PIERRE DUHEM
ATOMIC NOTATION AND ATOMISTIC HYPOTHESES Translated by Paul Needham
This article was first published as “Notation atomique et hypothèses atomistiques”, Revue des questions scientifiques, 31 (1892), 391– 457. It is the second of a series of articles Duhem was to publish in the Catholic journal Revue des questions scientifiques, in which he presents his understanding of what can justifiably be said about the structure of chemical substances as captured by chemical formulas. The argument unfolds following a broadly historical development of events throughout the course of the century which was coming to a close as he wrote. He later reflected in his classic The Aim and Structure of Physical Theories1 – based in large part on articles which had appeared in the Revue – that “To give the history of a physical principle is at the same time to make a logical analysis of it” (p. 269). Logical analysis clearly dominates in the present article. The historical context was elaborated considerably in a later work, Le mixte et la combinaison chimique: Essai sur l’évolution d’une idée,2 which did not lead him to retract any aspect of his earlier position but provided a broader setting in which it could be elaborated. In particular, the Aristotelian influence, which is only hinted at here in some of the formulations (see especially the beginning of section VII) without mentioning Aristotle by name, is explicit in the later work, making Duhem’s own ontological conception a little clearer. A discussion of stereoisomerism, conspicuously absent in the present article, is also integrated into the later book. The same holds for Avogadro’s hypothesis. Duhem was 31 when this article appeared. It is of interest to Duhem scholars as a formulation of his views on central issues related to atomism at this early stage in his career. It should also be of interest to those concerned with the history and philosophy of chemistry as a masterly statement of a position on one of the major controversies of 19th century science which clearly demonFoundations of Chemistry 2: 127–180, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.
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strates that opposition to atomism was not always motivated by the positivist’s concern with what can be seen with the naked eye. In order to distinguish my own additions and comments from the direct translation of Duhem’s text, they have been enclosed in square brackets. This includes the original pagination, which is placed as nearly as possible to the point corresponding to the beginning of a new page in the original. An exception is made where new section headings begin a new page, in which case the pagination is written after the first word of the running text. I have usually translated the French word “corps” with “substance”, but occasionally “body” where this seemed more appropriate. The reader should be aware that these two English words correspond to the same word in the original. This translation was completed as part of a project supported by the Swedish Council for Research in the Humanities and Social Sciences.
TRANSLATION
In a recent article, in which the Revue des questions scientifiques willingly opened its hospitable pages,3 we insisted on some ideas relating to physical theories – ideas which were certainly neither new nor personal. We believe, however, that they are far from being as widespread as they might be. Giving these ideas a concrete form to show how they should be applied to a particular theory would surely be the best way of conveying their role and significance. But the theories of mathematical physics to which the reflections that we have developed are directly applied are, in general, so abstract. They are engulfed in an analytic apparatus too complicated, too mysterious for those for whom a long initiation has not familiarised them with the symbols which comprise [392] the geometric language.4 The very questions that they concern are so remote from ordinary preoccupations that it would be very difficult to submit any one of these theories to a detailed critique in the pages of this Revue. We will therefore have to look elsewhere to find a good example in which the general considerations whose object has been the theories of physics can be brought to life in the form of a concrete illustration. We haven’t believed it possible to do better than
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to choose the modern theory of chemistry. Its appealing form, its language and symbols really strike the imagination, the prodigious elucidation which it has projected onto the chaos of organic chemistry, its syntheses which have extended the already vast domains of this science and which, at the same time, have enriched both industry and the arts with a multitude of useful or brilliant products, the passionate debates to which its principles have given rise, all contribute to attract attention to it, and it would be an injustice to the readers of the Revue to suppose that they do not know of it, at least the principal lines of development. Chemical theory, it is true, is of a completely different nature from physical theories. They have the object of representing to us laws in accordance with which certain phenomena are produced, whereas chemical theory seeks to classify substances. Chemical theory describes the systems which compose the physical world, where physical theories seek to show us how these systems function. Between them there is a difference of the same order as that between morphology and physiology. But this difference, far from being detrimental to the purpose of our enquiries, will in fact come to our aid. If the principles tailored to suit the theories of mathematical physics are applied to a doctrine of as different a nature as chemical doctrine and if they serve to clarify difficulties, to brush aside the controversy, is this not a good test of their generality?
