magazine, 1850, Vol.
XXXVII, p. 1, for a very philosophical account of the physical cause of the
magnecrystallic action, 1 and to the paper by Professor W. Thomson on the
theory of magnetic induction in crystalline and non-crystalline substances in
the Philosophical Magazine, 1851, Vol. I, p. 177, as being in all parts in perfect
accordance with the various experimental results which I have at different times
obtained.

With respect to paragraph 2967, and the intentions there expressed of
experimenting with oxygen at low temperatures, I have endeavoured to carry
these intentions out; but the extreme difficulty of working on such attenuated
matter as gases at low temperatures, without the production of air-currents
able to influence the very delicate torsion-balance and apparatus required to
measure the result, is so great as to have prevented me as yet from obtaining
any results worthy of confidence.

I owe many thanks to the Royal Society and to the Proprietors of the Phil-
osophical Magazine, for the great kindness I have received in the loan of plates,
&c., and in other facilities granted to me for the printing of the volume.

1 Marchand and Scheerer say that bismuth is expanded by pressure and has its struc-
ture changed. Gmelin's Handbook, iv. p. 428.

204 FARADAY

As the Index belongs both to the Experimental Researches and to the other
papers, its references are of necessity made in two ways ; those to the Researches
are, as before, to the numbers of the paragraphs, and are easily recognized by
the greatness of the numbers : the other references are to the pages, and being
always preceded by p. or pp., are known by that mark.

MICHAEL, FARADAY

January, 1855

FIRST SERIES

1. On the Induction of Electric Currents 2. On the Evolution of
Electricity from Magnetism 3. New Electrical Condition of Matter
4. Explication of Arago's Magnetic Phenomena
READ NOVEMBER 24, 1831

1. THE power which electricity of tension pos-
sesses of causing an opposite electrical state in
its vicinity has been expressed by the general
term Induction; which, as it has been received
into scientific language, may also, with propri-
ety, be used in the same general sense to express
the power which electrical currents may possess
of inducing any particular state upon matter
in their immediate neighbourhood, otherwise
indifferent. It is with this meaning that I pur-
pose using it in the present paper.

2. Certain effects of the induction of elec-
trical currents have already been recognised
and described: as those of magnetization; Am-
pSre's experiments of bringing a copper disc
near to a flat spiral; his repetition with electro-
magnets of Arago's extraordinary experiments,
and perhaps a few others. Still it appeared un-
likely that these could be all the effects which
induction by currents could produce; espe-
cially as, upon dispensing with iron, almost the
whole of them disappear, whilst yet an infinity
of bodies, exhibiting definite phenomena of in-
duction with electricity of tension, still remain
to be acted upon by the induction of electricity
in motion.

3. Further: Whether Ampere's beautiful
theory were adopted, or any other, or whatever
reservation were mentally made, still it ap-
peared very extraordinary, that as every elec-
tric current was accompanied by a correspond-
ing intensity of magnetic action at right angles
to the current, good conductors of electricity,
when placed within the sphere of this action,
should not have any current induced through
them, or some sensible effect produced equiva-
lent in force to such a current.

4. These considerations, with their conse-
quence, the hope of obtaining electricity from
ordinary magnetism, have stimulated me at
various times to investigate experimentally
the inductive effect of electric currents. I lately
arrived at positive results; and not only had
my hopes fulfilled, but obtained a key which

appeared to me to open out a full explanation
of Arago's magnetic phenomena, and also to dis-
cover a new state, which may probably have
great influence in some of the most important
effects of electric currents.

5. These results I purpose describing, not as
they were obtained, but in such a manner as
to give the most concise view of the whole.

1. On the Induction of Electric Currents

6. About twenty-six feet of copper wire one
twentieth of an inch in diameter were wound
round a cylinder of wood as a helix, the differ-
ent spires of which were prevented from touch-
ing by a thin interposed twine. This helix was
covered with calico, and then a second wire ap-
plied in the same manner. In this way twelve
helices were superposed, each containing an
average length of wire of twenty-seven feet,
and all in the same direction. The first, third,
fifth, seventh, ninth, and eleventh of these hel-
ices were connected at their extremities end to
end, so as to form one helix; the others were
connected in a similar manner; and thus two
principal helices were produced, closely inter-
posed, having the same direction, not touching
anywhere, and each containing one hundred
and fifty-five feet in length of wire.

7. One of these helices was connected with a
galvanometer, the other with a voltaic battery
of ten pairs of plates four inches square, with
double coppers and well charged; yet not the
slightest sensible deflection of the galvanom-
eter-needle could be observed.

8. A similar compound helix, consisting of
six lengths of copper and six of soft iron wire,
was constructed. The resulting iron helix con-
tained two hundred and fourteen feet of wire,
the resulting copper helix two hundred and
eight feet; but whether the current from the
trough was passed through the copper or the
iron helix, no effect upon the other could be
perceived at the galvanometer.

9. In these and many similar experiments

265

266

FARADAY

SERIES I

no difference in action of any kind appeared
between iron and other metals.

10. Two hundred and three feet of copper
wire in one length were coiled round a large
block of wood; other two hundred and three
feet of similar wire were interposed as a spiral
between the turns of the first coil, and metallic
contact everywhere prevented by twine. One
of these helices was connected with a galvan-
ometer, and the other with a battery of one
hundred pairs of plates four inches square,
with double coppers, and well charged. When
the contact was made, there was a sudden and
very slight effect at the galvanometer, and
there was also a similar slight effect when the
contact with the battery was broken. But
whilst the voltaic current was continuing to
pass through the one helix, no galvanometrical
appearances nor any effect like induction upon
the other helix could be perceived, although the
active power of the battery was proved to be
great, by its heating the whole of its own helix,
and by the brilliancy of the discharge when
made through charcoal.

11. Repetition of the experiments with a
battery of one hundred and twenty pairs of
plates produced no other effects; but it was as-
certained, both at this and the former time,
that the slight deflection of the needle occur-
ring at the moment of completing the conne-
xion, was always in one direction, and that the
equally slight deflection produced when the
contact was broken, was in the other direction;
and also, that these effects occurred when the
first helices were used (6, 8).

12. The results which I had by this time ob-
tained with magnets led me to believe that the
battery current through one wire, did, in real-
ity, induce a similar current through the other
wire, but that it continued for an instant only,
and partook more of the nature of the elec-
trical wave passed through from the shock of a
common Leyden jar than of the current from a
voltaic battery, and therefore might magnetise
a steel needle, although it scarcely affected the
galvanometer.

13. This expectation was confirmed; for on
substituting a small hollow helix, formed round
a glass tube, for the galvanometer, introducing
a steel needle, making contact as before be-
tween the battery and the inducing wire (7,
10), and then removing the needle before the
battery contact was broken, it was found mag-
netised.

14. When the battery contact was first made,
then an unmagnetised needle introduced into

the small indicating helix (13), and lastly the
battery contact broken, the needle was found
magnetised to an equal degree apparently as
before; but the poles were of the contrary kind.

15. The same effects took place on using the
large compound helices first described (6, 8).

16. When the unmagnetised needle was put
into the indicating helix, before contact of the
inducing wire with the battery, and remained
there until the contact was broken, it exhibited
little or no magnetism; the first effect having
been nearly neutralised by the second (13, 14).
The force of the induced current upon making
contact was found always to exceed that of the
induced current at breaking of contact; and if
therefore the contact was made and broken
many times in succession, whilst the needle re-
mained in the indicating helix, it at last came
out not unmagnetised, but a needle magne-
tised as if the induced current upon making
contact had acted alone on it. This effect may
be due to the accumulation (as it is called) at
the poles of the unconnected pile, rendering
the current upon first making contact more
powerful than what it is afterwards, at the mo-
ment of breaking contact.

17. If the circuit; between the helix or wire
under induction and the galvanometer or in-
dicating spiral was not rendered complete be-
fore the connexion between the battery and the
inducing wire was completed or broken, then
no effects were perceived at the galvanometer.
Thus, if the battery communications were first
made, and then the wire under induction con-
nected with the indicating helix, no magnetis-
ing power was there exhibited. But still retain-
ing the latter communications, when those
with the battery were broken, a magnet was
formed in the helix, but of the second kind (14) ,
i.e., with poles indicating a current in the same
direction to that belonging to the battery cur-
rent, or to that always induced by that current
at its cessation.

18. In the preceding experiments the wires
were placed near to each other, and the con-
tact of the inducing one with the battery made
when the inductive effect was required ; but as
the particular action might be supposed to be
exerted only at the moments of making and
breaking contact, the induction was produced
in another way. Several feet of copper wire
were stretched in wide zigzag forms, represent-
ing the letter W, on one surface of a broad
board; a second wire was stretched in precisely
similar forms on a second board, so that when
brought near the first, the wires should every-

Nov. 1831

ELECTRICITY

267

where touch, except that a sheet of thick paper
was interposed. One of these wires was con-
nected with the galvanometer, and the other
with a voltaic battery. The first wire was then
moved towards the second, and as it ap-
proached, the needle was deflected. Being then
removed, the needle was deflected in the op-
posite direction. By first making the wires ap-
proach and then recede, simultaneously with
the vibrations of the needle, the latter soon be-
came very extensive; but when the wires
ceased to move from or towards each other,
the galvanometer-needle soon came to its usual
position.

19. As the wires approximated, the induced
current was in the contrary direction to the in-
ducing current. As the wires receded, the in-
duced current was in the same direction as the
inducing current. When the wires remained
stationary, there was no induced current (54).

20. When a small voltaic arrangement was
introduced into the circuit between the gal-
vanometer (10) and its helix or wire, so as to
cause a permanent deflection of 30 or 40, and
then the battery of one hundred pairs of plates
connected with the inducing wire, there was an
instantaneous action as before (11); but the
galvanometer-needle immediately resumed and
retained its place unaltered, notwithstanding
the continued contact of the inducing wire
with the trough: such was the case in which-
ever way the contacts were made (33) .

21. Hence it would appear that collateral
currents, either in the same or in opposite di-
rections, exert no permanent inducing power
on each other, affecting their quantity or ten-
sion.

22. I could obtain no evidence by the tongue,
by spark, or by heating fine wire or charcoal,
of the electricity passing through the wire un-
der induction; neither could I obtain any chem-
ical effects, though the contacts with metallic
and other solutions were made and broken al-
ternately with those of the battery, so that the
second effect of induction should not oppose or
neutralise the first (13, 16).

23. This deficiency of effect is not because
the induced current of electricity cannot pass
fluids, but probably because of its brief dura-
tion and feeble intensity; for on introducing
two large copper plates into the circuit on the
induced side (20), the plates being immersed
in brine, but prevented from touching each
other by an interposed cloth, the effect at the
indicating galvanometer, or helix, occurred as
before. The induced electricity could also pass

through a voltaic trough (20). When, however,
the quantity of interposed fluid was reduced to
a drop, the galvanometer gave no indication.

24. Attempts to obtain similar effects by the
use of wires conveying ordinary electricity were
doubtful in the results. A compound helix sim-
ilar to that already described, containing eight
elementary helices (6), was used. Four of the
helices had their similar ends bound together
by wire, and the two general terminations thus
produced connected with the small magnet-
ising helix containing an unmagnetised needle
(13). The other four helices were similarly ar-
ranged, but their ends connected with a Leyden
jar. On passing the discharge, the needle was
found to be a magnet; but it appeared prob-
able that a part of the electricity of the jar had
passed off to the small helix, and so magnetised
the needle. There was indeed no reason to ex-
pect that the electricity of a jar possessing as
it docs great tension, would not diffuse itself
through all the metallic matter interposed be-
tween the coatings.

