on ■ ^■, !^,-^: 'j^":^.^-'~;.-'y'': 1^ ►■s- 'Vr-.. ^ h?'f i .^^9 :^>n-?i <« yy^o^ A 10 t THE GIFT OF \< Z[A.Q,q_%._ ^ L^iJlmp-^,. 7673-1 The date shows when this volume was taken. -■■f CORNELL UNIVERSITY LIBRARY 3 1924 052 989 047 OLIN LlSr.ARY-CiRCUlATION DATE DUE tlAY ttf~ 188)*^^ tT^ QAYLORD PRINTED IN U.S.A. Avogadro and Dalton The Standing in Chemistry of their Hypotheses ANDREW N. MELDRUM, D.Sc. WITH A l>REl'A<:ii: IIV FRANCIS R. JAPP, M.A., LL.D., F.R.S. /V.yior';- of Cluiiiislry in llie Lhinmily of -M'lidetn Aberdeen Printed for the University 1904 Cornell University Library The original of this bool< is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924052989047 Aberdeen University- Studies : No. lo Avogadro and Dalton .n ^ Aio UNIVERSITY OF ABERDEEN. COMMITTEE ON PUBLICATIONS. Convener: Professor James W. H. Trail, M.A., M.D., F.R.S., Curator of the University Library. UNIVERSITY STUDIES. General Editor: Peter John Anderson, M.A., LL.B., Librarian to the University. No. I. — Roll of Alumni in Arts of the University and King's College of Aberdeen, 1596-1860. Edited by P. J. Anderson, igoo. No. 2.— The Records of Old Aberdeen, 1157-1891. Edited by Alexander Mac- donald Munro, F.S.A. Scot. Vol. I. igcxj. No. 3. — Place Names of West Aberdeenshire. By the late James Macdonald, F.S.A. Scot. 1900. No. 4. — The Family of Burnett of Leys. By the late George Burnett, LL.D., Lyon King of Arms. 1901. No. 5. — The Records of Invercauld, 1547-1828. Edited by the Rev. John Grant Michie, M.A. 1901. No. 6. — Rectorial Addresses delivered in the Universities of Aberdeen, 1835-1900. Edited by P. J. Anderson. 1902. No. 7. — The Albemarle Papers, 1746-48. Edited by Charles Sanford Terry, M.A., Professor of History in the University. 1902. No. %.—The House of Gordon. Edited by John Malcolm Bulloch, M.A. Vol, I. 1903. No. 9. — The Records of Elgin. Compiled by William Cramond, LL. D. Vol.1. 1903. No. 10. — Avogadro and Dalton — the Standing in Chemistry of their Hypo- theses. By Andrew N. Meldrum, D.Sc. 1904. No. II. — The Records of the Sheriff Court of Aberdeenshire. Edited by David Littlejohn, LL.D., Sheriff-Clerk. Vol. I. 1904. No. 12. — Roll of Graduates of the University of Aberdeen, 1860-1900. Edited by Colonel William Johnston, C.B. (/« the Press). No. 13. — The Registers of the Scots Colleges at Douai, Rome, Madrid, Valladolid, and Ratisbon, 1581-1860. Edited by the Rev. William Forbes- Leith, S.J. (/« the Press.) Avogadro and Dalton The Standing in Chemistry of their Hypotheses BY ANDREW N. MELDRUM, D.Sc. WITH A PRErACE BY FRANCIS R. JAPP, M.A., LL.D., F.R.S. Professor of Chemistry in the University of Aberdeen Aberdeen Printed for the University 1904 THE GREVFRIARS PRESS, ABERDEEN PREFACE. The important question whether, in discussing the constitution of matter, the atom or the molecule should be first considered, is one regarding which there has been considerable difference of opinion among chemists. Formerly, few would have disputed the claim of the atom to prior consideration. Not only did Dalton's atomic hypothesis precede Avogadro's molecular hypothesis in order of time, but this chronological order seemed also to be the natural order, involving, as it did, only the usual transition from the simpler to the more complex conception. But the history of the science shows that, enormous as were the services which Dalton's atomic hypothesis rendered to chemistry, the chief object of that hypothesis — the determination of a set of consistent atomic weights — remained for a long time merely a pious hope. Avogadro's rule supplied a means of determining the molecular weights of substances, and, from these molecular weights, of ascertaining which of several possible atomic weights of a contained element was the correct one. Until this step had been taken, the marvellous developments of theoretical chemistry which have characterised the last fifty years would have been impossible. In the study of the constitution of matter, therefore, we are compelled, by the very nature of the particular problems of scientific measurement and calculation involved, to reverse what is apparently the natural order of things and to proceed from the more complex to the simpler — from highly complex objects of sense to successively simpler and simpler conceptual structures underlying these. Thus the order of quantitative determination is : — (i) relative weights of comparable amounts oi matter in bulk (gaseous or dissolved) ; (2) relative weights of molecules ; (3) relative weights of atoms ; and (4), if subsequent experiment should justify the most recent speculations, mass of electrons. The view here stated as to the true ratiocinative order of precedence of the molecular and atomic hypotheses has been held by various chemists ; but I have nowhere else seen it expounded with such wealth of illustration and with so exhaustive a knowledge of the fundamental literature of the subject, as in the present monograph by Dr. Meldrum. Francis R. J.-vpf. ' University of Aberdeen, ■yith September, 1904. AUTHOR'S PREFACE. Some of the books required for the purposes of this essay were purchased by means of a grant from the Carnegie Trustees. The publication of the essay has been made possible by another grant from the same body. I am indebted to Mr. Joseph Knox, B.Sc, who went over the essay in a friendly, critical way, and canvassed difficulties with me till a solution was reached. Andrew N. Meldrum. University of Aberdeen, 1904. CONTENTS. Part I. — The Standing in Chemistry of Avogadro's Hypothesis, 9 Chapter I. — Introduction, 9 „ II. — The relation between the Hypothesis and Gay- Lussac's Law, - 14 „ III. — The relation between the Hypothesis and the Kinetic Theory of Gases, - - - - 20 „ IV. — The Hypothesis as a Principle of Chemistry : the Molecule, 25 „ V. — The Hypothesis as a Principle of Chemistry (continued) : the Atom, - - - - 29 ,, VI, — The Molecular Formulae of the Elements, - 39 ,, VII. — The Hypothesis in relation to " Purely Chemical " Methods, 43 Part II. — The Standing in Chemistry of Dalton's Atomic Theory, - 50 Chap. VIII. — Introduction, 50 IX.— The Essentials of Dalton's Theory, - - - 56 X. — The Atomic Weight Systems of Berzelius, - 68 XL— The Atomic Weight System of Gmelin, - - 76 XII. — The Chemical System of Gerhardt and Laurent, 83 XIIL— The Chemical System of Cannizzaro, - - 95 XIV.