I CRUDE FORMULAS AND EQUIVALENT WEIGHTS
The [393] weights of the various elements composing a given compound stand in an absolutely fixed proportion. Thus, in water, the weight of oxygen is always eight times as great as the weight of hydrogen, and in sulphuric acid, the weight of sulphur is equal to the weight of oxygen. That is the law of definite proportions. This law, taken in isolation, allows each compound to be determined by a concise formula somewhat like the formulas which serve the pharmacist for the reproduction of a given medicine. To make water, combine one gramme of hydrogen with eight grammes of
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oxygen; to make ammonium hydrochlorate, combine 4 grammes of hydrogen, 14 grammes of nitrogen and 35.5 grammes of chlorine. Such is the appearance of the chemical formula. Such formulas would make considerable demands on memory since nothing relates the one to the other. It is, however, they alone which represent the experimental givens of chemical analysis. But the introduction here of a first remark simplifies them considerably. To each simple substance can be made to correspond a number, more or less complicated, characteristic of that simple substance. We could, for example, have 1 for hydrogen, 16 for oxygen, 32 for sulphur, 14 for nitrogen, 35.5 for chlorine, etc. . . . The number corresponding to each simple substance is called the proportional number of that substance. In all the cases in which two or more simple substances are combined, the weights of these combining substances stand to one another in the ratio of the corresponding proportional numbers, or products of these numbers with generally simple whole numbers. Thus, [394] when nitrogen is combined with hydrogen to form ammonia, the combining weights of nitrogen and of hydrogen stand to one another as the number 14, the proportional number of nitrogen, and the number 3, the product of the proportional number of hydrogen and 3, which is a simple whole number. When chlorine is combined with oxygen to form perchloric acid, the combining weights of chlorine and oxygen stand to one another as 71 and 112; this is the ratio of twice the proportional number of chlorine and seven times the proportional number of oxygen. An analogous remark applies to all the compounds of chlorine and oxygen: the weights of chlorine and oxygen which form one of these compounds would be as 35.3 × M and 16 × N, M and N being two simple whole numbers such as 1, 2, 3, 4, 5, 6, 7. This observation is the basis on which the introduction of the chemical formula rests. Instead of constantly writing the proportional number of each simple substance, it is represented by a letter. Thus, the letter H represents the proportional number 1 of hydrogen, the letter O the proportional number 16 of oxygen and the symbol Cl the proportional number 35.5 of chlorine. A table placed at the beginning
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of treatises on chemistry displays the number represented by these symbols and the simple substance to which it corresponds. Thus, it can be read in the table that: Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulphur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitrogen5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chlorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
H=1 O = 16 S = 32 N = 14 Cl = 35.5
This table being given, suppose that we wish to represent the composition of perchloric acid. Instead of writing [395] that this acid is formed by the combination of 71 grammes of chlorine and 112 grammes of oxygen, it suffices to recall with a symbol that the weights of chlorine and oxygen which form this acid stand in the ratio of twice the proportional number of chlorine to seven times the proportional number of oxygen. The symbol adopted is thus Cl2 O7 . Similarly, ammonia would be represented by the symbol NH3 . Can it be seen how this manner of representing the chemical composition of substances relieves the memory? An example will show us: take the compounds of oxygen and nitrogen. In the pharmaceutical manner of formulation, we will say: The protoxide of nitrogen embodies 28 gr. of nitrogen and 16 gr. of oxygen The bioxide of nitrogen " 14 " " 16 " " Nitrous acid " 28 " " 48 " " Hyponitric acid " 14 " " 32 " " Nitric acid " 28 " " 80 " "
On the other hand, with the aid of chemical formulas, we will say: The protoxide of nitrogen has the formula . . . . . . . . . The bioxide of nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitrous acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyponitric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
N2 O, NO, N 2 O3 , NO2 , N 2 O5 .
