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COPYRIGHT UNDER INTERNATIONAL COPYRIGHT UNION BY ENCYCLOPAEDIA BRITANNICA, INC. ALL RIGHTS RESERVED UNDER PAN AMERICAN COPYRIGHT CONVENTIONS BY ENCYCLOPEDIA BRITANNICA, INC. 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. IX 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 lf 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 XI 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 Lixiviationr 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 5 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 S3rstem. 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 6 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 zero1 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. 10 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 17771, I gave it the names of igneous fluid and matter of heat: And, since that time, in the work2 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 11 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 ether1 a small narrow glass vessel A (Plate vu, Fig. 77), standing upon its stalk P, the vessel, which is from twelve to fifteen lines2 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 32P (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. 12 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, 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 29 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 o£us. 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 30 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 31 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. 32 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 Ddf. 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 Dd1, 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 place3 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 apparatus1 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 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. 40 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 41 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. 42 LAVOISIER TABLE I. Materials of Fermentation Water Sugar Yeast in paste, 10 Ibs. composed of Water Dry yeast Total Ibs. oz. gros grs. 400 0 0 0 100 0 0 0 7 3 6 44 2 12 1 28 510 0 0 0 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 61 1 2 71.40 Oxygen 346 2 3 44.60 Hydrogen 8 0 0 0 Oxygen 64 0 0 0 Charcoal 28 0 0 0 Hydrogen 0 4 5 9.30 Oxygen 1 10 2 28.76 Charcoal 0 12 4 59 Azote 0 0 5 2.94 Total 510 0 0 0 TABLE III. Recapitulation of these Elements Ibs. oz. gros grs. Ibs. oz. gros grs. of water 340 0 0 0 i § of water in yeast of sugar 6 64 2 0 3 0 44.60 0 411 12 6 1.36 of dry yeast 1 10 2 28.76 g of water 60 0 0 0 $>» of water in yeast of sugar 1 8 1 0 2 0 71.40 0 69 6 0 8.70 w of dry yeast 0 4 5 9.30 |1 of sugar of yeast 28 0 0 12 0 4 0 59.00 28 12 4 59.00 Azote of yeast 0 0 5 2.94 Total 510 0 0 0 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 proper1 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 43 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 10 0 '59 of water, composed of Hydrogen 61 5 4 27 Oxygen, combined with hydrogen 31 6 1 64 Hydrogen, combined 57 Ibs. 1 1 oz. 1 gros 58 grs. of with oxygen 5 8 5 3 dry alcohol, composed Hydrogen, combined of with charcoal 4 0 5 0 Charcoal, combined with hydrogen 16 11 5 63 2 Ibs. 8 oz. of dry acetous acid, composed of Hydrogen 0 Oxygen 1 Charcoal 0 2 11 10 4 4 0 0 0 0 4 Ibs. 1 oz. 4 gros 3 grs. of Hydrogen 0 5 1 67 residuum of sugar, Oxygen 2 9 7 27 composed of Charcoal 1 2 2 53 Hydrogen 0 2 2 41 1 Ib. 6 oz. 0 gros 5 grs. of Oxygen 0 13 1 14 dry yeast, composed of Charcoal 0 6 2 30 Azote 0 0 2 37 510 Ibs. Total 510 0 0 0 TABLE V. Recapitulation of the Products Ibs. oz. gros grs. Water 347 10 0 59 Carbonic acid 25 7 1 34 409 Ibs. 10 oz. 0 gros 54 grs. Alcohol 31 6 1 64 of oxygen contained in Acetous acid 1 11 4 0 the Residuum of sugar 2 9 7 27 Yeast 0 13 1 14 Carbonic acid 9 14 2 57 28 Ibs. 12 oz. 5 gros 59 grs. of charcoal contained in thft Alcohol 16 Acetous acid 0 Residuum of sugar 1 11 10 2 5 0 2 63 0 53 I/ 11" Yeast 0 6 2 30 Water 61 5 4 27 Water of the alcohol 5 8 5 3 71 Ibs. 8 oz. 6 gros 66 grs. of hydrogen, contained in Combined with the charcoal of the al- cohol 4 0 5 0 the Acetous acid 0 2 4 0 Residuum of sugar 0 5 1 67 Yeast 0 2 2 41 2 gros 37 grs. of azote in the yeast 0 0 2 37 510 Ibs. Total 510 0 0 0 44 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 45 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. 46 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 47 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 alkalies1 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 48 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 49 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- 50 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 51 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 52 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 53 54 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, 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- 64 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 65 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 66 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 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 iron in nitrous and nitric acids, manganese manganese metallic salts must of con- cobalt* cobalt sequence be formed having nickel nickel different degrees of oxygen- ation. Those wherein the lead lead metal is least oxygenated tin tin must be called Nitrites, when more so, Nitrates; but copper bismuth copper bismuth the limits of this distinc- tion are difficultly ascertain- antimony antimony able. The older chemists arsenic arsenic were not acquainted with any of these salts. mercury 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 67 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 iron manganese manganese cobalt cobalt nickel nickel lead lead tin tin copper copper bismuth bismuth antimony antimony arsenic 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 lime2 Phosphates of lime3 Barytes barytes barytes Magnesia magnesia magnesia Potash potash potash Soda soda soda Ammonia ammonia ammonia Argill argill argill Oxides of zinc1 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. 70 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 Bases1 New Names Barytes Carbonates of barytes Lime lime Potash potash Soda soda Magnesia magnesia Ammonia ammonia Argill argill Oxide of zinc zinc iron iron manganese cobalt manganese cobalt nickel nickel lead lead tin tin copper bismuth copper bismuth antimony antimony arsenic arsenic mercury silver mercury silver gold platinum gold platinum CHEMISTRY 71 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. 