25. Still it does not follow that the discharge
of ordinary electricity through a wire does not
produce analogous phenomena to those arising
from voltaic electricity; but as it appears im-
possible to separate the effects produced at the
moment when the discharge begins to pass,
from the equal and contrary effects produced
when it ceases to pass (16), inasmuch as with
ordinary electricity these periods are simulta-
neous, so there can be scarcely any hope that
in this form of the experiment they can be per-
ceived.

26. Hence it is evident that currents of vol-
taic electricity present phenomena of induction
somewhat analogous to those produced by elec-
tricity of tension, although, as will be seen here-
after, many differences exist between them.
The result is the production of other currents,
(but which are only momentary), parallel, or
tending to parallelism, with the inducing cur-
rent. By reference to the poles of the needle
formed in the indicating helix (13, 14) and to
the deflections of the galvanometer-needle (11),
it was found in all cases that the induced cur-
rent, produced by the first action of the induc-
ing current, was in the contrary direction to
the latter, but that the current produced by
the cessation of the inducing current was in the
same direction (19). For the purpose of avoid-
ing periphrasis, I propose to call this action of
the current from the voltaic battery, volta-elec-
tric induction. The properties of the second
wire, after induction has developed the first

PLATE I

Fig. i

Fig- 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 10

Fie. 9

Fig. 8

Fig. it

268

Nov. 1831

ELECTRICITY

269

current, and whilst the electricity from the bat-
tery continues to flow through its inducing
neighbour (10, 18), constitute a peculiar elec-
tric condition, the consideration of which will
be resumed hereafter (60). All these results
have been obtained with a voltaic apparatus
consisting of a single pair of plates.

2. On the Evolution of Electricity from Mag-
netism

27. A welded ring was made of soft round
bar-iron, the metal being seven-eighths of an
inch in thickness, and the ring six inches in ex-
ternal diameter. Three helices were put round
one part of this ring, each containing about
twenty-four feet of copper wire one-twentieth
of an inch thick; they were insulated from the
iron and each other, and superposed in the man-
ner before described (6), occupying about nine
inches in length upon the ring. They could be
used separately or conjointly; the group may
be distinguished by the letter A (PL I, Fig. 1).
On the other part of the ring about sixty feet
of similar copper wire in two pieces were ap-
plied in the same manner, forming a helix B,
which had the same common direction with
the helices of A, but being separated from it at
each extremity by about half an inch of the
uncovered iron.

28. The helix B was connected by copper
wires with a galvanometer three feet from the
ring. The helices of A were connected end to
end so as to form one common helix, the ex-
tremities of which were connected with a bat-
tery of ten pairs of plates four inches square.
The galvanometer was immediately affected,
and to a degree far beyond what has been de-
scribed when with a battery of tenfold power
helices without iron were used (10) ; but though
the contact was continued, the effect was not
permanent, for the needle soon came to rest in
its natural position, as if quite indifferent to
the attached electro-magnetic arrangement.
Upon breaking the contact with the battery,
the needle was again powerfully deflected, but
in the contrary direction to that induced in the
first instance.

29. Upon arranging the apparatus so that B
should be out of use, the galvanometer be con-
nected with one of the three wires of A (27),
and the other two made into a helix through
which the current from the trough (28) was
passed, similar but rather more powerful ef-
fects were produced.

30. When the battery contact was made in
one direction, the galvanometer-needle was de-

flected on the one side; if made in the other
direction, the deflection was on the other side.
The deflection on breaking the battery contact
was always the reverse of that produced by
completing it. The deflection on making a bat-
tery contact always indicated an induced cur-
rent in the opposite direction to that from the
battery; but on breaking the contact the de-
flection indicated an induced current in the
same direction as that of the battery. No mak-
ing or breaking of the contact at B side, or in
any part of the galvanometer circuit, produced
any effect at the galvanometer. No continu-
ance of the battery current caused any deflec-
tion of the galvanometer-needle. As the above
results are common to all these experiments,
and to similar ones with ordinary magnets to
be hereafter detailed, they need not be again
particularly described.

31. Upon using the power of one hundred
pairs of plates (10) with this ring, the impulse
at the galvanometer, when contact was com-
pleted or broken, was so great as to make the
needle spin round rapidly four or five times,
before the air and terrestrial magnetism could
reduce its motion to mere oscillation.

32. By using charcoal at the ends of the B
helix, a minute spark could be perceived when
the contact of the battery with A was com-
pleted. This spark could not be due to any di-
version of a part of the current of the battery
through the iron to the helix B ; for when the
battery contact was continued, the galva-
nometer still resumed its perfectly indifferent
state (28). The spark was rarely seen on break-
ing contact. A small platina 1 wire could not be
ignited by this induced current; but there seems
every reason to believe that the effect would be
obtained by using a stronger original current
or a more powerful arrangement of helices.

33. A feeble voltaic current was sent through
the helix B and the galvanometer, so as to de-
flect the needle of the latter 30 or 40, and
then the battery of one hundred pairs of plates
connected with A; but after the first effect was
over, the galvanometer-needle resumed exactly
the position due to the feeble current transmit-
ted by its own wire. This took place in which-
ever way the battery contacts were made, and
shows that here again (20) no permanent in-
fluence of the currents upon each other, as to
their quantity and tension, exists.

34. Another arrangement was then employed
connecting the former experiments on volta-

\Platina: early form for platinum, used often in
this work. ED.

270

FARADAY

SERIES I

electric induction (6 26) with the present. A
combination of helices like that already de-
scribed (6) was constructed upon a hollow cyl-
inder of pasteboard: there were eight lengths
of copper wire, containing altogether 220 feet;
four of these helices were connected end to end,
and then with the galvanometer (7); the other
intervening four were also connected end to
end, and the battery of one hundred pairs dis-
charged through them. In this form the effect
on the galvanometer was hardly sensible (11),
though magnets could be made by the induced
current (13). But when a soft iron cylinder
seven-eighths of an inch thick, and twelve
inches long, was introduced into the pasteboard
tube, surrounded by the helices, then the in-
duced current affected the galvanometer pow-
erfully and with all the phenomena just de-
scribed (30). It possessed also the power of
making magnets with more energy, apparently,
than when no iron cylinder was present.

35. When the iron cylinder was replaced by
an equal cylinder of copper, no effect beyond
that of the helices alone was produced. The
iron cylinder arrangement was not so powerful
as the ring arrangement already described (27) .

36. Similar effects were then produced by
ordinary magnets: thus the hollow helix just de-
scribed (34) had all its elementary helices con-
nected with the galvanometer by two copper
wires, each five feet in length; the soft iron cyl-
inder was introduced into its axis; a couple of
bar magnets, each twenty-four inches long, were
arranged with their opposite poles at one end in
contact, so as to resemble a horse-shoe magnet,
and then contact made between the other poles
and the ends of the iron cylinder, so as to con-
vert it for the time into a magnet (PL I, Fig.
2) : by breaking the magnetic contacts, or re-
versing them, the magnetism of the iron cylin-
der could be destroyed or reversed at pleasure.

37. Upon making magnetic contact, the nee-
dle was deflected; continuing the contact, the
needle became indifferent, and resumed its first
position; on breaking the contact, it was again
deflected, but in the opposite direction to the
first effect, and then it again became indiffer-
ent. When the magnetic contacts were reversed
the deflections were reversed.

38. When the magnetic contact was made,
the deflection was such as to indicate an in-
duced current of electricity in the opposite di-
rection to that fitted to form a magnet, having
the same polarity as that really produced by
contact with the bar magnets. Thus when the
marked and unmarked poles were placed as in

PI. I, Fig. 8, the current in the helix was in the
direction represented, P being supposed to be
the end of the wire going to the positive pole of
the battery, or that end towards which the
zinc plates face, and N the negative wire. Such
a current would have converted the cylinder
into a magnet of the opposite kind to that
formed by contact with the poles A and B ; and
such a current moves in the opposite direction
to the currents which in M. Ampere's beautiful
theory are considered as constituting a magnet
in the position figured. 1

39. But as it might be supposed that in all
the preceding experiments of this section, it
was by some peculiar effect taking place during
the formation of the magnet, and not by its
mere virtual approximation, that the momen-
tary induced current was excited, the following
experiment was made. All the similar ends of
the compound hollow helix (34) were bound
together by copper wire, forming two general
terminations, and these were connected with
the galvanometer. The soft iron cylinder (34)
was removed, and a cylindrical magnet, three-
quarters of an inch in diameter and eight inches
and a half in length, used instead. One end of
this magnet was introduced into the axis of the
helix (PI. I, Fig. 4\ and then, the galvano-
meter-needle being stationary, the magnet was
suddenly thrust in; immediately the needle was
deflected in the same direction as if the magnet
had been formed by either of the two preceding
processes (34, 36). Being left in, the needle re-
sumed its first position, and then the magnet
being withdrawn the needle was deflected in
the opposite direction. These effects were not
great; but by introducing and withdrawing the
magnet, so that the impulse each time should
be added to those previously communicated to
the needle, the latter could be made to vibrate
through an arc of 180 or more.

! The relative position of an electric current and
a magnet is by most persons found very difficult to
remember, and three or four helps to the memory have
been devised by M. Ampere and others. I venture to
suggest the following as a very simple and effectual
assistance in these and similar latitudes. Let the ex-
perimeter think he is looking down upon a dipping-
needle, or upon the pole of the earth, and then let him
think upon the direction of the motion of the hands of
a watch, or of a screw moving direct; currents in that
direction round a needle would make it into such a
magnet as the dipping needle, or would themselves
constitute an electro-magnet of similar qualities; or
if brought near a magnet would tend to make it take
that direction ; or would themselves be moved into that
position by a magnet so placed; or in M. Ampere's
theory are considered as moving in that direction in
the magnet. These two points of the position of the
dipping-needle and the motion of the watch hands
being remembered, any other relation of the current
and magnet can be at once deduced from it.

Nov. 1831

ELECTRICITY

271

40. In this experiment the magnet must not
be passed entirely through the helix, for then a
second action occurs. When the magnet is in-
troduced, the needle at the galvanometer is de-
flected in a certain direction ; but being in, wheth-
er it be pushed quite through or withdrawn,
the needle is deflected in a direction the reverse
of that previously produced. When the magnet
is passed in and through at one continuous mo-
tion, the needle moves one way, is then suddenly
stopped, and finally moves the other way.

41. If such a hollow helix as that described
(34) be laid east and west (or in any other con-
stant position), and a magnet be retained east
and west, its marked pole always being one
way; then whichever end of the helix the
magnet goes in at, and consequently whichever
pole of the magnet enters first, still the needle
is deflected the same way: on the other hand,
whichever direction is followed in withdrawing
the magnet, the deflection is constant, but con-
trary to that due to its entrance.

42. These effects are simple consequences of
the law hereafter to be described (114) .

43. When the eight elementary helices were
made one long helix, the effect was not so great
as in the arrangement described. When only
one of the eight helices was used, the effect was
also much diminished. All care was taken to
guard against any direct action of the inducing
magnet upon the galvanometer, and it was
found that by moving the magnet in the same
direction, and to the same degree on the out-
side of the helix, no effect on the needle was
produced.