— The Relative Standing of Dalton's Atomic Theory and Avogadro's Hypothesis, - 102 ABBREVIATIONS. A. C. R., Chemical Philosophy, Cooke, - - - C. N., - Delamdtherie, - Divers, - E. B., - Essai, 1819, Essai, 1835, Gmelin, - Heat, Henry, - J. C. S., - Klassiker, Ladenburg, Von Meyer, - Morley, - Nernst, - Ostwald, Roscoe, - Short History, - Thorpe, - Traitd, - - - Zeitschrift, Alembic Club Reprints. Tilden's Chemical Philosophy, 1901. Cooke's New Chemistry, 1874. Chemical News, Delam^therie's Journal de Physique. British Association, 1902, Section 13, President's Address, Separate Reprint. Encyclopedia Britannica, 9th Ed. Berzelius' Essai sur la Th^orie des Propor- tions Chimiques, 1819. Berzelius' Essai sur la Thdorie des Propor- tions Chimiques, 1835. Gmelin's Handbook of Chemistry, Watt's Translation. Clerk Maxwell's Theory of Heat, loth Ed. Henry's Memoirs of Dalton, 1854. Journal of the Chemical Society of London. Ostwald's Klassiker. Ladenburg's History of the Development of Chemistry, Dobbin's Translation, 1900. Ernst von Meyer's History of Chemistry, McGowan's Translation, 1898. Smithsonian Contributions to Knowledge, 980, The Densities of Oxygen and Hydrogen, Morley. Nernst's Theoretical Chemistry, Palmer's Translation, 1895. Ostwald's Principles of Inorganic Chemistry, Findlay's Translation, 1902. Roscoe's John Dalton and the Rise of Modern Chemistry, 1895. Tilden's Short History of the Progress of Scientific Chemistry, 1899. Essays in Historical Chemistry, 1902. Gerhardt's Traitd de Chimie Organique. Zeitschrift fiir Physikalische Chemie. PART I. The Standing in Chemistry of Avogadro^s Hypothesis. CHAPTER I. INTRODUCTION. Truth on these subjects is militant and can only establish itself by means of conflict.— ']. S. Mill. At the outset of this essay, it is well to state an axiom which is much used in the course of the argument. It is assumed that there is an essential distinction between what are known on the one hand as laws and on the other hand as hypotheses. A hypothesis is the creation of the mind, and is of service in interpreting a law. There is good ground for the belief that in science the recognition of this distinction between law and hypothesis is an indispensable condition of clear thinking. The distinction has been insisted on by Faraday. His words are .- — " It is always safe and philosophic to distinguish, as much as is in our power, fact from theory; the experi- ence of past ages is sufficient to show us the wisdom of such a course ; and considering the constant tendency of the mind to rest on an assumption, and, when it answers every present purpose, to forget that it is an assumption, we ought to remember that it, in such cases, becomes a prejudice, and inevitably interferes, more or less, with a clear-sighted judg- ment. I cannot doubt but that he who, as a wise philosopher, has most power of penetrating the secrets of nature, and guessing by hypothesis at her mode of working, will also be most careful, for his own safe progress and that of others, to distinguish that knowledge which consists of assumption, by B 9 10 Standing in Chemistry of Avogadrds Hypothesis. which I mean theory and hypothesis, from that which is the knowledge of facts and laws ; never raising the former to the dignity or authority of the latter, nor confusing the latter more than is inevitable with the former." ^ Very recently Richards, his views on a question of the day having been much misunderstood, had occasion to emphasise the distinction. He refers to a question the discussion of which, " as of so many scientific questions, has been much confused by the inability of many writers to distinguish between fact and hypothesis. . . . Facts are determined by observation and experiment, and their truth depends only upon the accuracy of the observation and experiment. Their discovery is a lasting addition to the knowledge of mankind. On the other hand, hypotheses are attempts to interpret the facts ; and many hypotheses, from their very nature, can never be proved." ^ Obvious as this distinction may seem, it is necessary to lay emphasis on it here, in view of the persistence with which certain chemists use the term Avogadro's law, instead of Avogadro's hypothesis. In this essay, Avogadro's hypothesis is regarded as an interpretation put upon Gay-Lussac's law. The law, unlike the hypothesis, is matter of fact, and must remain so, even should the hypotheses which are made to explain it be multiplied. Science is coming more and more into use in education. So used, one of the benefits of science is understood to be that it inculcates logical ways of thinking. " What a retrospect," says Gibbon, " is it to a genius truly philosophical . . .to find true consequences falsely deduced from the most erroneous principles." As a training in thinking, the study of experimental science presents one risk : logic is one thing, and experiment is another. The chemist habitually examines 'how far his conclusions square with the facts, and as to the facts, need not go very far wrong. Nevertheless, " true consequences may be falsely deduced from the most erroneous principles." The conclusions squaring ' Experimental Researches in Electricity, vol. II., 1844, p. 285. '■'C.N., 88, 69. \ \ Introduction. 1 1 with the facts, it does not follow that the logic which yields the conclusions is sound. To show that the logic of chemistry is not always sound, it is sufficient to consider the treatment, in many of the books on chemistry, of the subjects of molecular-weight and atomic- weight determination. The connection between the several molecular-weight methods and the definition of the molecule is left in obscurity. How different is the treatment in physics of the subject of specific-gravity, for instance ! Specific- gravity having been defined, some effort is made to show that the several specific-gravity methods are in accordance with the definition. On the other hand, the molecular-weight methods are stated in such a way as to leave on the student's mind the impression that each of these methods stands on its own footing, and is independent of the definition of the molecule. The treatment of the subject of atomic-weight methods is similar ; the books give the impression that the different atomic-weight methods have no connection that can be shown with one another, or with the definition of atomic-weight, and that they yield concordant results for all that. The " Theoretical Chemistry " of Nernst is written, as the title-page states, " from the standpoint of Avogadro's Rule and Thermodynamics." The subject of Thermodynamics may be regarded as non-hypothetical, since it consists essentially of a development by the aid of mathematics and dynamics of the two fundamental laws of Thermodynamics, and makes no assumption as to the continuity or discontinuity of matter. The theoretical basis of Nernst's system of chemistry is Avogadro's hypothesis. Nernst's book is a comprehensive one, suitable for the student of research. It goes as far as the debatable ground between the known and the unknown. It was doubtless foreign to Nernst's purpose to expatiate on the rudiments of chemistry. There is reason to believe that it would be of interest, and even of value, to trace the development, in logical order, of the cardinal doctrines of chemistry on the basis of Avogadro's