72 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 copper bismuth antimony antimony arsenic 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 73 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 manganese iron iron lead lead tin tin cobalt cobalt copper copper nickel nickel arsenic arsenic bismuth bismuth mercury mercury silver silver gold gold platinum 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, 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 90 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 91 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 92 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 93 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- 94 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 95 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 96 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 97 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 27.5—6 = 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,0 ,. . , x=~ = 92.143 cubic inches. ^o 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 }^i5 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 Zo 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%Q0 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 Sty 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%0o 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 Boyle1 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 sey 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 Beaume1 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 IV 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 AA Fig. 6 Fig. 7 Fig. 3 Fig. 5 Fig. 8 Fig. 10 PLATE IX PLATE XI 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: P , 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-gtcos 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*~CDSV' 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 d£o d*v dx* dy* 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'+P2)*. 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 (Soci£t6 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. 1Gay-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 xt yt 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 (x) of the dis- tance x, at which the section is situated. It is required to find an analytical expression of the function (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 0 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 0 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 0 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 0 : 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, py 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, qy 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 M9 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 a11 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 Mf 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)(p) -dt. We denote by (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 an ', £", 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 mf 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', zf 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 vr of the point mf 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 v—v' = (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 Bf; 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 0 = 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 V /*' \ 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 nf in the first body, one of which n is be- low the plane L and the other n' above this plane: x, yy z are the co-ordinates of n: and x'9 y', zr 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 — uf. Substituting v and then v1 in the equation which belongs to the first solid, and subtracting, we find v — vf — (2 — z')] we have also by means of the 6 second equation u — uf= — -f — (2 — 2'), whence the ratio of the two actions in x- • xu * ra~fcx *'-*>' 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 6 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 ef 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 „ Tra~-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 rra~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 e 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. e 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. c From this may be derived a— ft = h -\-K ' an e(luat^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 <2 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 G 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 - - , G 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 = 0 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 = 0 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 4Z2 : 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 — 4l2Kd ( -T- J, whence -7-7 = -7^ v. \dxj' dx2 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 —4l2K-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 6 which passes through the first surface into the lamina, whose thickness is dx9 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- mal1) ; 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 BG+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 whence J 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 1Reaumer'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 x2 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 xz 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 , whence ^ = ^. 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 \/2Khl3 • 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 ey 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 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 j9 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 sy 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(b—a'). 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 Trnm~~ 'n shell, KS - . € Lastly, as the expression of the quantity which passes through the outer surface into the air, hS(n—a). All these quantities must be equal, we have therefore the following equa- tions: T£ h(n — d)— — (ra — n), Tf moreover we write down the identical equation h(n—a) =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\, m2, ?i2, m3, n3, m4, n4, &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 : b—mi = b — m\, He ,, ^ mi—ni = -g- (6 — mi), ni — m2 = & — Wi, He ^ ^ m2— n2 = -£- (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 mf 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', zf 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 m1 depends on the distance mm', which separates these molecules, and it is proportional to the difference v — vf 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')dty and the coefficient q is the same as in the expression q(v — v')dty 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 — wr 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(v—w) the action of m on M during the unit of time, we shall have q(v — w') to express the action of m on M7, 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 —cKy 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 mf 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 yy 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/, zf; 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, 0 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 0 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 = 0 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- a 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 a 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 g 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 0 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 0 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 dx2 It acquires therefore by reason of its position a quantity of heat equal to the difference of the two preceding quantities, that is rf2D KS^dxdt. dx2 On the other hand, the same slice, whose external surface is Idx and whose temperature differs infinitely little from vy 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 d2v 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 0 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 0 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 dx2 CDSV ' " " 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, x2j x3, x4, &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 — - - = ax+a~x. 02 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, 02, 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 ax+«~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 v% 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 ax+c*-x = <7. One of the roots is ax, and other root is a~x. This quantity being determined, we may derive from it the value of the ratio jz , which is o y (log a)2. Denoting ax by w, we shall have a?2 — qu+l =0. Thus the ratio of the or two conductivities is found by multiplying y by the square of the hyperbolic logarithm of one of the roots of the equation co2 — qu+1 = 0, and dividing the product by X2. 