44. The Royal Society are in possession of a
large compound magnet formerly belonging to
Dr. Gowin Knight, which, by permission of the
President and Council, I was allowed to use in
the prosecution of these experiments: it is at
present in the charge of Mr. Christie, at his
house at Woolwich, where, by Mr. Christie's
kindness, I was at liberty to work; and I have
to acknowledge my obligations to him for his
assistance in ail the experiments and observa-
tions made with it. This magnet is composed of
about 450 bar magnets, each fifteen inches long,
one inch wide, and half an inch thick, arranged
in a box so as to present at one of its extremi-
ties two external poles (PL I, Fig. 6). These
poles projected horizontally six inches from the
box, were each twelve inches high and three
inches wide. They were nine inches apart; and
when a soft iron cylinder, three-quarters of an
inch in diameter and twelve inches long, was
put across from one to the other, it required a

force of nearly one hundred pounds to break
the contact. The pole to the left in the figure is
the marked pole. 1

45. The indicating galvanometer, in all ex-
periments made with this magnet, was about
eight feet from it, not directly in front of the
poles, but about 16 or 17 on one side. It was
found that on making or breaking the connex-
ion of the poles by soft iron, the instrument
was slightly affected ; but all error of observa-
tion arising from this cause was easily and care-
fully avoided.

46. The electrical effects exhibited by this
magnet were very striking. When a soft iron
cylinder thirteen inches long was put through
the compound hollow helix, with its ends ar-
ranged as two general terminations (39), these
connected with the galvanometer, and the iron
cylinder brought in contact with the two poles
of the magnet (PI. I, Fig. 5), so powerful a rush
of electricity took place that the needle whirled
round many times in succession. 2

47. Notwithstanding this great power, if the
contact was continued, the needle resumed its
natural position, being entirely uninfluenced
by the position of the helix (30). But on break-
ing the magnetic contact, the needle was whirled
round in the opposite direction with a force
equal to the former.

48. A piece of copper plate wrapped once
round the iron cylinder like a socket, but with
interposed paper to prevent contact, had its
edges connected with the wires of the galvano-
meter. When the iron was brought in contact
with the poles the galvanometer was strongly
affected.

49. Dismissing the helices and sockets, the
galvanometer wire was passed over, and conse-
quently only half round the iron cylinder (PI.
I, Fig. 6) ; but even then a strong effect upon
the needle was exhibited, when the magnetic
contact was made or broken.

50. As the helix with its iron cylinder was
brought towards the magnetic poles, but with-
out making contact, still powerful effects were
produced. When the helix, without the iron cyi-

iTo avoid any confusion as to the poles of the
magnet, I shall designate the pole pointing to the
north as the marked pole ; I may occasionally speak
of the north and south ends of the needle, but do not
mean thereby north and south poles. That is by
many considered the true north pole of a needle
which points to the south; but in this country it is
often called the south pole.

8 A soft iron bar in the form of a lifter to a horse-
shoe magnet, when supplied with a coil of this kind
round the middle of it, becomes, by juxtaposition
with a magnet, a ready source of a brief but deter-
minate current of electricity.

272

FARADAY

SERIES I

inder, and consequently containing no metal
but copper, was approached to, or placed be-
tween the poles (44), the needle was thrown
80, 90, or more, from its natural position. The
inductive force was of course greater, the nearer
the helix, either with or without its iron cylin-
der, was brought to the poles; but otherwise
the same effects were produced, whether the
helix, &c. was or was not brought into contact
with the magnet; i.e., no permanent effect on
the galvanometer was produced; and the effects
of approximation and removal were the re-
verse of each other (30) .

51. When a bolt of copper corresponding to
the iron cylinder was introduced, no greater ef-
fect was produced by the helix than without it.
But when a thick iron wire was substituted,
the magneto-electric induction was rendered
sensibly greater.

52. The direction of the electric current pro-
duced in all these experiments with the helix,
was the same as that already described (38) as
obtained with the weaker bar magnets.

53. A spiral containing fourteen feet of cop-
per wire, being connected with the galvano-
meter, and approximated directly towards the
marked pole in the line of its axis, affected the
instrument strongly; the current induced in it
was in the reverse direction to the current
theoretically considered by M. Ampere as ex-
isting in the magnet (38), or as the current in
an electro-magnet of similar polarity. As the
spiral was withdrawn, the induced current was
reversed.

54. A similar spiral had the current of eighty
pairs of 4-inch plates sent through it so as to
form an electro-magnet, and then the other
spiral connected with the galvanometer (53)
approximated to it; the needle vibrated, indi-
cating a current in the galvanometer spiral the
reverse of that in the battery spiral (18, 26).
On withdrawing the latter spiral, the needle
passed in the opposite direction.

55. Single wires, approximated in certain di-
rections towards the magnetic pole, had cur-
rents induced in them. On their removal, the
currents were inverted. In such experiments
the wires should not be removed in directions
different to those in which they were approxi-
mated; for then occasionally complicated and
irregular effects are produced, the causes of
which will be very evident in the fourth part of
this paper.

56. All attempts to obtain chemical effects
by the induced current of electricity failed,
though the precautions before described (22),

and all others that could be thought of, were
employed. Neither was any sensation on the
tongue, or any convulsive effect upon the limbs
of a frog, produced. Nor could charcoal or fine
wire be ignited (133). But upon repeating the
experiments more at leisure at the Royal In-
stitution, with an armed loadstone belonging
to Professor Daniell and capable of lifting about
thirty pounds, a frog was very powerfully con-
vulsed each time magnetic contact was made.
At first the convulsions could not be obtained
on breaking magnetic contact; but conceiving
the deficiency of effect was because of the com-
parative slowness of separation, the latter act
was effected by a blow, and then the frog was
convulsed strongly. The more instantaneous
the union or disunion is effected, the more pow-
erful the convulsion. I thought also I could per-
ceive the sensation upon the tongue and the
flash before the eyes; but I could obtain no
evidence of chemical decomposition.

57. The various experiments of this section
prove, I think, most completely the produc-
tion of electricity from ordinary magnetism.
That its intensity should be very feeble and
quantity small, cannot be considered wonder-
ful, when it is remembered that like thermo-
electricity it is evolved entirely within the sub-
stance of metals retaining all their conducting
power. But an agent which is conducted along
metallic wires in the manner described ; which
whilst so passing possesses the peculiar mag-
netic actions and force of a current of electric-
ity; which can agitate and convulse the limbs
of a frog; and which, finally, can produce a
spark 1 by its discharge through charcoal (32),
can only be electricity. As all the effects can be
produced by ferruginous electro-magnets (34),
there is no doubt that arrangements like the
magnets of Professors Moll, Henry, Ten Eyke,
and others, in which as many as two thousand
pounds have been lifted, may be used for these
experiments; in which case not only a brighter
spark may be obtained, but wires also ignited,
and, as the current can pass liquids (23), chem-
ical action be produced. These effects are still
more likely to be obtained when the magneto-
electric arrangements to be explained in the
fourth section are excited by the powers of
such apparatus.

1 For a mode of obtaining the spark from the com-
mon magnet which I have found effectual, see the
Philosophical Magazine for June, 1832, p. 5. In the
same journal for November, 1834, Vol. V, p. 349, will
be found a method of obtaining the magneto-electric
spark, still simpler in its principle, the use of soft iron
being dispensed with altogether. Dec. 1838.

Nov. 1831

ELECTRICITY

273

58. The similarity of action, almost amount-
ing to identity, between common magnets and
either electro-magnets or volta-electric cur-
rents, is strikingly in accordance with and con-
firmatory of M. Ampere's theory, and furnishes
powerful reasons for believing that the action
is the same in both cases ; but, as a distinction in
language is still necessary, I propose to call the
agency thus exerted by ordinary magnets, mag-
neto-electric or magnelectric induction (26).

59. The only difference which powerfully
strikes the attention as existing between volta-
electric and magneto-electric induction, is the
suddenness of the former, and the sensible time
required by the latter; but even in this early
state of investigation there are circumstances
which seem to indicate that upon further in-
quiry this difference will, as a philosophical
distinction, disappear (68) .*

3. New Electrical State or Condition
of Matter*

60. Whilst the wire is subject to either volta-
electric or magneto-electric induction, it ap-
pears to be in a peculiar state; for it resists the
formation of an electrical current in it, where-
as, if in its common condition, such a current
would be produced; and when left uninfluenced
it has the power of originating a current, a pow-
er which the wire does not possess under com-
mon circumstances. This electrical condition
of matter has not hitherto been recognised, but
it probably exerts a very important influence
in many if not most of the phenomena pro-
duced by currents of electricity. For reasons
which will immediately appear (71), I have,
after advising with several learned friends,
ventured to designate it as the electro-tonic
state.

61. This peculiar condition shows no known
electrical effects whilst it continues; nor have I
yet been able to discover any peculiar powers
exerted, or properties possessed, by matter
whilst retained in this state.

62. It shows no reaction by attractive or re-
pulsive powers. The various experiments which

i For important additional phenomena and devel-
opments of the induction of electrical currents, see
now the ninth series, 1048-1118. Dec. 1838.

* This section having been read at the Royal So-
ciety and reported upon, and having also, in conse-
quence of a letter from myself to M. Hachette, been
noticed at the French Institute, I feel bound to let it
stand as part of the paper; but later investigations
(intimated 73, 76, 77) of the laws governing these
phenomena, induce me to think that the latter can
be fully explained without admitting the electro-
tonic state. My views on this point will appear in the
second series of these researches. M. F.

have been made with powerful magnets upon
such metals, as copper, silver, and generally
those substances not magnetic, prove this
point; for the substances experimented upon, if
electrical conductors, must have acquired this
state; and yet no evidence of attractive or re-
pulsive powers has been observed. I have placed
copper and silver discs, very delicately sus-
pended on torsion balances in vacuo near to the
poles of very powerful magnets, yet have not
been able to observe the least attractive or re-
pulsive force.

63. I have also arranged a fine slip of gold-
leaf very near to a bar of copper, the two being
in metallic contact by mercury at their extrem-
ities. These have been placed in vacuo, so that
metal rods connected with the extremities of
the arrangement should pass through the sides
of the vessel into the air. I have then moved
powerful magnetic poles, about this arrange-
ment, in various directions, the metallic circuit
on the outside being sometimes completed by
wires, and sometimes broken. But I never could
obtain any sensible motion of the gold-leaf,
either directed to the magnet or towards the
collateral bar of copper, which must have been,
as far as induction was concerned, in a similar
state to itself.

64. In some cases it has been supposed that,
under such circumstances, attractive and re-
pulsive forces have been exhibited, i.e., that
such bodies have become slightly magnetic.
But the phenomena now described, in conjunc-
tion with the confidence we may reasonably re-
pose in M. Amp&re's theory of magnetism, tend
to throw doubt on such cases; for if magnetism
depend upon the attraction of electrical cur-
rents, and if the powerful currents at first ex-
cited, both by volta-electric and magneto-elec-
tric induction, instantly and naturally cease
(12, 28, 47), causing at the same time an entire
cessation of magnetic effects at the galvanom-
eter needle, then there can be little or no ex-
pectation that any substances not partaking of
the peculiar relation in which iron, nickel, and
one or two other bodies, stand, should exhibit
magneto-attractive powers. It seems far more
probable, that the extremely feeble permanent
effects observed have been due to traces of
iron, or perhaps some other unrecognised cause
not magnetic.