hypothesis. The standing of Avogadro's hypothesis in chemistry is still an open question. Strange as this may seem, it can 12 Standing in Chemistry of Avogadro's Hypothesis. easily be made manifest by reference to the literature of chemistry. For instance, I quote the verdicts on this question of Cooke and Divers. Cooke states that in writing "The New Chemistry" he made it his object "to present the modern theories of chemistry," and " to give to the philosophy of the science a logical consistency, by resting it on the law of Avogadro." ^ Divers, as President of the Chemical Section of the British Association in igo2, took a very different view from Cooke. The credit given to Avogadro by Cooke, is given by Divers to Dalton. In the Presidential Address, Divers had occasion " to restate and examine most of the fundamental and familiar principles of our science." ^ Accordingly, Divers expounds " the theory of chemistry, which, with all its modern develop- ments, I take to be indisputably the theory of Dalton." ' Again, " the theory of chemical molecules was brought to light ... not by Avogadro's hypothesis," he says, " but in the first place by Dalton's atomic theory and Gay- Lussac's law . . . ; and then, much more fully in the middle of the last century, through the brilliant work of Gerhardt, Williamson, Laurent, Odling, Wurtz, and others, in the purely chemical field." " Apparently, in Divers' judg- ment, the historical importanoe of Avogadro's hypothesis is slight. Not only so, but speaking of the same hypothesis. Divers says, " unfortunately it does not hold good in the case of not a few simple substances." ^ True, chemical theory did not stand still in the interval between 1873, when Cooke was writing, and 1902, the date of Divers' address. There was in the interval development and expansion of the old ideas; but nobody maintains that there has been, since 1870, a revolution in chemical ideas. It is impossible to maintain that this contradiction between Cooke and Divers is significant of some change, amounting to an upheaval, in chemical theory. If a sound method for the advancement of a science con- sists in " constant recurrence to first principles," in what a ^ Cooke, p. 5. ^ Divers, p. 2. ' Loc. cit., p. 3. * Loc. cit., p. 8. * Loc. cit., p. 12. Introduction. \ 3 position of difficulty and embarrassment are the devotees of chemistry placed. In regard to first principles, here are the high-priests of chemistry giving decisions which, to use plain language, are in flat contradiction to one another. Controversy is not always a bad thing. Subjects there are on which " truth is militant, and can only establish itself by means of conflict." Surely chemists would do well to make up their minds about first principles, and to make their reasons known, even at the risk of raising controversy. No further explanation can be given for the attempt in the following essay to consider the questions of the standing in chemistry first of Avogadro's hypothesis, and afterwards of Dalton's atomic theory. Reasons will be given later for taking the questions in this order. Avogadro's hypothesis is the subject of the first part of this essay. After consideration of the hypothesis as such, it is taken as a starting-point, from which to develop, as logically as may be, the ideas such as molecular-weight, atomic-weight, valency, radicals, etc., which are second nature to the chemist. CHAPTER II. THE RELATION OF THE HYPOTHESIS TO GAY-LUSSAC'S LAW. Since all progi-ess of mind consists for the most fart in differentiation, in the resolution of an obscure and complex object into its component aspects, it is surely the stupidest of losses to confuse things which right reasoti has prut asunder. — Pater. Gay-Lussac's " Memoir on the Combination of Gaseous Substances with each other " was read in 1 808 and issued in print in 1 809. The subject of this paper is what is known as Gay-Lussac's law. The law is : " Not only do gases combine in very simple proportions " by volume, " but the apparent contraction of volume which they experience on combination has also a simple relation to the volume of the gases, or at least to that of one of them." ^ Rich in experimental discoveries, Gay-Lussac's memoir is comparatively destitute of speculations and hypotheses. Ber- zelius remarks on this : " M. Gay-Lussac was satisfied with having determined the ratios in which gaseous substances combine, but he made no wider application of this discovery." ^ In 181 1, on consideration of this law, Avogadro published his hypothesis, namely, " That the number of (integral) mole- cules in any gases is always the same for equal volumes, or always proportional to the volumes " ^ It is surprising that Gay-Lussac did not himself anticipate Avogadro. The reason why can only be guessed at. With some men of science, with Dalton, for instance, the faculty of speculation is predominant ; with others, with Bunsen, for instance, the ruling passion is the making of experiments. It may be that Gay-Lussac resembled Bunsen. But whatevef the explanation, a division of labour there was between Gay- Lussac and Avogadro. Stronger witness there could hardly be to the distinction between law and hypothesis, than the 1 A.C.R., 4, 15. '^ " M. Gay-Lussac se contenta d' avoir dteontri les rapports dans lesquels se combinent les substances gaz^iformes, mais il ne fit point d' application plus gen^rale de cette decouverte." — Essai, 1819, p. 14. 'A.C.R., 4, 29. 14 The Relation of the Hypothesis to Gay-Lussac's Law. i J enunciation of a law in 1808 by Gay-Lussac, and the enuncia- tion of a hypothesis, by way of explanation of the law, in 1 8 1 1 by Avogadro.i Plain as is the above distinction between Gay-Lussac's teaching and Avogadro's, all the more surprising is the amount of established error on the subject in the books, and the extent to which the distinction 'has been ignored by men of science. Error has arisen in three several ways. In the first place, the assertion is made that the object of Avogadro's hypothesis was other than the interpretation of Gay-Lussac's law. One of the traditions of chemistry is that Avogadro formed his hypothesis on contemplation of the physical properties of gases and as an interpretation of these properties. Among the authorities who maintain and diffuse this tradition is the great Encyclopedia Britannica. " In 181 1, Avogadro, remarking that equal variations of tempera- ture and pressure produce in all gases and vapours the same change of volume, enunciated the hypothesis that equal volumes of any gas or vapour contain the same number of atoms." ^ According to this account of the genesis of the hypothesis, the physical properties of gases, i.e., Boyle's law and Charles' law, formed the main consideration with Avogadro, so that Gay-Lussac's law was at most a minor consideration, if it was considered at all. This account is in no way confirmed by a scrutiny of Avogadro's paper ; the contrary is evidently the case, that what suggested the hypothesis to Avogadro was Gay-Lussac's law. What Avogadro had in view when he formulated his hypothesis, what he refers to at the outset of his paper and takes into consideration throughout, is Gay- Lussac's law. This erroneous account was corrected by Ostwald in. 1889.' Nevertheless Ladenburg, in a book published in 1900, persists 1 The statement, that Avogadro's hypothesis is an explanation of the properties of gases, does not mean that Avogadro explained why one gas combines with another. There is little need to emphasise this, so far as the main purpose of this essay is concerned, because chemical affinity was explained just as little by Dalton as by Avogadro. * E. B., Article Chemistry— Historical Introduction by F.H.B. SRlassiker, 8, 48. 