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 xt 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 dty the extent 4wx2 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 x2-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 0 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 4irCDx2dx is the quantity of heat necessary to raise the intervening shell from temperature 0 to temperature 1. Hence it is requisite to divide the quantity of heat which accumulates in this shell by 47rCDx2dx, and we shall then find the increase of its temperature v during the time dt. We thus obtain the equation * K ^ = JL (^ 4. ? d"\ ( \ dt CD ' \dx* + x dx) ' (C)' or 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 0 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 (x, t) the function of x and t, which expresses the value of Vj the two equations dv K Sd2v . 2 dv Further, it is necessary that the initial state should be represented by the same function 0(#, 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?rX2. 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 ^hirX2Vdt to the value which the expression —4K7rX2 -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 <^(xy 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, (xy 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 0 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 ax 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 aPPlles 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. j 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(^\ , dy the last differential being taken with respect to y only. Hence the difference of d2v the two quantities, or Kdxdydz -T-J , expresses the quantity of heat which the dy 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 d2v d2v d2v n dx2 + dy2 + dz2 ' 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- . ay 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 d2v d*v dx2 + 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 = 0 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 dty 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+dx9 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 $d2v . d'2v . d2v\ ,. or A dx dy dz < -=-= + -p-r + -r-^ > dt. \dx* dy2 dz2) 128. If the quantity which has just been found be divided by that which is necessary to raise the molecule from the temperature 0 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 /d2v d2v , d2v Tt ~~ C^D\dx2 + dy* + 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+ 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 = A—ax — by — cz, whence we conclude that, v — w = a 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 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 vf. 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 mf on JJL, or the quantity of heat which n receives from m and from m', is expressed by q(v—w+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 = c—c(z+h), v = c—cz, 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 mf 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 = A—ax— by—cz. 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 xy 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/', zf 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 dvf . dvf . to dv' t 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 vf, -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 \dx2 + dy2 "*" dz2) 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. az 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-rdt—K 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-dzdxdt—K -~ — —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 mf 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 0 to the temperature 1 ; the product CD dx dy dz expresses the quantity of heat required to raise from 0 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? + dy2 + 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 (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{_ /d2v d2^ dv2\ dt ~~ CD \dx2 + dy2 + dz2) ' 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 (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 = 0 ; 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: a. 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 (m2+n2+p2)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 : aa dz 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 dv dz 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\Txdx+Txdx+Tydy)> dv 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 , , KTxdxdxdy- 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 dz \dz/ dz2 ' and consequently __ , , , w + w +r \^ + a?/ • The first equation, whose first member is equal to r2, gives the second gives, when we substitute for its value 1, dz2 r ' If the values given by equations (6) and (c) be now substituted in (a), we have d^v.cPvdfv.l dv ~dy* + dz2 ~ dr2 + r dr * Hence the equation which expresses the movement of heat in the cylinder, is *!? j. 1 *! dr2 + 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 jd2^^^ /dr\2_, dv dV dx ~ dr dx an(1 dz2 ~ dr2 \dx) + dr dx* ' dv _ dv dr .d^^d2^ /dr\2 , dv dy "" dr dy aml dy2 ~ dr2 \dy) + dr 248 FOURIER CHAP. II ^_ — — — A — — d2v f^!\2 i ^ d*T "dz ~ dr ~dz ancl dz2 ~~ d72 \^5/ + dr 5F2 * Making these substitutions in the equation dv = _K_ {d?± , d^; d2^) dt CD Idz2 + dy2 + d22J f we shall have dv K_ rd2v (/dr\2 , /dr\2 , /dr\2l , dv (d2r , d2r dt ~~ CD (dr\\ dv \dz) ] + Tr The equation x*+y2+z2 = r2 gives the following results: dr , , (dr\ , cPr x = r -j- and 1 = 1 3- I +r ~r-9 , dx \dx/ dx2 ' dr . t fdr\ , d2r y = r -r- and 1 = ( -r- 1 +r ^-^ , % \rft// dy2> dr , , /dr\2 . d*r z = r -7- and 1 = I -5- I +r -7-^ . d-e \d^/ dz2 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 W2 W d^) : and substituting for /drV /drV / Vrfxy + Vw \ its value 1, we have dV dV dV = 2 dx2 + dy2 ~*~ dz2 r ' Making these substitutions in the equation (a) we have the equation dv K (d2v 2 dv\ dt CD (dr2 ^ 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 0 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 0 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 mxy 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, hy becomes — -5 ; for it tn 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 ' m2 ' m3 > > > 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 xt 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 1 0 0 t( a a ft * 0 1 0 it tt tt tt .. 0 0 1 The specific conducibility, K —1 1 -1 The surface conducibility, h -2 -1 — 1 The canacitv for heat. c ^ 0 -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 0 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,