65. This peculiar condition exerts no retard-
ing or accelerating power upon electrical cur-
rents passing through metal thus circumstanced
(20, 33). Neither could any such power upon
the inducing current itself be detected; for

274

FARADAY

SERIES I

when masses of metal, wires, helices, &c., were
arranged in all possible ways by the side of a
wire or helix, carrying a current measured by
the galvanometer (20), not the slightest per-
manent change in the indication of the instru-
ment could be perceived. Metal in the sup-
posed peculiar state, therefore, conducts elec-
tricity in all directions with its ordinary facil-
ity, or, in other words, its conducting power is
not sensibly altered by it.

66. All metals take on the peculiar state.
This is proved in the preceding experiments
with copper and iron (9), and with gold, silver,
tin, lead, zinc, antimony, bismuth, mercury,
&c., by experiments to be described in the
fourth part (132), admitting of easy applica-
tion. With regard to iron, the experiments
prove the thorough and remarkable independ-
ence of these phenomena of induction, and the
ordinary magnetical appearances of that metal.

67. This state is altogether the effect of the
induction exerted, and ceases as soon as the in-
ductive force is removed. It is the same state,
whether produced by the collateral passage of
voltaic currents (26), or the formation of a
magnet (34, 36), or the mere approximation of
a magnet (39, 50) ; and is a strong proof in ad-
dition to those advanced by M. Ampere, of the
identity of the agents concerned in these sev-
eral operations. It probably occurs, momen-
tarily, during the passage of the common elec-
tric spark (24), and may perhaps be obtained
hereafter in bad conductors by weak electrical
currents or other means (74, 76).

68. The state appears to be instantly assumed
(12), requiring hardly a sensible portion of
time for that purpose. The difference of time
between voita-eiectric and magneto-electric in-
duction, rendered evident by the galvanom-
eter (59), may probably be thus explained.
When a voltaic current is sent through one of
two parallel wires, as those of the hollow helix
(34), a current is produced in the other wire, as
brief in its continuance as the time required for
a single action of this kind, and which, by ex-
periment, is found to be inappreciably small.
The action will seem still more instantaneous,
because, as there is an accumulation of power
in the poles of the battery before contact, the
first rush of electricity in the wire of communi-
cation is greater than that sustained after the
contact is completed; the wire of induction be-
comes at the moment electro-tonic to an equiv-
alent degree, which the moment after sinks to
the state in which the continuous current can
sustain it, but in sinking, causes an opposite in-

duced current to that at first produced. The con-
sequence is that the first induced wave of elec-
tricity more resembles that from the discharge
of an electric jar than it otherwise would do.

69. But when the iron cylinder is put into the
same helix (34), previous to the connexion be-
ing made with the battery, then the current
from the latter may be considered as active in
inducing innumerable currents of a similar kind
to itself in the iron, rendering it a magnet. This
is known by experiment to occupy time ; for a
magnet so formed, even of soft iron, does not
rise to its fullest intensity in an instant, and it
may be because the currents within the iron
are successive in their formation or arrange-
ment. But as the magnet can induce, as well as
the battery current, the combined action of
the two continues to evolve induced electricity,
until their joint effect is at a maximum, and
thus the existence of the deflecting force is pro-
longed sufficiently to overcome the inertia of
the galvanometer needle.

70. In all those cases where the helices or
wires are advanced towards or taken from the
magnet (50, 55), the direct or inverted current
of induced electricity continues for the time
occupied in the advance or recession; for the
electro-tonic state is rising to a higher or falling
to a lower degree during that time, and the
change is accompanied by its corresponding
evolution of electricity; but these form no ob-
jections to the opinion that the electro-tonic
state is instantly assumed.

71. This peculiar state appears to be a state
of tension, and may be considered as equivalent
to a current of electricity, at least equal to
that produced either when the condition is in-
duced or destroyed. The current evolved, how-
ever, first or last, is not to be considered a
measure of the degree of tension to which the
electro-tonic state has risen; for as the metal
retains its conducting powers unimpaired (65),
and as the electricity evolved is but for a mo-
ment, (the peculiar state being instantly as-
sumed and lost [68] ), the electricity which may
be led away by long wire conductors, offering
obstruction in their substance proportionate to
their small lateral and extensive linear dimen-
sions, can be but a very small portion of that
really evolved within the mass at the moment
it assumes this condition. Insulated helices and
portions of metal instantly assumed the state;
and no traces of electricity could be discov-
ered in them, however quickly the contact
with the electrometer was made, after they
were put under induction, either by the current

Nov. 1831

ELECTRICITY

275

from the battery or the magnet. A single drop
of water or a small piece of moistened paper
(23, 56) was obstacle sufficient to stop the cur-
rent through the conductors, the electricity
evolved returning to a state of equilibrium
through the metal itself, and consequently in
an unobserved manner.

72. The tension of this state may therefore
be comparatively very great. But whether great
or small, it is hardly conceivable that it should
exist without exerting a reaction upon the orig-
inal inducing current, and producing equilib-
rium of some kind. It might be anticipated
that this would give rise to a retardation of the
original current; but I have not been able to
ascertain that this is the case. Neither have I
in any other way as yet been able to distinguish
effects attributable to such a reaction.

73. All the results favour the notion that the
electro-tonic state relates to the particles, and
not to the mass, of the wire or substance under
induction, being in that respect different to the
induction exerted by electricity of tension. If
so, the state may be assumed in liquids when
no electrical current is sensible, and even in
non-conductors; the current itself, when it oc-
curs, being as it were a contingency due to the
existence of conducting power, and the mo-
mentary propulsive force exerted by the par-
ticles during their arrangement. Even when
conducting power is equal, the currents of elec-
tricity, which as yet are the only indicators of
this state, may be unequal, because of differ-
ences as to numbers, size, electrical condition,
&c., &c., in the particles themselves. It will
only be after the laws which govern this new
state are ascertained, that we shall be able to
predict what is the true condition of, and what
are the electrical results obtainable from, any
particular substance.

74. The current of electricity which induces
the electro-tonic state in a neighbouring wire,
probably induces that state also in its own
wire; for when by a current in one wire a col-
lateral wire is made electro-tonic, the latter
state is not rendered any way incompatible or
interfering with a current of electricity passing
through it (62). If, therefore, the current were
sent through the second wire instead of the
first, it does not seem probable that its induc-
ing action upon the second would be less, but
on the contrary more, because the distance be-
tween the agent and the matter acted upon
would be very greatly diminished . A copper bolt
had its extremities connected with a galvanom-
eter, and then the poles of a battery of one hun-

dred pairs of plates connected with the bolt, so
as to send the current through it; the voltaic
circuit was then suddenly broken, and the gal-
vanometer observed for any indications of a
return current through the copper bolt due to
the discharge of its supposed electro-tonic state.
No effect of the kind was obtained, nor indeed,
for two reasons, ought it to be expected; for
first, as the cessation of induction and the
discharge of the electro-tonic condition are
simultaneous, and not successive, the return
current would only be equivalent to the neu-
tralization of the last portion of the inducing
current, and would not therefore show any
alteration of direction; or assuming that time
did intervene, and that the latter current was
really distinct from the former, its short, sud-
den character (12, 26) would prevent it from
being thus recognised.

75. No difficulty arises, I think, in consider-
ing the wire thus rendered electro-tonic by its
own current more than by any external cur-
rent, especially when the apparent non-inter-
ference of that state with currents is consid-
ered (62, 71). The simultaneous existence of
the conducting and electro-tonic states finds
an analogy in the manner in which electrical
currents can be passed through magnets, where
it is found that both the currents passed, and
those of the magnets, preserve all their prop-
erties distinct from each other, and exert their
mutual actions.

76. The reason given with regard to metals
extends also to fluids and all other conductors,
and leads to the conclusion that when electric
currents are passed through them they also
assume the electro-tonic state. Should that
prove to be the case, its influence in voltaic de-
composition, and the transference of the ele-
ments to the poles, can hardly be doubted. In
the electro-tonic state the homogenoeus parti-
cles of matter appear to have assumed a regu-
lar but forced electrical arrangement in the di-
rection of the current, which if the matter be
undecomposable, produces, when relieved, a
return current; but in decomposable matter
this forced state may be sufficient to make an
elementary particle leave its companion, with
which it is in a constrained condition, and as-
sociate with the neighbouring similar particle,
in relation to which it is in a more natural con-
dition, the forced electrical arrangement being
itself discharged or relieved, at the same time,
as effectually as if it had been freed from induc-
tion. But as the original voltaic current is con-
tinued, the electro-tonic state may be instantly

276

FARADAY

SERIES I

renewed, producing the forced arrangement of
the compound particles, to be as instantly dis-
charged by a transference of the elementary
particles of the opposite kind in opposite direc-
tions, but parallel to the current. Even the dif-
ferences between common and voltaic electric-
ity, when applied to effect chemical decompo-
sition, which Dr. Woilaston has pointed out, 1
seem explicable by the circumstances connected
with the induction of electricity from these
two sources (25). But as I have reserved this
branch of the inquiry, that I might follow out
the investigations contained in the present pa-
per, I refrain (though much tempted) from of-
fering further speculations.

77. Marianini has discovered and described
a peculiar affection of the surfaces of metallic
discs, when, being in contact with humid con-
ductors, a current of electricity is passed through
them; they are then capable of producing a re-
verse current of electricity, and Marianini has
well applied the effect in explanation of the
phenomena of Hitter's piles. 2 M. A. de la Rive
has described a peculiar property acquired by
metallic conductors, when being immersed in a
liquid as poles, they have completed, for some
time, the voltaic circuit, in consequence of
which, when separated from the battery and
plunged into the same fluid, they by themselves
produce an electric current. 3 M. A. Van Beek
has detailed cases in which the electrical rela-
tion of one metal in contact with another has
been preserved after separation, and accom-
panied by its corresponding chemical effects. 4
These states and results appear to differ from
the electro-tonic state and its phenomena ; but
the true relation of the former to the latter can
only be decided when our knowledge of all
these phenomena has been enlarged.

78. I had occasion in the commencement of
this paper (2) to refer to an experiment by Am-
p6re, as one of those dependent upon the elec-
trical induction of currents made prior to the
present investigation, and have arrived at con-
clusions which seem to imply doubts of the ac-
curacy of the experiment (62, &c.) ; it is there-
fore due to M. Ampere that I should attend to
it more distinctly. When a disc of copper (says
M. Amp&re) was suspended by a silk thread
and surrounded by a helix or spiral, and when
the charge of a powerful voltaic battery was
sent through the spiral, a strong magnet at the
same time being presented to the copper disc,

t Philosophical Transactions, 1801, p. 247.

Annalea de Chimie, XXXVIII. 5.

Ibid., XXVIIJ. 190.

Annole* de Chimie, XXXVIII. 49.

the latter turned at the moment to take a po-
sition of equilibrium, exactly as the spiral it-
self would have turned had it been free to move.
I have not been able to obtain this effect, nor
indeed any motion; but the cause of my failure
in the latter point may be due to the momen-
tary existence of the current not allowing time
for the inertia of the plate to be overcome (11,
12). M. Ampere has perhaps succeeded in ob-
taining motion from the superior delicacy and
power of his electro-magnetical apparatus, or
he may have obtained only the motion due to
cessation of action. But all my results tend to
invert the sense of the proposition stated by
M. Amp&re, "that a current of electricity tends
to put the electricity of conductors near which
it passes in motion in the same direction/' for
they indicate an opposite direction for the pro-
duced current (26, 53) ; and they show that the
effect is momentary, and that it is also pro-
duced by magnetic induction, and that certain
other extraordinary effects follow thereupon.