1 6 Standing in Chemistry of Avogadrds Hypothesis. in the error. " The physical properties of the gases (especi- ally the similarity in their behaviour towards changes of pressure and of temperature) lead Avogadro to assume in equal volumes of all gases, the same number of molecules." ^ The matter can be put beyond doubt by quoting Avo- gadro's own statement, in his second paper on the subject. " In my essay on ' A Method of Determining the Relative Masses of the Molecules of Substances, etc.,' I have advanced a hypothesis ... in order to explain the fact discovered by M. Gay-Lussac, that the volumes of the gaseous sub- stances which combine with one another, and of the compound gases which are produced, are always in simple ratios to one another." ^ In the second place, Gay-Lussac's law and Avogadro's hypothesis have been regarded as the same thing. Clerk Maxwell mentions " a very important law established by Gay- Lussac, that the densities of gases are proportional to their molecular weights." ^ The statement which Clerk Maxwell here describes as Gay-Lussac's law is familiar to chemists as the equivalent of Avogadro's hypothesis. Nevertheless, Gay-Lussac's law and Avogadro's hypothesis are not the same thing. The two generalisations are distinct, no matter how natural the step from the law to the hypo- thesis may seem, and no matter how obvious a corollary of the hypothesis the law may be. On this point the history of the subject affords a decisive verdict. The two generalisa- tions were enunciated at different times by different men. Again, while the law came at once into almost, if not quite, universal acceptance with chemists, the hypothesis for long met with neglect, or was revived only to be rejected. Revived, and applied successfully at last to organic chemistry by Gerhardt and Laurent, the hypothesis was accepted ' Ladenburg, p. 6i. " "Dans mon Essai d' une Manih-e de ditertniner les Masses relatives des Molecules des corps, etc. , j'ai propose une hypothese pour expliquer le fait d^couvert par M. Gay-Lussac, que les volumes des substances gazeuses qui se combinent entre elles, et des gaz composes qui en r^sultent, sont toujours dans des rapports tres simples entre eux." Delamitherie, 1814, 78, 131. The reference to the first paper is Delam^therie, 181 1, 73, 58 ' Heat, p. 326. The Relation of the Hypothesis to Gay-Lussads Law. 17 without reserve, and applied successfully to both organic and inorganic chemistry, first by Cannizzaro about the year 1858. In the third place, Avogadro's hypothesis is frequently described as a law. Tilden, for instance, under the heading, " the law of Avogadro," remarks, " This statement, originally enunciated by an Itahan physicist, Avogadro, . . . may now be regarded as a- well-estabUshed truth." ^ This is not a mere matter of words. The point lies in the statement that this particular doctrine, whether it be called Avogadro's hypothesis or Avogadro's law, is "now a well- established truth." It is one of the tenets of this essay that the doctrine, far from being a " well-established truth" is, on the contrary, one of the hypotheses, which, from their very nature, have never been proved. Avogadro himself, presumably, regarded the doctrine as an assumption ; he uses the term " hypothesis." To use the term " law " is only to give way to what Faraday calls " the constant tendency of the mind to rest on an assumption, and, when it answers every present purpose, to forget that it is an assump- tion." / The use of the term " law " in this connection has two results. First, it tends to keep the hypotheses which form the basis of nineteenth century science out of sight. Second, and this will be considered in the next chapter, it is likely to /conceal the truth that hypotheses are of a transient nature. About the constitution of matter, there are, according to Clerk Maxwell, " two modes of thinking, which have had their adherents both in ancient and in modern times. They corre- spond to the two methods of regarding quantity — the arith- metical and the geometrical. To the atomist the true method of estimating the quantity of matter in a body is to count the atoms in it. The void spaces between the atoms count for nothing. To those who identify matter with extension, the volume of space occupied by a body is the only measure of the quantity of matter in it." ^ From this point of view it is of much interest to consider the measurement of matter in chemistry. The method is, to ' Chemical Philosophy, p. 16. ^ E. B., Article Atom. 1 8 Standing in Chemistry of Avogadrds Hypothesis. measure matter in the gaseous state, by taking equal volumes of the different gases. At the present time, the use of this method pure and simple is being inculcated by Ostwald. Chemistry, as expounded by him, is a science which " identifies matter with extension." On the contrary, as understood by the chemists of the school of Dalton and of Avogadro, chemistry is a science of molecules and atoms. Yet, so far as results go, there is no difference between the opposing schools ; they both measure matter in the same way, by taking equal volumes of different gases. This, according to Avogadro, is a means of taking equal numbers of the different molecules. Ostwald, on the other hand, simply refrains from postulating the existence of molecules. The accepting of Avogadro's hypothesis as a law lies open to the objection that the hypothesis assumes the dis- continuity of matter. As Clerk Maxwell has stated, " there are two ways of thinking about the constitution of bodies, which have had their adherents both in ancient and in modern times." Avogadro's hypothesis is not a law, because it implies the adoption of the atomistic way of thinking about matter, and the rejection of the other way. The trend of nineteenth century science, obviously, has not been such as to train and brace the mind for the concepV tion of continuous matter. It is sometimes said that a theor\^' of continuous