79. The momentary existence of the phe-
nomena of induction now described is sufficient
to furnish abundant reasons for the uncertain-
ty or failure of the experiments, hitherto made
to obtain electricity from magnets, or to effect
chemical decomposition or arrangement by
their means. 8

80. It also appears capable of explaining fully
the remarkable phenomena observed by M.
Arago between metals and magnets when nei-
ther are moving (120), as well as most of the
results obtained by Sir John Herschel, Messrs.
Babbage, Harris, and others, in repeating his
experiments; accounting at the same time per-
fectly for what at first appeared inexplicable;
namely, the non-action of the same metals and
magnets when at rest. These results, which also

The Lycee, No. 36, for January 1st, has a long
and rather premature article, in which it endeavours
to show anticipations by French philosophers of my
researches. It however mistakes the erroneous re-
sults of MM. Fresnel and Ampere for true ones, and
then imagines my true results are like those errone-
ous ones. I notice it here, however, for the purpose of
doing honour to Fresnel in a much higher degree
than would have been merited by a feeble anticipa-
tion of the present investigations. That great philos-
opher, at the same time with myself and fifty other
persons, made experiments which the present paper
proves could give no expected result. He was de-
ceived for the moment, and published his imaginary
success; but on more carefully repeating his trials,
he could find no proof of their accuracy; and, in the
high and pure philosophic desire to remove error as
well as discover truth, he recanted his first state-
ment. The example of Berzelius regarding the first
Thorina is another instance of this fine feeling; and
as occasions are not rare, it would be to the dignity
of science if such examples were more frequently
followed. February 10th, 1832.

Nov. 1831

ELECTRICITY

277

afford the readiest means of obtaining elec-
tricity from magnetism, I shall now proceed to
describe.

4. Explication of Arago's Magnetic
Phenomena /

81. If a plate of copper be revolved close to a
magnetic needle, or magnet; suspended 1 , in such
a way that the latter may rotate in a plane
parallel to that of the former, the magnet tends
to follow the motion of the plate; or if the mag-
net be revolved, the plate tends to follow its
motion ; and the effect is so powerful, that mag-
nets or plates of many pounds weight may be
thus carried round. If the magnet and plate be
at rest relative to each other, not the. slightest
effect, attractive or repulsive, or of any kind,
can be observed between them (62). This is the
phenomenon discovered by M. Arago; and he
states that the effect takes place not only .with
all metals, but with solids, liquids, and even
gases, i.e., with all substances (130).

82. Mr. Babbage and Sir John Herschel, on
conjointly repeating the experiments in this
country, 1 could obtain the effects only with the
metals, and with carbon in a peculiar state
(from gas retorts), i.e., only with excellent con-
ductors of electricity. They refer the effect to
magnetism induced in the plate by the mag-
net; the pole of the latter causing an opposite
pole in the nearest part of the plate, and round
this a more diffuse polarity of its own kind
(120). The essential circumstance in producing
the rotation of the suspended magnet is, that
the substance revolving below it shall acquire
and lose its magnetism in sensible time, and
not instantly (124). This theory refers the ef-
fect to an attractive force, and is not agreed to
by the discoverer, M. Arago, nor by M. Am-
pre, who quote against it the absence of all
attraction when the magnet and metal are at
rest (62, 126), although the induced magnetism
should still remain; and who, from experiments
made with a long dipping-needle, conceive the
action to be always repulsive (125).

83. Upon obtaining electricity from magnets
by the means already described (36, 46), I
hoped to make the experiment of M. Arago a
new source of electricity; and did not despair,
by reference to terrestrial magneto-electric in-
duction, of being able to construct a new elec-
trical machine. Thus stimulated, numerous, ex-
periments were made with the magnet of the
Royal Society at Mr. Christie's house, in all of
which I had the advantage of his assistance. As

Philosophical Transactions, 1825, p r 467.

many of these were in the course of the investi-
gation superseded by more perfect arrange-
ments, I shall consider myself at liberty to re-
arrange them in a manner calculated to convey
' most readily what appears to me to be a cor-
rect view of the nature of the phenomena.

84. The magnet has been already described
(44). To concentrate the poles, and bring them
nearer to each other, two iron or steel bars,
each about six or seven inches long, one inch
wide, and half an inch thick, were put across
the poles as in PI. I, Fig. 7, and being support-
ed by twine from slipping, could be placed as
near to or far from each other as was required.
Occasionally two bars of soft iron were em-
ployed, so bent that when applied, one to each
pole, the two smaller resulting poles were ver-
tically over each other, either being uppermost
at pleasure.

85. A disc of copper, twelve inches in diam-
eter, and about one-fifth of an inch in thickness,
fixed upon a brass axis, was mounted in frames
so as to allow of revolution either vertically or
horizontally, its edge being at the same time
introduced more or less between the magnetic
poles PL I, (Fig. 7). The edge of the plate was
well-amalgamated for the purpose of obtaining
a good but moveable contact, and a part round
the axis was also prepared in a similar manner.

86. Conductors or electric collectors of cop-
per and lead were constructed so as to come in
contact with the edge of the copper disc (85),
or with other forms of plates hereafter to be
described (101). These conductors were about
four inches long, one-third of an inch wide, and
one-fifth of an inch thick; one end of each was
slightly grooved, to allow of more exact adap-
tation to the somewhat convex edge of the
plates, and then amalgamated. Copper wires,
one-sixteenth of an inch in thickness, attached,
in the ordinary manner, by convolutions to the
other ends of these conductors, passed away to
the galvanometer.

87. The galvanometer was roughly made, yet
sufficiently delicate in its indications. The wire
was of copper covered with silk, and made six-
teen or eighteen convolutions. Two sewing-
needles were magnetized and fixed on to a stem
of dried grass parallel to each other, but in op-
posite directions, and about half an inch apart;
this system was suspended by a fibre of unspun
silk, so that the lower needle should be between
the convolutions of the multiplier, and the up-
per above them. Th0 latter was by much the
most powerful magnet, and gave terrestrial di-
rection to tip wjiole; Pi. I, Fig. 8. represents

Ffg.i

Fig. 2

Fig. 3

B-
A-

UN'

Fig. j

Fig. 6

Fig. 13

Fig. 8

. 11

Fig. 14

Fig. 16

278

ELECTRICITY

279

the direction of the wire and of the needles
when the instrument was placed in the mag-
netic meridian : the ends of the wires are marked
A and B for convenient reference hereafter.
The letters 8 and N designate the south and
north ends of the needle when affected merely
by terrestrial magnetism; the end N is there-
ford the marked pole (44). The whole instru-
ment was protected by a glass jar, and stood,
as to position and distance relative to the large
magnet, under the same circumstances as be-
fore .(45).

88. All these arrangements being made, the
copper disc was adjusted as in PI. I, Fig. 7, the
small magnetic poles being about half an inch
apart, and the edge of the plate inserted about
half their width between them. One of the gal-
vanometer wires was passed twice or thrice
loosely round the brass axis of the plate, and
the other attached to a conductor (86), which
itself was retained by the hand in contact with
the amalgamated edge of the disc at the part
immediately between the magnetic poles. Un-
der these circumstances all was quiescent, and
the galvanometer exhibited no effect. But the
instant the plate moved, the galvanometer was
influenced, and by revolving the plate quickly
the needle could be deflected 90 or more.

89. It was difficult under the circumstances
to make the contact between the conductor
and the edge of the revolving disc uniformly
good and extensive; it was also difficult in the
first experiments to obtain a regular velocity
of rotation: both these causes tended to retain
the needle in a continual state of vibration ; but
no difficulty existed in ascertaining to which
side it was deflected, or generally, about what
line it vibrated. Afterwards, when the experi-
ments were made more carefully, a permanent
deflection of the needle of nearly 45 could be
sustained.

90. Here therefore was demonstrated the
production of a permanent current of electri-
city by ordinary magnets (57).

91. When the motion of the disc was reversed,
every other circumstance remaining the same,
thfe galvanometer needle was deflected with
equal power as before; but the deflection was
on the opposite side, and the current of elec-
tricity evolved, therefore, the reverse of the
former.

92. When the conductor was placed on the
edge of the disc a little to the right or left, as in
the dotted positions PL I, Fig. 9, the current of
electricity was still evolved, and in the same
direction as at first (88, 91). This occurred to a

considerable distance, i.e., 50 or 60 on each
side of the place of the magnetic poles. The
current gathered by the conductor and con-
veyed to the galvanometer was of the same
kind on both sides of the place of greatest in-
tensity, but gradually diminished in force from
that place. It appeared to be equally powerful
at equal distances from the place of the mag-
netic poles, not being affected in that respect
by the direction of the rotation. When the ro-
tation of the disc was reversed, the direction of
the current of electricity was reversed also ; but
the other circumstances were not affected.

93. On raising the plate, so that the magnetic
poles were entirely hidden from each other by
its intervention, (a, PI. I, Fig. 10), the same
effects were produced in the same order, and
with equal intensity as before. On raising it still
higher, so as to bring the place of the poles to
c, still the effects were produced , and apparently
with as much power as at first.

94. When the conductor was held against the
edge as if fixed to it, and with it moved be-
tween the poles, even though but for a few de-
grees, the galvanometer needle moved and in-
dicated a current of electricity, the same as
that which would have been produced if the
wheel had revolved in the same direction, the
conductor remaining stationary.

95. When the galvanometer connexion with
the axis was broken, and its wires made fast to
two conductors, both applied to the edge of the
copper disc, then currents of electricity were
produced, presenting more complicated appear-
ances, but in perfect harmony with the above
results. Thus, if applied as in PI. I, Fig. 11, a
current of electricity through the galvanom-
eter was produced ; but if their place was a little
shifted, as in PL I, Fig. 12, a current in the
contrary direction resulted ; the fact being, that
in the first instance the galvanometer indi-
cated the difference between a strong current
through A and a weak one through B, and in
the second, of a weak current through A and a
strong one through B (92), and therefore pro-
duced opposite deflections.