matter is " inconceivable." Those who say scj) may be supposed to know their own minds best. There is, nevertheless, the possibility that the theory of the future may not regard matter as atomic. Ostwald, in the theory whiclji he is at present formulating, makes no assumption as to thf constitution of matter. j Whatever the event, it is certain that some leaders of| science have been agnostics in regard to the atomic theory. Of these Faraday was one, and Frankland another. In ' 1869, in the course of a discussion at the Chemical Society of London on the atomic theory, Frankland said he was " averse to accepting the theory as an absolute truth." " He considered it impossible to get at the truth as to whether matter was composed of small and indivisible particles, or whether it was continuous — ^the question belonged to what Tlie Relation of the Hypothesis to Gay-Lussads Law. 19 the metaphysicians termed ' the unknowable ' ; but he acknowledged the importance of the fullest use of the theory as a kind of ladder to assist the chemist in progressing from one position to another in his science." " He did not wish to be considered a blind believer in the theory, or as unwilling to renounce it if anything better presented itself to assist him in his work." ^ In 1853, Faraday, invited to express his opinions on the atomic theory, for publication in Henry's " Life of Dalton," wrote — "/ believe in matter and its atoms as freely as most people, at least I think so. As to the little solid particles ' which are by some supposed to exist independent of the forces of matter ... as I cannot form any idea of them apart from the forces, so I neither admit nor deny them. They do not afford me the least help in my endeavour to form an idea of a particle of matter. On the contrary, they greatly embarrass me . . . the notion of a solid nucleus without properties is a natural figure or stepping-stone to the mind at its first entrance on the consideration of natural phenomena ; but when it has become instructed, . . . the notion becomes to me hypothetical, and what is more, a very clumsy hypothesis." ^ J. C. S., 22, 43S- Plenty, p. 132. CHAPTER III. THE RELATION BETWEEN THE HYPOTHESIS AND THE KINETIC THEORY OF GASES. Generally, let this be a rule, that all partitions of knowledges be accepted rather for lines and veins than for sections and separations ; and that the contimiance and entireness of knowledge be preserved. For the contraiy hei-eof hath made particular sciences to become barren, shallow, and erroneous, while they have not been nourished and maintained from the common fountain. — Bacon. The term molecule is used both in chemistry and physics. The physical molecule, as defined by Clerk Maxwell, is " that minute portion of a substance which moves about as a whole, so that its parts, if it has any, do not part company during the motion of agitation of the gas." ^ The question is sometimes considered, is the physical molecule the same thing as the chemical molecule? One answer that may be given is, that the two ideas, though they have different phenomena in view, are not incom- patible with one another. The physical molecule can doubtless, on occasion, take part in chemical action. The chemical molecule, while its chemical activity is in abey- ance, doubtless " moves about as a whole, so that its parts, if it has any, do not part company during the motion of agitation of the gas." This is important, because it means the possibility of a molecular theory which shall bring both chemical and physical phenomena into co-ordination with one another. Thus a collision between two molecules must occur, as one condition that chemical action shall take place between them. Divers, in his British Association address in 1902, opposes any identification of the chemical with the physical molecule. . . . " the atomic theory should be called the molecular theory of chemistry, . . . were it not for fear of con- founding it with the mechanical theory of that name." ^ What Divers understands by the atomic theory he has ! explained in the most explicit manner. " Divested of all ' 1 E. B., Article Atom. s Divers, p. 4. The Hypothesis and the Kinetic Theory. 2 1 reference to the physical constitution of matter, the atomic theory is that the quantities of substances which interact in single chemical changes are equal to one another — as truly equal in one way as equal masses are in another— and, there- fore, that chemical interaction is a measure of quantity of unlike substances, distinct from and independent of dynamical or mass measurement." ^ Divers admits that " Dalton, indeed, did not express him- self in any such terms, his mind being fully possessed with the ancient and current belief upon which he framed his theory that substances are made up of minute discrete par- ticles. But it is clear enough that his theory was that of the existence of another order of equality between substances than that of weight." ^ Accordingly, Divers formulates an atomic theory which is " divested of all reference to the physical constitution of matter." It is no easy matter to do justice to a version of Dalton's atomic theory so out of the ordinary as this. What I under- stand Divers to maintain is, that, in addition to the two ways, recognised by Clerk Maxwell, of thinking about matter, there is a third way, of which chemists are the exponents. In case the conclusion of this essay is just, namely, that in chemical theory Avogadro's hypothesis is the " controlling and organising principle," this third way of thinking about matter is fallacious. In any case, the phraseology of this third way, as fixed by Divers, is likely to lead to confusion. The words " atom " and " molecule " are characteristic of one of the two ways of thinking about matter recognised by Clerk Maxwell, and they distinguish it from the other way. The words " atom " and " molecule " being used also by Divers in connection with his way of thinking about matter, the result is, that he makes use of the same words as Clerk Maxwell as a means of conveying totally different ideas. Since the words " atom " and " molecule " were used by Dalton with reference to the physical constitution of matter, surely, in the eyes of the followers of Dalton, one is justified in continuing to use them exclusively in this sense. 1 Loc. cit., pp. 3-4. " Loc. cil., p. 4. 22 Standing in Chemistry of Avogadrd s Hypothesis. The function of physical science is seen to be much more modest than was at one time supposed. We no longer hope by levers and screws to pluck out the heart of the mystery of the universe. But there are compensations. The conception of the physical world as a mechanism, coitstructed on a rigid mathematical plan, whose most intimate details might possibly some day be guessed, was, I think, somewhat depressing. We have been led to recognise that the formal and mathematical element is of our own introduction ; that it is merely the apparatus by which we map out our knowledge, and has no tnore objective reality than circles of latitude and longitude on the sun. . . . The world remains a more wondeiful place than ever ; we may be sure that it abounds in riches not yet dreamed a/'.— Horace Lamb. Not only is it objectionable to call Avogadro's hypothesis a " law," since Avogadro used the term " hypothesis," but also because it is likely to keep the hypotheses which form the basis of nineteenth century science out of sight. This has been shown in Chapter II. There is another objection, which will now be considered, that it tends to conceal the truth that hypotheses are of a transient nature. Avogadro's hypothesis is found to be a deduction from , the kinetic theory of gases. Primarily, this theory contem- plates the physical properties of gases. It makes certain assumptions as to the nature of gaseous matter, from which, by mathematical and dynamical reasoning, Boyle's law, Charles' law, Avogadro's hypothesis and Gay-Lussac's law can be deduced. It is on this account, doubtless, that many scientific writers have come to regard Avogadro's hypothesis as being on precisely the same footing as Boyle's, Charles', and Gay-Lussac's laws. It is accordingly described by these writers as a law. This is a specious reason for calling Avogadro's hypothesis a law. A deduction from a theory must stand or fall with the theory. What then are the fundamental assumptions of the kinetic theory of gases ? They are : — 1. That matter is composed of a finite number of mole- cules. In a gas the volume of a single molecule is small compared with the space which the molecule is occupying. 2. That the molecules are in perpetual motion from place to place, the motion of single molecules being disturbed by collisions with other molecules and with the containing wall. 3. That on collision, there is no change of energy of The Hypothesis and the Kinetic Theory. 23 translation into energy of rotation. Hence it is necessary to picture the molecule as a smooth hard sphere. 4. That the condition of dynamic equilibrium between two sets of molecules of different kinds {i.e., M.^c\=yL^c\, M denoting mass and c velocity), is also the condition of thermal equilibrium. On the four assumptions of the kinetic theory of gases, it can be shown by dynamics that when p denotes the pressure of a gas, and N the number of molecules in unit volume of the gas, 3p = MNc2. For two different gases, 3pj=MiNicf, and 3p2 = M3N2C^ If the pressures be equal, MiNjCf = M2Nj,c| If the temperatures be equal, M^cf = M2c| Hence Ni = N2 and this is Avogadro's hypothesis. The accepting of Avogadro's hypothesis as a law, on the strength of the kinetic theory of gases, is open to objec- tion, because the kinetic theory of gases itself is not above suspicion. In reference to the current view of the molecule, Tait says, " the hard atom . . . survives to this day . . . as at least an unrefuted, though a very improbable hypothesis." ^ The successive changes, from the emission theory of light to the undulatory theory, and from the undulatory theory to the electro-magnetic theory, were made in order to embrace a wider and wider range of phenomena.^ The kinetic theory ignores the problems of gravitation and chemical affinity, and therefore can hardly be final. Were the kinetic theory abandoned, in favour of a theory which does explain gravitation and chemical affinity, then the laws of Boyle, Charles, and Gay-Lussac must be deductions from the new theory, but who can say in advance that the theory will lead to Avogadro's hypothesis ? Scrutiny of the fundamental assumptions of the kinetic theory of gases shows that one of- them lies open to particular objection. This is the doctrine, namely, that two sets of ^ Properties of Matter, 4th ed., p. 18. ^ This illustration of the transient nature of scientific theories is taken from Ostwald's "Emancipation from Scientific Materialism." 24 Standing in Chemistry of Avogadro's Hypothesis. molecules in d3mamical equilibrium are also in thermal equi- librium. By iClerk Maxwell this doctrine has been expressly recognised to be a pure assumption. He says, " If the system is a gas or mixture of gases not acted on by external forces, the theorem that the average kinetic energy for a single molecule is the same for molecules of different gases is not sufficient to establish the condition of equilibrium of temperature between gases of different kinds, such as oxygen or nitrogen, because when the gases are mixed we have no means of ascertaining the temperature of the oxygen and of the nitrogen separately. We can only ascertain the temperature of the mixture by putting a ther- mometer into it." 1 There is, however, an alternative to the assumption that Mic5 = M2c|, for gases at equal temperatures. Avogadro's hypothesis can be assumed, i.e., that Ni=N2 At equal pressures MjNicJ = M2N2c| Therefore Mjcf = M2c^ That is, when gases are in thermal equilibrium, the condition of dynamical equilibrium is fulfilled. Hence, by assuming Avogadro's hypothesis, we can deduce the hypothesis that two systems of molecules in thermal equilibrium are also in dynamical equilibrium, and again, by assuming the latter hypothesis, we can deduce Avogadro's hypothesis. This puts the proof of Avogadro's hypothesis from the kinetic theory of gases in its true light. The hypothesis is but one out of two hypotheses which are contingent on one another. Either granted, the other can be proved. In such a case, the simpler hypothesis is naturally selected as the basis of reasoning. To the chemist, Avogadro's hypothesis is the simpler of the two. Whether physicists agree to this or not, two conclusions may safely be drawn. First, that it is possible to develop a modified kinetic theory of gases, a fundamental assumption of which is Avogadro's hypothesis. Second, that the transmutation of Avogadro's hypothesis into a law, by means of the kinetic theory of gases, is not a genuine transmutation. ^ Camb. Trans., 1879, quoted, Heat, p. 326. CHAPTER IV. AVOGADRO'S HYPOTHESIS AS A PRINCIPLE OF CHEMISTRY; THE MOLECULE. Sometimes by Principle we mean a small particular Seed, the Growth or ' gradual unfolding of which doth produce an organised Body, animal or vegetable, in its proper Size and Shape. — Berkeley. A hypothesis not only serves to explain the facts origin- ally in contemplation, but becomes a principle by being adopted and carried out to its logical conclusions. The first consequence of the adoption of Avogadro's hypothesis is as follows : — The molecular weights of all gaseous substances are directly proportional to their densities. This means that molecular weights are arrived at, primarily, independently of chemical action. At the same time, the molecule, whose relative weight is