96. So also when the two conductors were
equidistant from the magnetic poles, as in PL
II, Fig. 1, no current at the galvanometer was
perceived, whichever way the disc was rotated,
beyond whfct was momentarily produced by ir-
regularity of contact; because equal currents
in the same direction tended to pass into both.
But when the two conductors were connected
with one wire, and the axis with the other wire,
(PL II, Fig. 2) then the galvanometer showed

lEARADAY

a current according with the direction of rota-
tion (91) ; both conductors now acting consen-
taneously, and as a single conductor did be*
fore (88). >

97. All these effects could be obtained when
only one df the poles of the magnet was brought
near to th plate; they were of the same kind
as to direction, &c., but by no means so pow-
erful. <

98. All care was taken to render these results
independent of the earth's magnetism, or of
the mutual magnetism of the magnet and gal-
vanometer needles. The contacts were made in
the magnetic equator of the plate, and at other
parts; the plate was placed horizontally, and
the poles vertically; and other precautions
were taken. But the absence of ,any interfer-
ence of the kind referred to, was readily shown
by the want of all effect when the disc was re-
moved from the poles, or the poles from the
disc; every other circumstance remaining the
same. <

99. The relation of the current of electricity
produced, to the magnetic pole, to the direc-
tion of rotation of the plate, &c., &c., may be
expressed by saying, that when the unmarked
pole (44, 84) is beneath the edge of the plate,
and the latter revolves horizontally, screw-
fashion, the electricity which can be collected
at the edge of the plate nearest to the pole is
positive. As the pole of the earth may mentally
be considered the unmarked pole, this relation
of the rotation, the pole, and the electricity
evolved, is not difficult to remember. Or if, in
PI. II, Fig. 8, the circle represent the copper
disc revolving in the direction of the arrows,
and a the outline of the unmarked pole placed
fobneath the plate, then the electricity collect-
ed at 6 and the neighbouring parts is positive,
whilst that collected at the centre c and other
parts is negative (88) . The currents in the lafce
are therefore from the centre by the magnetic
poles towards the circumference.

, 100. If the marked pole be placed above, all
other things remaining the same; the electri-
city at 6, PL II, Fig. 8, is still positive. If the
marked pole be placed below, or the unmarked
pole above, the electricity is reversed. If the
direction of revolution in any case is reversed,
the electricity is also reversed/' i , t

101. It is now evident that the, rota ting iplate
is merely 1 another form of the simpler experi-
ment of passing a piece of metal between^the
magnetic poles in a rectilinear direction* and
that in such cases currents of electricity! are
produced at right angles to the direction^ .the

motion, and crossing it at the place of the mag-*-
netic pole or pole& This was sufficiently shown
by the following simple experiment: A piecie of
copper plate one-fifth of &n inch thick, one inch
and a half wide, and twelve inches long, being
amalgamated at the edges, was placed between
the magnetic poles, whilst the two .conductors
from the galvanometer were held in contact
with its edges; it was then drawn through be*
tween the poles of the conductors in the direc-
tion of the arrow, PI. II, Fig. 4', immediately
the galvanometer needle was deflected, its north
or marked end passed eastward, indicating that
the wire A received Negative and the. wire B
positive electricity; and as the marked pole
was above, the result is in perfect accordance
with the effect obtained by the rotatory plate
(99).

102. On reversing the motion of the plate,
the needle at the galvanometer was deflected
in the opposite direction, showing an opposite
current. ^

103. To render evident the character) of the
electrical current existing in various parts of
the moving copper 4 plate, differing in their re-
lation to the inducing poles, one collector (86)
only was applied at the part to be examined
near to the pole, the other being connected
with the end of the plate as the most neutral
place: the results are given at PI. II, Figs. 5-8,
the marked pole being above the plate. In Fig.
5, B received positive electricity; but the plate
moving in the same direction, it received on
the opposite side, Fig. 6, negative electricity:
reversing the motion of the latter, a in Fig.
8, B received positive electricity; or reversing
the motion of the first arrangement, that of
Fig. 6 to Fig. 7 y B received negative electricity.

104. When the plates were previously re-
moved sideways from between the magnets, as
in PI. II, Fig. 9, so as to be quite out.df the po*
lar axis, still the same effects were produced,
though not so strongly.

105. When the magnetic poles were in con-
tact, and the copper plate was drawn- between
the conductors near to the place, there was but
very little effect produced. When -thb; .poles
were opened by the width* of a card, the effect
was somewhat more; but still very small.

106. When an! amalgamated copper, wire,
one-eighth of an inch thick, was drawn through
between the conductors and poles (101), it-pro-
duced a very considerable effect, though not so
much as the plates.; * i ,

107 . If the conductors were held permanent-
ly against any particular parts of the, copper

Nov. 1831

ELECTRICITY

281

plates, and carried between the magnetic poles
with them, effects the same as those described
were produced, in accordance with the results
obtained with the revolving disc (94).

108. On the conductors being held against
the ends of the plates, and the latter then passed
between the magnetic poles, in a direction trans-
verse to their length, the same effects were
produced (PI. II, Fig. 10). The parts of the
plates towards the end may be considered either
as mere conductors, or as portions of metal in
which the electrical current is excited, accord-
ing to their distance and the strength of the
magnet; but the results were in perfect har-
mony with those before obtained. The effect
was as strong as when the conductors were held
against the sides of the plate (101).

109. When a mere wire, connected with the
galvanometer so as to form a complete circuit,
was passed through between the poles, the gal-
vanometer was affected ; and upon moving the
wire to and fro, so as to make the alternate im-
pulses produced correspond with the vibra-
tions of the needle, the latter could be increased
to 20 or 30 on each side of the magnetic me-
ridian.

110. Upon connecting the ends of a plate of
metal with the galvanometer wires, and then
carrying it between the poles from end to end
(as in PI. II, Fig. 11), in either direction, no ef-
fect whatever was produced upon the galva-
nometer. But the moment the motion became
transverse, the needle was deflected.

111. These effects were also obtained from
electro-magnetic poles, resulting from the use of
copper helices or spirals, either alone or with
iron cores (34, 54). The directions of the mo-
tions were precisely the same; but the action
was much greater when the iron cores were
used, than without.

112. When a flat spiral was passed through
edgewise between the poles, a curious action at
the galvanometer resulted ; the needle first went
strongly one way, but then suddenly stopped,
as if it struck against some solid obstacle, and
immediately returned. If the spiral were passed
through from above downwards, or from below
upwards, still the motion of the needle was in
the same direction, then suddenly stopped, and
then was reversed. But on turning the spiral
half-way round, i.e., edge for edge, then the di-
rections of the motions were reversed, but still
were suddenly interrupted and inverted as be-
fore. This double action depends upon the
halves of the spiral (divided by a line passing
through its centre perpendicular to the direc-

tion of its motion) acting in opposite direc-
tions; and the reason why the needle went to
the same side, whether the spiral passed by
the poles in the one or the other direction, was
the circumstance, that upon changing the mo-
tion, the direction of the wires in the approach-
ing half of the spiral was changed also. The ef-
fects, curious as they appear when witnessed,
are immediately referable to the action of sin-
gle wires (40, 109).

113. Although the experiments with the re-
volving plate, wires, and plates of metal, were
first successfully made with the large magnet
belonging to the Royal Society, yet they were
all ultimately repeated with a couple of bar
magnets two feet long, one inch and a half
wide, and half an inch thick; and, by render-
ing the galvanometer (87) a little more deli-
cate, with the most striking results. Ferro-
electro-magnets, as those of Moll, Henry, &c.
(57), are very powerful. It is very essential,
when making experiments on different sub-
stances, that thermo-electric effects (produced
by contact of the fingers, &c.) be avoided, or at
least appreciated and accounted for; they are
easily distinguished by their permanency, and
their independence of the magnets, or of the
direction of the motion.

114. The relation which holds between the
magnetic pole, the moving wire or metal, and
the direction of the current evolved, i.e., the
law which governs the evolution of electricity
by magneto-electric induction, is very simple,
although rather difficult to express. If in PI. II,
Fig. 12, PN represent a horizontal wire passing
by a marked magnetic pole, so that the direc-
tion of its motion shall coincide with the curved
line proceeding from below upwards; or if its
motion parallel to itself be in a line tangential
to the curved line, but in the general direction
of the arrows; or if it pass the pole in other di-
rections, but so as to cut the magnetic curves 1
in the same general direction, or on the same
side as they would be cut by the wire if moving
along the dotted curved line then the cur-
rent of electricity in the wire is from P to N.
If it be carried in the reverse directions, the
electric current will be from N to P. Or if the
wire be in the vertical position, figured P' N',
and it be carried in similar directions, coincid-
ing with the dotted horizontal curve so far, as
to cut the magnetic curves on the same side

* By magnetic curves, I mean the lines of mag-
netic forces, however modified by the juxtaposition
of poles, which would be depicted by iron filings; or
those to which a very small magnetic needle would
form a tangent,

282

FARADAY

SERIES I

with it, the current will be from P' to N'. If the
wire be considered a tangent to the curved sur-
face of the cylindrical magnet, and it be carried
round that surface into any other position, or
if the magnet itself be revolved on its axis, so
as to bring any part opposite to the tangential
wire still, if afterwards the wire be moved in
the directions indicated, the current of elec-
tricity will be from P to N ; or if it be moved in
the opposite direction, from N to P ; so that as
regards the motions of the wire past the pole,
they may be reduced to two, directly opposite
to each other, one of which produces a current
from P to N, and the other from N to P.

115. The same holds true of the unmarked
pole of the magnet, except that if it be substi-
tuted for the one in the figure, then, as the
wires are moved in the direction of the arrows,
the current of electricity would be from N to
P, and when they move in the reverse direc-
tion, from P to N.

116. Hence the current of electricity which
is excited in metal when moving in the neigh-
bourhood of a magnet, depends for its direc-
tion altogether upon the relation of the metal
to the resultant of magnetic action, or to the
magnetic curves, and may be expressed in a
popular way thus : Let A B (PL II, Fig. 13) rep-
resent a cylinder magnet, A being the marked
pole, and B the unmarked pole; let P N be a
silver knife-blade, resting across the magnet
with its edge upward, and with its marked or
notched side towards the pole A; then in what-
ever direction or position this knife be moved
edge foremost, either about the marked or the
unmarked pole, the current of electricity pro-
duced will be from P to N, provided the inter-
sected curves proceeding from A abut upon
the notched surface of the knife, and those
from B upon the unnotched side. Or if the knife
be moved with its back foremost, the current
will be from N to P in every possible position
and direction, provided the intersected curves
abut on the same surfaces as before. A little
model is easily constructed, by using a cylinder
of wood for a magnet, a flat piece for the blade,
and a piece of thread connecting one end of
the cylinder with the other, and passing through
a hole in the blade, for the magnetic curves:
this readily gives the result of any possible di-
rection.

117. When the wire under induction is pass-
ing by an electro-magnetic pole, as for instance
one end of a copper helix traversed by the elec-
tric current (34), the direction of the current in
the approaching wire is the same with that of

the current in the parts or sides of the spirals
nearest to it, and in the receding wire the re-
verse of that in the parts nearest to it.

118. All these results show that the power of
inducing electric currents is circumferentially
exerted by a magnetic resultant or axis of pow-
er, just as circumferential magnetism is de-
pendent upon and is exhibited by an electric
current.

119. The experiments described combine to
prove that when a piece of metal (and the same
may be true of all conducting matter [213]) is
passed either before a single pole, or between
the opposite poles of a magnet, or near electro-
magnetic poles, whether ferruginous or not,
electrical currents are produced across the met-
al transverse to the direction of motion; and
which therefore, in Arago's experiments, will
approximate towards the direction of radii. If
a single wire be moved like the spoke of a
wheel near a magnetic pole, a current of elec-
tricity is determined through it from one end
towards the other. If a wheel be imagined,
constructed of a great number of these radii,
and this revolved near the pole, in the manner
of the copper disc (85) , each radius will have a
current produced in it as it passes by the pole.
If the radii be supposed to be in contact later-
ally, a copper disc results, in which the direc-
tions of the currents will be generally the same,
being modified only by the coaction which can
take place between the particles, now that
they are in metallic contact.