determined apart from chemical change, is made the unit of chemical action. Accordingly, in terms of this molecule, Avogadro gives an account of the facts of Gay-Lussac's law. The formation of two volumes of hydrochloric acid from one of hydrogen and one of chlorine consists in the formation of two molecules of hydrochloric acid from one of hydrogen and one of chlorine ; the formation of two volumes of steam from one of oxygen and two of hydrogen consists in the formation of two molecules of steam from one of oxygen and two of hydrogen. The molecular weight methods are all related to Avo- gadro's h}^othesis; they are (i) the gas density method, (2) the osmotic pressure methods. I. The determination of the density of a gas leads at once to a knowledge of its relative molecular weight. For a long time molecular weights were measured relatively to hydro- gen. As the standard substance, oxygen has great advan- tages, and is now much used. The standard amount of oxygen is 32 grammes, and is called the gramme molecular weight. The gramme molecular weight of any other sub- stance than oxygen is that weight of it which, in the state of c 25 26 Standing in Chemistry of Avogadro's Hypothesis. gas, occupies the same volume as the gramme molecular weight of oxygen, the two being at the same temperature and pressure. Our knowledge, at first hand, of molecular weights, has been immensely extended by the use of Victor Meyer's vapour density apparatus. 2. Of late years there has been investigated a class of methods related to the osmotic pressure of solutions. The methods are empirical, inasmuch as they involve experiments with substances of known molecular weight. An example of this class is the freezing-point method. In terms of this method, the definition of molecular weight is as follows : — The molecular weight of a substance is that weight of it which produces the same depression in the freezing point of a solvent, as the known molecular weight of some other sub- stance.i There is not only this empirical connection between all osmotic pressure methods and the gas density methods, but something more. Van't Hoff has shown that the osmotic pressure of a dissolved substance is closely analogous to the pressure of a gaseous substance. For equal changes of concentration, or of temperature, the two pressures alter to the same extent. With a given amount of a substance, at the same temperature and volume, the pressure of the sub- stance in the state of gas is equal to the osmotic pressure of the substance when in the dissolved state. In a very striking way Van't Hoff has tested this identity. Just as work can be done against the pressure of a gas, work can be done against osmotic pressure. Regarding the freezing-point method of molecular weight determination as consisting essentially in the separation of solvent from solu- tion, accompanied by freezing of the pure solvent, Van't Hoff calculates the work done against osmotic pressure, in separat- ing solvent from solution. Thus, a formula for the solvent constant is arrived at, which involves as factors, the tempera- ture of fusion, and the latent heat of fusion, of the solvent. There is good agreement between the constant as found empirically, and as calculated from this formula. The foUow- ' It is well known that the dissolved substance must not be an electrolyte. The Hypothesis a Principle of Chemistry— The Molecule. 27 ing figures, taken from Walker's Introduction to Physical Chemistry, 1899, P- 329, show the extent of the agreement: — CONSTAN'l Solvent. ' Calculated. Empirical. Water, 1850 1840 Formic Acid, 2840 2770 Acetic Acid, 3880 3900 Benzene, 5100 4900 Phenol, 7600 7400 Nitrobenzene, 6950 7070 Ethylene Dibromide, 1190 1180 Accurate molecular weight determination by the measure- ment of gas densities has been carried out in the case of only a few gases. The gas laws are of limited accuracy, Gay- Lussac's law being only an imperfect description of the facts, even in the case of the combination of hydrogen and oxygen. With one volume of oxygen there combine, not two volumes of hydrogen, but, according to Scott 2'00285, to Leduc 2'oo37 and to Morley 2'oo269;'- From gas density measurements, therefore, accurate molecular weight data are to be got only by the application of a special correction. The necessity of making such a correction was recognised in 1892 by Ray- leigh.^ A systematic way of making the necessary correc- tion was proposed and successfully applied to certain gases first by Daniel Berthelot.'' In general, determinations of gas density are not supposed to give the most accurate molecular weight data. Nearly always, these are got by using the results of gas density measurements in order to interpret the chemical combining weights. Thus, Morley found that 30'3966 g. of oxygen combine with 3'8286 g. of hydrogen and give 34'226i g. of water; that is, the molecular weight of oxygen, 32 g., com- bines with 4*0306 g. of hydrogen, yielding 36'03i5 g. of water.* From the gas density we know that the molecular weight of oxygen being 32, that of hydrogen is about 2, and that of water about 18. Combining these two sets of data, it is evident that 4'03o6 is the accurate weight of two mole- 1 Morley, p. no. ^ Proceedings of the Royal Society, 1S92, 50, 461. 3 Comptes Rendus, 1S98, 126, 954- ■* Morley, p. 109. 28 Standing in Chemistry of Avogadro's Hypothesis. cules of hydrogen, and 36'03IS of two molecules of water. Hence, from this experiment, the molecular weight of hydro- gen is 2"oi53, and that of water i8"Oi57. Yet another illustration may be given of this combination of two sets of data in order to arrive at accurate molecular weights. Hardin found that o'i963i g. mercuric oxide con- tained o'i8i77 g. mercury, and therefore, by difference, o'Oi454 g. oxygen.^ That is, to form mercuric oxide, the molecular weight of oxygen (32 g.) combines with 400^0 g. mercury. From gas density data we know that the molecular weight of mercury is about 200. Evidently 400*0 is the accurate weight of two molecules of mercury, and the accurate molecular weight of mercury is 200"o. ' Smith. Misc. Collections, 1075, Clarke's Recalculation of Atomic Weights, p. l68. CHAPTER V. AVCXJADRO'S HYPOTHESIS AS A PRINCIPLE OF CHEMISTRY (continued): THE ATOM. The harmony of a scieme, supporting each part the other, is and ought to be the true and brief confutalion and suppression of all the smaller sort of obfutions. — Bacox. The adoption of Avogadro's hyjxjthesis as a principle of chemistry leads, in the second place, to the conclusion that the moleCTiles of many of the elements consist of parts. Consider the molecule of hydrogen. In the formation of hydrochloric acid from its elements, one molecule of hydrogen gives rise to two molecules of acid Each molecule of acid containing hydrogen, it appejirs that in this chemical change, the molecule