120. Now that the existence of these currents
is known, Arago's phenomena may be account-
ed for without considering them as due to the
formation in the copper, of a pole of the oppos-
ite kind to that approximated, surrounded by
a diffuse polarity of the same kind (82) ; neither
is it essential that the plate should acquire and
lose its state in a finite time; nor on the other
hand does it seem necessary that any repulsive
force should be admitted as the cause of the ro-
tation (82).

121. The effect is precisely of the same kind
as the electro-magnetic rotations which I had
the good fortune to discover some years ago. 1
According to the experiments then made which
have since been abundantly confirmed, if a
wire P N, (PI. II, Fig. 14) be connected with
the positive and negative ends of a voltaic bat-
tery, so that the positive electricity shall pass
from P to N, and a marked magnetic pole N be
placed near the wire between it and the spec-

i Quarterly Journal of Science, Vol. XII, pp. 74, 186,
416, 283.

Nov. 1831

ELECTRICITY

283

tator, the pole will move in a direction tangen-
tial to the wire, i.e., towards the right, and the
wire will move tangentially towards the left,
according to the directions of the arrows. This
is exactly what takes place in the rotation of a
plate beneath a magnetic pole; for let N (PI.
II, Fig. 15) be a marked pole above the circu-
lar plate, the latter being rotated in the direc-
tion of the arrow: immediately currents of pos-
itive electricity set from the central parts in
the general direction of the radii by the pole
to the parts of the circumference a on the other
side of that pole (99, 119), and are therefore
exactly in the same relation to it as the current
in the wire (PN, Fig. 14), and therefore the pole
in the same manner moves to the right hand.

122. If the rotation of the disc be reversed,
the electric currents are reversed (91), and the
pole therefore moves to the left hand. If the
contrary pole be employed, the effects are the
same, i. e. in the same direction, because cur-
rents of electricity, the reverse of those de-
scribed, are produced, and by reversing both
poles and currents, the visible effects remain
unchanged. In whatever position the axis of
the magnet be placed, provided the same pole
be applied to the same side of the plate, the
electric current produced is in the same direc-
tion, in consistency with the law already stat-
ed (114, &c.) ; and thus every circumstance re-
garding the direction of the motion may be ex-
plained.

123. These currents are discharged or return
in the parts of the plate on each side of and
more distant from the place of the pole, where,
of course, the magnetic induction is weaker;
and when the collectors are applied, and a cur-
rent of electricity is carried away to the gal-
vanometer (88), the deflection there is merely
a repetition, by the same current or part of it,
of the effect of rotation in the magnet over the
plate itself.

124. It is under the point of view just put
forth that I have ventured to say it is not nec-
essary that the plate should acquire and lose
its state in a finite time (120) ; for if it were pos-
sible for the current to be fully developed the
instant before it arrived at its state of nearest
approximation to the vertical pole of the mag-
net, instead of opposite to or a little beyond it,
still the relative motion of the pole and plate
would be the same, the resulting force being in
fact tangential instead of direct.

125. But it is possible (though not necessary
for the rotation) that time may be required for
the development of the maximum current in

the plate, in which case the resultant of all the
forces would be in advance of the magnet when
the plate is rotated, or in the rear of the mag-
net when the latter is rotated, and many of the
effects with pure electro-magnetic poles tend
to prove this is the case. Then, the tangential
force may be resolved into two others, one par-
allel to the plane of rotation, and the other per-
pendicular to it; the former would be the force
exerted in making the plate revolve with the
magnet, or the magnet with the plate; the lat-
ter would be a repulsive force, and is probably
that, the effects of which M. Arago has also
discovered (82).

126. The extraordinary circumstance accom-
panying this action, which has seemed so inex-
plicable, namely, the cessation of all phenom-
ena when the magnet and metal are brought to
rest, now receives a full explanation (82); for
then the electrical currents which cause the
motion cease altogether.

127. Ail the effects of solution of metallic
continuity, and the consequent diminution of
power described by Messrs. Babbage and Her-
schel, 1 now receive their natural explanation,
as well also as the resumption of power when
the cuts were filled up by metallic substances,
which, though conductors of electricity, were
themselves very deficient in the power of in-
fluencing magnets. And new modes of cutting
the plate may be devised, which shall almost
entirely destroy its power. Thus, if a copper
plate (81) be cut through at about a fifth or
sixth of its diameter from the edge, so as to sep-
arate a ring from it, and this ring be again
fastened on, but with a thickness of paper inter-
vening (PI. II, Fig. 77), and if Arago's experi-
ment be made with this compound plate so ad-
justed that the section shall continually travel
opposite the pole, it is evident that the mag-
netic currents will be greatly interfered with,
and the plate probably lose much of its effect. 2

An elementary result of this kind was ob-
tained by using two pieces of thick copper,
shaped as in Fig. 16. When the two neighbour-
ing edges were amalgamated and put together,
and the arrangement passed between the poles
of the magnet, in a direction parallel to these
edges, a current was urged through the wires
attached to the outer angles, and the galvanom-
eter became strongly affected; but when a sin-
gle film of paper was interposed, and the exper-

i Philosophical Transactions, 1825, p. 481.

This experiment has actually been made by Mr.
Christie, with the results here described, and is re-
corded in the Philosophical Transactions for 1827,
p. 82.

284

FARADAY

SERIES I

iment repeated, no sensible effect could be pro-
duced.

128. A section of this kind could not inter-
fere much with the induction of magnetism,
supposed to be of the nature ordinarily re-
ceived by iron.

129. The effect of rotation or deflection of
the needle, which M. Arago obtained by ordi-
nary magnets, M. Ampere succeeded in pro-
curing by electro-magnets. This is perfectly in
harmony with the results relative to volta-
electric and magneto-electric induction de-
scribed in this paper. And by using flat spirals
of copper wire, through which electric currents
were sent, in place of ordinary magnetic poles
(111), sometimes applying a single one to one
side of the rotating plate, and sometimes two
to opposite sides, I obtained the induced cur-
rents of electricity from the plate itself, and
could lead them away to, and ascertain their
existence by, the galvanometer.

130. The cause which has now been assigned
for the rotation in Arago's experiment, name-
ly, the production of electrical currents, seems
abundantly sufficient in all cases where the
metals, or perhaps even other conductors, are
concerned; but with regard to such bodies as
glass, resins, and, above all, gases, it seems im-
possible that currents of electricity, capable of
producing these effects, should be generated in
them. Yet Arago found that the effects in
question were produced by these and by all
bodies tried (81). Messrs. Babbage and Her-
schel, it is true, did not observe them with any
substance not metallic, except carbon, in a
highly conducting state (82). Mr. Harris has
ascertained their occurrence with wood, mar-
ble, freestone and annealed glass, but obtained
no effect with sulphuric acid and saturated so-
lution of sulphate of iron, although these are
better conductors of electricity than the former
substances.

131. Future investigations will no doubt ex-
plain these difficulties, and decide the point
whether the retarding or dragging action spok-
en of is always simultaneous with electric cur-
rents. 1 The existence of the action in metals,
only whilst the currents exist, i.e., whilst mo-
tion is given (82, 88), and the explication of
the repulsive action observed by M. Arago

1 Experiments which I have since made convince
me that this particular action is always due to the
electrical currents formed; and they supply a test
by which it may be distinguished from the action of
ordinary magnetism, or any other cause, including
those which are mechanical or irregular, producing
similar effects (254).

(82, 125), are powerful reasons for referring it
to this cause; but it may be combined with
others which occasionally act alone.

132. Copper, iron, tin, zinc, lead, mercury,
and all the metals tried, produced electrical
currents when passed between the magnetic
poles: the mercury was put into a glass tube
for the purpose. The dense carbon deposited in
coal gas retorts, also produced the current, but
ordinary charcoal did not. Neither could I ob-
tain any sensible effects with brine, sulphuric
acid, saline solutions, &c., whether rotated in
basins, or inclosed in tubes and passed between
the poles.

133. 1 have never been able to produce any
sensation upon the tongue by the wires con-
nected with the conductors applied to the edges
of the revolving plate (88) or slips of metal
(101). Nor have I been able to heat a fine plat-
ina wire, or produce a spark, or convulse the
limbs of a frog. I have failed also to produce
any chemical effects by electricity thus evolved
(22, 56).

134. As the electric current in the revolving
copper plate occupies but a small space, pro-
ceeding by the poles and being discharged right
and left at very small distances comparatively
(123) ; and as it exists in a thick mass of metal
possessing almost the highest conducting pow-
er of any, and consequently offering extraor-
dinary facility for its production and discharge;
and as, notwithstanding this, considerable cur-
rents may be drawn off which can pass through
narrow wires, forty, fifty, sixty, or even one
hundred feet long; it is evident that the cur-
rent existing in the plate itself must be a very
powerful one, when the rotation is rapid and
the magnet strong. This is also abundantly
proved by the obedience and readiness with
which a magnet ten or twelve pounds in weight
follows the motion of the plate and will strong-
ly twist up the cord by which it is suspended.

135. Two rough trials were made with the in-
tention of constructing magneto-electric ma-
chines. In one, a ring one inch and a half broad
and twelve inches external diameter, cut from
a thick copper plate, was mounted so as to re-
volve between the poles of the magnet and rep-
resent a plate similar to those formerly used
(101), but of interminable length; the inner
and outer edges were amalgamated, and the
conductors applied one to each edge, at the
place of the magnetic poles. The current of
electricity evolved did not appear by the gal-
vanometer to be stronger, if so strong, as that
from the circular plate (88).

Nov. 1831

ELECTRICITY

285

136. In the other, small thick discs of copper
or other metal, half an inch in diameter, were
revolved rapidly near to the poles, but with
the axis of rotation out of the polar axis; the
electricity evolved was collected by conductors
applied as before to the edges (86). Currents
were procured, but of strength much inferior
to that prodi^ed by the circular plate.

137. The latter experiment is analogous to
those made by Mr. Barlow with a rotating iron
shell, subject to the influence' of the earth. 1 The
effects obtained by him have been referred by
Messrs. BabrJage and Herschel to the same
cause as that considered as influential ,in Ara-
go's experiment', 2 but it would be investing
to' know hbw far the electric current which
might be produced in the experiment would ac-
count for the deflexion of the needle. The mere
inversion of a copper wire six or seven times
near the poles of the magnet, and isochronous-
ly with the vibrations of the galvanorrieier
needle connected with it, was sufficient to make
the needle vibrate through an arc of 60 or 70.
The rotation of a copper shell would perhaps
decide the point, and might even throw light
upon the mom permanent, though somewhat
analogous effects obtained by Mr. Christie.

138. The remark which has already been
made respecting iron (66), and the independ-
erice of the ordinary magnetical phenomena of
that substance and the phenomena now de-
scribed of magneto-electric induction 1 in that
and other metals, was fully confirmed by many
results of the kind detailed in this section.
When an iron plate similar to the copper one
formerly described (101) was passed between
the magnetic poles, it gave a current of elec-
tricity like the copper plate, but decidedly of
less power; and in the experiments upon the in-
duction of electric currents (9), ho difference
in the kind of action between iron and other
metals could be perceived. The power there-
fore of an iron plate to drag a magnet after it,
or to intercept magnetic action, should be care-
fully distinguished from the similar power of
such metals as silver, copper, &c. ; &c., inas-
much as in the iron by far the greater part of
the effect is due to what may 'be called ordi-
nary magnetic action. There can be no doubt
that the cause assigned by Messrs. Babbage
and Herschel in explication cff Arago's phenom-
ena is the trtie one, when iron is the inetal used.