of hydrogen is spHt in two. In the case of the molecules of chlorine and oxygen, similar reasoning leads to a similar conclusion. Each of these molecules can be spht in two. This is a most important consequence of Avogadro's hypothesis. Returning to the case of hydrogen, it is found, in general, that hydrogen enters into its compounds by half- molecules. Compounds of hydrogen are known, the molecules of which contain, some a half-molecule of hydrogen, some two half-molecules, some three, and so on No compoimd of hydrogen being known which contains, per molecule, less than a half -molecule of hydrogen, it is supposed that the molecule of hydrogen consists of no more than two equal parts. Such parts are called atoms. A protest against the use of the word " atom " hcis been made by Guthrie. " The heavenly bodies in their orbits are types of the particles of matter which we handle. Call these small parts particles if you please, or call them molecules, but do not call them atoms, do not write finis to the book of nature." With the spirit of this all chemists cire now con- strained to agree. The word " atom," which can hardly be given up, is not now used in the rigid sense to which Guthrie makes objectioiL Even apart from the analysis of the atom into electrons, the modem conception of the atom is a quite 29 30 Sf,7//ifi/i£- in Cheinhiry of Avogodros Hypothesis. pliable one. The atom is the smallest part of an element which is found to enter into the composition of a molecule. This definition, as an appeal to our experience of molecules, implies a readiness to accept whatever addition to our know- ledge of molecules the day may bring forth. Of the two problems of atomic-weight determination, the first, how to ascertain the experimental data, hardly comes into consideration in this essay. The present question is the other problem, namely, the interpretation of the data. Pre- cisely stated, this problem is the determination of chemical formulae, or, in the words of Berzelius, " the determination of the relative number of atoms in chemical compounds." As a preliminary to the determination of formulae, there is to be considered the question of classification. This may be carried out on chemical or on physical grounds. As a result of experience, a method of classification on physical grounds has been arrived at, which is in accordance with chemical considerations also. This is the method of isomor- phism. Isomorphism is a means of classification essentially ; truly isomorphous substances are classed together, those in the same class subsequently receiving the same general formula. Sodium and potassium chlorides being isomorphous, they receive the general formula M^ Cly . This implies that isomorphism is a molecular weight method in the first place. Sodium and potassium chlorides being isomorphous, the respective quantities of each which contain the same amount of chlorine are the relative molecular weights. These relative weights are the same, whatever values be assigned to x and y in the formula M, Cly and consequently whatever atomic weights for sodium and potas- sium may finally be decided upon. In the second place, in arriving at atomic weights, isomor- phism in itself is not sufficient ; it affords no means of assigning values to x and y in the formula M^ Cly . That must be done on other grounds. Isomorphism may be called a subordinate atomic weight method, inasmuch as it does not stand by itself, but must be used in subordination to other methods, The Hypothesis a Principle of Chemistry — The Atom. 3 1 In addition to the method by isomorphism, the atomic weight of an element is determined (i) on consideration of the molecules into which the element enters, (2) from the specific heat of gases, (3) from the specific heat of solids, (4) from the periodic system of the elements. These methods will now be considered in order. The first of these, the predominant method, is based on the definition of the atom as the " smallest part of an element which is found to enter into the composition of a molecule." It has already been explained. There remains only to con- sider the extent to which recourse can be had to it. By this method, the easiest atomic weights to decide are those of the non-metallic elements. They, on combination with one another, form numerous compounds which are gaseous or easy to convert into gas. Hence, of all atomic weights, so far as these depend upon formulae, those of the non-metallic elements are least subject to uncertainty. The study of the non-metallic elements in this way reveals the existence of compounds of certain types. They are, for instance, (i) hydrochloric acid, HCl ; (2) water, H2O ; (3) ammonia, H3N ; (4) methane, H^C ; (5) phosphoric chloride, CI3P ; (6) fluoride of sulphur, FsS. Accordingly there are elements which combine with hydrogen or its equivalent, some atom with atom, some one atom with two, some one atom with three, and so on. This is the basis of the idea of valency. An element which combines with hydrogen atom for atom is said to be univalent, an element one atom of which combines with two atoms of hydrogen, is said to be bivalent, and so on in order, trivalent, quadri- valent, etc. The case of the metallic elements is harder to solve, their compounds being much less volatile. The diiliculty is often overrated, seeing that, for evidence as to the atomic weights of the metals, their compounds with the hydrocarbon radicals methyl, ethyl, etc., might be quoted far oftener than they are. Even apart from these compounds, the molecular weights of a number of metallic compounds have been found. Victor Meyer's vapour density apparatus is very handy for all such purposes. One thing is specially important, namely, to show that there are univalent, bivalent, ,V^ Sfaitdiiigin C/n'iiiistry of Avo^iinr/t-o's Uypot/ifxix. triw-vlent, and quadrivalenl metals. The roUowinK fununUr-, for instance, have been estahhsluni ; -{l) Kl, {:) HgCl.j, (3) BiCln, (4) SnCl,, In deciding on the nidU'culav rormnla of a suhslancc, a knowledge is useful of the specific heat of the substance in the state of ^as. There are two detinite ways of measuring the specific heal of a gas, the gas Heiiig niainlaiued (l) at constant pressure, (^) at eonstant volume. These Iwo (luan- tities of heal are differenl, and their r.ilio for each j^as is an imiiurtaut constant of the 14,1s. The ratio is usually denoted by Cp / Cv . The value of this, for substances which con- sist of two atoms to the inoU-cule, such as oxypen and nitric oxide, is ^\\o. The value for sulphuretted hydro(.jeii is I'3J, and for methane r27, For more complex molecules, still lower values are f^ot. The empirical law is, the sinii^ler the molecule, the higher the value of Cp/(\ . Meiciii)' vapour and ari;on pivc the value I '66. This is evidence that the mercury and argon molecules consist