Philosophical Transactions, 18?5, p. 317.
*Ibid., 1825; D. 485.

139. The very feeble powers which were found
by those philosophers to belong to bismuth
and antimony, when moving, of affecting the
suspended magnet, and which has been con-
firmed by Mr. Harris, seem at first dispropor-
tionate to their conducting powers; whether it
be so o* not must be decided by future experi-
ment (73) . 3 These metals are highly crystalline,
and probably conduct electricity with different
degrees of facility in different directions; and
it is not Unlikely that where a mass is made up
of a number of crystals heter.ogeneously assoc-
iated, an effect approaching to that of actual
division rimy occur (127); or the currents of
electricity may become more suddenly deflect-
ed at the confines of similar crystalline arrange-
ments, and so be more readily and completely
discharged within the mass.

Royal Institution, November 1831.

Note. In consequence of the long period which has
intervened between the reading and printing bf the
foregoing paper, accounts of the experiments have
been dispersed, and, through a letter of my qwn to
M. Hachette, have reachea France and Italy. That
letter was translated (with some errors) , and read to
the Academy of Sciences at Paris, 26th December,
1831. A copy of it in Le Temps of the 28th December
quickly reached Signor Nobili, who, with Signor An-
tinori, immediately experimented upon the subject,
and obtained many of the results mentioned in my
letter; others they could not obtain or understand,
because of the brevity of my account. These results
by Signor Nobili and Antinori have been embodied
in a paper dated 31st January, 1832, and printed
and published in the number of the Antologia dated
November, 1831 (according at, least to the copy of
the paper kindly sent me by Signor Nobili). It is evi-
dent the work could not have been then printed ; and
though Signor Nobili,- in his paper, has inserted my
letter as the text of his experiments, yet the circum-
stance of back date has caused many here, who have
hear.d of Nobili 's experiments by report only, to im-
agine his results were anterior to, instead of being
dependent upon, mine. (

I may be allowed under these circumstances to re-
mark, that I experimented on this subject several
years ago, and have published results. (See Quarterly
Journal of Science for July, 1825, p. 338.) The follow-
ing, also is an extract from my note-book, dated No-
vember 2$, 1825: "Experiments on induction by
cbnriecting wire of voltaic battery: a battery of four
troughs, ten pairs of plates, each arranged side by
side the poles connected by a wire about, four feet
long, parallel to which was another similar wire sep-
arated from it only by two thicknesses of paper, the
ends of the latter were attached to a galvanometer:
exhibited ho action, &c., &c., &c. Could not in any
way reiider any induction evident from the connect-
ing wire." The cause of failure at that time is now
evident (70). M. F. April, 1832.

8 1 have since been able to explain these differ-
ences, and prove, with several metals, that the effect
is in the order of the conducting power; for, I have
been able t6 obtain, by magneto-electric induction,
currents of electricity which are proportionate in
strength to the conducting power of the bodies ex-
perimented with (211).

SECOND SERIES

5. Terrestrial Magneto-electric Induction 6. General Remarks
and Illustrations of the Force and Direction of Magneto-electric In-
duction

THE BAKERIAN LECTURE, Read January 12, 1832

5. Terrestrial Magneto-ekctric Induction
140. WHEN the general facts described in the
former paper were discovered, and the law pf
magneto-electric induction relative to direction
was ascertained (114), it was not difficult to
perceive that the earth would produce the same
effect as a magnet, and to an extent that would,
perhaps, render it available in the c6nstruc-
tiqn of new electrical machines. The following
are some of the results obtained in pursuance
of this view.

J.41. The hollow helix already described (6)
was connected with a galvanometer by wires
eight feet long; and the soft iron cylinder (34)
after being heated red-hot and slowly cooled,
to remove ail traces of magnetism, was put into
the helix so as to project equally at both ends,
and fixed there. The combined helix and bar
were held in the magnetic direction or line of
dip, and (the galvanometer needle being mo-
tionless) were then inverted, so that the lower
end shpuld become the upper, but the whole
still correspond to the magnetic direction; the
needle was immediately deflected. As the lat-
ter returned to its first position, the helix and
bar were again inverted; and by doing this two
or three times, making the inversions and vi-
brations to coincide, the needle swung through
an arc of 160 or 160.

142. When one end of the helix, which may
be called A, was uppermost at first (B end con-
sequently being below), then it mattered not
in which direction it proceeded during the
inversion, whether to the right hand or left
hand, or through any other course; still the
galvanometer needle passed in the same di-
rection. Again, when B end was uppermost,
the inversion of the helix and bar 'in any di-
rection always caused the needle to be de-
flected one way; that way being the opposite
to the course of the deflection in the former
case.

143. When the helix with its iron core in any
given position was inverted, the effect was as

if a magnet with its marked pole downwards
had been introduced from above into the in-
verted helix. Thus, if the end B were upwards,
such a magnet introduced from above would
make the marked end of the galvanometer
needle pass west. Or the end B being down-
wards, and the soft iron in its place, inversion
of the whole produced the same effect.

144. When the soft iron bar was taken out of
the helix and inverted in various directions
within four feet of the galvanometer, not the
slightest effect upon it was produced.

145. These phenomena are the necessary con-
sequence of the inductive magnetic power of
the earth, rendering the soft iron cylinder a
magnet with its marked pole downwards. The
experiment is analogous to that in which two
bar magnets were used to magnetize the same
cylinder in the same helix (36), and the inver-
sion of position in the present experiment is
equivalent to a change of the poles in that ar-
rangement. But the result is not less an in-
stance of the evolution of electricity by means
of the magnetism of the globe.

146. The helix alone was then held perman-
ently in the magnetic direction, and the soft
iro/i cylinder afterwards introduced; the gal-
vanometer needle was instantly deflected; by
withdrawing the cylinder as the needle re-
turned, and Continuing the two actions simulta-
neously, the vibrations soon, extended through
an arc of 180. The effect was precisely the
same as that obtained by using a cylinder mag-
net with its marked pole downwards; and the
direction of motion, &c. was perfectly in ac-
cordance with the results of former experiments
obtained with such a magnet (39). A magnet
in that position being used, gave the same de-
flection^, but stronger. When the helix was put
at right angles to the magnetic direction or
dip, then the introduction or removal of the
soft iron cylinder produced no effect at the
needle. Any inclination to the dip gave results
of the same kind as those already described,

286

Jon. 1832

ELECTRICITY

287

but increasing in strength as the helix! approx-
imated to the direction of the dip.

147 . A cylinder magnet, although it has great
power of affecting the galvanometer when mov-
ing into or out of the helix, has no power of
continuing the deflection (39); and therefore,
though left in, still the magnetic needle 'comes
to its usual place of rest. But upon repeating
(with the magnet) the^xperiment of inversion
in the direction 6f the dip (141), the needle was
affected as powerfully as before; the disturb-
ance of the magnetism in the steel magnet, by
the earth's inductive force upon it, being thus
shown to be nearly, if not quite, equal in
amount and rapidity to that occurring in soft
iron. It is probable that in this way magneto-
electrical arrangements may become very use-
ful in indicating the disturbance of magnetic
forces, where other means will not apply; for
it is not the whole magnetic power which pro-
duces the visible effect, but only the difference
due to the disturbing causes.

148. These favourable results led me to hope
that the direct magneto-electric induction of
the earth might be rendered sensible; and I
ultimately succeeded in obtaining the effect in
several ways. When the helix just referred to
(141, 6) was placed in the magnetic dip, but
without any cylinder of iron or steel, and was
then inverted, a feeble action at the needle was
observed. Inverting the helix ten or twelve
times, and at such periods that the deflecting
forces exerted by the currents of electricity
produced in it should be added to the momen-
tum of the needle (39), the latter was soon
made to vibrate through an arc of 80 or 90.
Here, therefore, currents of electricity were
produced by the direct inductive power of the
earth's magnetism, without the use of any fer-
ruginous matter, and upon a metal not cap-
able of exhibiting any of the ordinary magnetic
phenomena. The experiment in everything rep-
resents the effects produced by bringing the
same helix to one or both poles of any power-
ful magnet <50).

1 149. Guided by the law already expressed
(114), I expected that all the electric phenom-
ena of the revolving metal plate could now be
produced without any other magnet than the
earth. The plate so often referred to (85) was
therefore fixed so as to rotate in a horizontal
plane. The magnetic curves of the earth (114,
note), i.e., the dip, passes through this plane at
angles of about 70, which it was expected
would be an approximation to perpendicular-
ity, quite enough >to allow of magneto-electric

induction sufficiently powerful to produce a
current of- electricity.

150. Upon rotation of the plate, the currents
ought, according to the law (114, 121), to tend
to pass in the direction of the radii, through all
parts of the plate, either from the centre to the
circutaference, or from the circumference to
the centre, as the direction of the rotation of
the plate was one way or the other. One of
the wires of the galvanometer was therefore
brought in contact with the axis of the plate,
and the other attached to a leaden collector or
conductor (86), which itself was placed against
the amalgamated edge of the disc. On rotating
the plate there was a distinct effect at the gal-
vanometer needle; on reversing the rotation,
the needle went in the opposite direction; and
by making the action of the plate coincide with
the vibrations of the needle, the 1 arc through
which the latter passed soon extended to half
a circle.

151. Whatever part of the edge of the plate
was touched by the conductor, the electricity
was the same, provided the direction of rota-
tion continued unaltered.

152. When the plate revolved screw-fashion,
or as the hands of a watch, the current of elec-
tricity (150) was from the centre to the circum-
ference; when the direction of rotation was un-
screw, the current was from the circumference
to the centre. These directions are the same
with those obtained when the unmarked pole
of a magnet was placed beneath the revolving
plate (99).

153. When the plate was in the magnetic
meridian, or in any other plane coinciding with
the magnetic dip, then its rotation produced
no effect upon the galvanometer. When inclined
to the dip but a few degrees, electricity began
to appear upon rotation. Thus when standing
upright in a plane perpendicular to the mag-
netic meridian, and when consequently its own
plane was inclined only about 20 to the dip,
revolution of the plate evolved electricity. As
the inclination was increased, the electricity
became more powerful until the angle formed
by the plane of the plate with the dip was 90,
when the electricity for a given velocity of the
plate was a maximum.

154. It is a striking thing to observe the re-
volving copper plate become thus a new elec-
trical machine; and curious results arise on com-
paring it with the common machine. In the
one, the plate is of the best non-conducting
substance that can be applied; in the other, it
is the most perfect conductor: in the one, insu-

288

FARADAY

SERIES II

,lation is esseiitial; in the other, it is fatal. In
comparison of the quantities of electricity pro-
duced, the metal machine does not at all fall
ibeiow the glasd one; for it can produce a con-
stant current capable of deflecting, the galva-
nometer needle, whereas the latter cannot. It
is quite true that the force of the current thus
evolved has not as yet been increased so as to
render it available in any of our ordinary appli-
cations of this .power; but there appears every
reasonable expectation that this may hereafter
be, effected; and probably by several arrange-
ments. Weak as the current may seem to be,
it is as strong as, if not stronger than, any
thermo-electric current; for it can pass fluids
(23), agitate the animal system, and in the case
of an electro-magnet has produced sparks (32).

155. A disc of copper, one-fifth of an inch
thi