Who doesn’t see how chemical formulas are easier to retain than pharmaceutical formulas? Nevertheless, in conjunction with a table
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of proportional numbers, they give us the same information; they allow us to reconstruct the pharmaceutical formulas. Now for some remarks on the subject of these chemical formulas. First, is the formula of a compound substance determined absolutely and without equivocation? Is it not possible to attribute several different formulas to the same compound? Certainly. Consider, for example, hyponitric acid. [396] You might say that the weights of nitrogen and oxygen which compose it stand to one another as 14 and 32, that is to say as one times the proportional number of nitrogen and two times the proportional number of oxygen. This substance therefore has the formula NO2 . But you might also say that hyponitric acid is formed from weights of nitrogen and oxygen standing to one another as 28 and 64, that is to say as two times the proportional number of nitrogen and four times the proportional number of oxygen. Hyponitric acid will then have N2 O4 as its formula. Similarly, nitrogen bioxide might be attributed the formulas NO, N2 O2 , N3 O3 , etc. A first point is therefore established: several different formulas may be made to correspond to one and the same compound. These different formulas are derived from the simplest of them by multiplying the numbers figuring in it as exponents by the same whole number. Second, is the proportional number of a simple substance determined absolutely and unequivocally? Evidently not. Suppose that instead of taking for the proportional number of oxygen the number 16, we were to take half this number, the number 8. Can we not repeat the preceding considerations in just the same way? The weights of oxygen entering into various combinations which are simple multiples of the number 16, will be simple multiples of the number 8. It will be possible to write chemical formulas of oxygen compounds with the new proportional number just as well as with the first; the formulas will merely no longer be the same. For example, with the new proportional number of oxygen, The protoxide of nitrogen has the formula . . . . . . . . . . . . The bioxide of nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitrous acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyponitric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NO, NO2 , NO3 , NO4 , NO5
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Here [397] we have a second conclusion of great importance. The proportional number of each simple substance can be replaced by another proportional number obtained by multiplying or dividing the first by a simple number. The principles we have just described cannot therefore suffice to banish confusion from chemical notation. Those who accept the number 16 as the proportional number of oxygen are going to attribute the formula H2 O to water, while those who adopt the number 8 as the proportional number of oxygen will write the formulas of water as HO or H2 O2 , this last formula being that which the former chemists would attribute to oxygenated water [hydrogen peroxide]. In order to avoid this confusion, it is necessary to introduce a new convention into chemical notation; this convention is as follows: Analogous chemical compounds are to be represented, as far as possible, by analogous formulas. An example will show us immediately how this principle allows for the restriction of the indeterminacy in chemical notation. Which proportional number do you adopt for sulphur? You may take one of the numbers 8, 16, 32, 48, 64, . . . To each of these numbers a different formula for hydrogen sulphide will correspond; there will thus be the formulas HS2 , HS, H2 S, H3 S, H4 S. If you don’t invoke the preceding convention, your choice between the different formulas remains free; but if you accept the preceding convention, a rule is soon imposed. Hydrogen sulphide is analogous to water, and you must give it a formula similar to that of water. If you accept the proportional number 8 for oxygen, you have given to water the formula HO. It is then necessary to give hydrogen sulphide the formula HS, which obliges [398] you to take 16 as the proportional number of sulphur. If you have adopted the proportional number of 16 for oxygen, you have given water the formula H2 O, which obliges you to give hydrogen sulphide the formula H2 S and sulphur the proportional number 32. Thus, the fact that oxygen and sulphur give rise to two compounds analogous to one another entails that the proportional numbers of the two substances cannot be chosen arbitrarily. When the proportional number of the one is chosen, the proportional number
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of the other has at the same time been fixed. This is a conclusion that we can generalise by saying: When two simple substances can give rise to two analogous compounds and the proportional number of one of the simple substances is known, then the proportional number of the other is fixed at the same time. These two proportional numbers thus connected with one another are called equivalent weights between the two simple substances. Thus, the number 8 for oxygen and the number 16 for sulphur are equivalent weights for oxygen and sulphur. The number 16 for oxygen and 32 for sulphur are also equivalent weights for oxygen and sulphur. Will the convention that we have just presented allow all ambiguity to be banished from chemical notation? Will it lead us to the determination of a unique system of proportional numbers all equivalent with one another? Will it ensure the concordance of the symbolic language employed by various chemists? This conciliation comes up against a first difficulty. If it is to result from the preceding convention, it is first necessary that all chemists agree in regarding the same chemical compounds as analogous. Such agreement is by no means necessary. All geometers are agreed in regarding all right [399] angles as equal to one another, and in declaring that only one perpendicular can be drawn from a straight line through a point. This agreement is necessary. In fact, what a right angle is, and what a perpendicular is, has been defined without ambiguity. These definitions entail, by logical implication, that all right angles are equal, and that two perpendiculars cannot be drawn through a point from a straight line. So if anyone were to deny one or other of these statements, it would be possible, by a series of syllogisms in due form, to drive him back to a contradiction. On the other hand, if one of two chemists affirms an analogy between two substances which the other denies, I don’t have the right to say to the one: what you say is certain, and to the other: what you say is absurd. My judgement about the disagreement which divides them cannot be reasonably formulated in such rigorous terms. I can only say to the one that I approve of your opinion, and to the other, that I am not of the same opinion. It is, in fact,
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impossible to define chemical analogy and indicate with a precision excluding all ambiguity the characteristics by which two compounds are recognised as being or not being analogues. In the absence of any such definition, I lack the basis on which to construct a proper argument to persuade anyone who would deny an analogy that I allow and who admits an analogy that I deny. In the absence of any such definition, the evaluation of chemical analogy remains personal, relative, variable from one chemist to another, and from one school to another. Certainly,6 there are analogies so striking that no sensible chemist would deny them. There are substances which present such similarities that no one hesitates to compare them. Thus, who would for example imagine separating the acids hydrogen sulphide, hydrogen selenide and hydrogen telluride from one another, or the acids hydrogen chloride, hydrogen bromide and hydrogen iodide? But [400] it is not always like this. A chemist might, with Dumas, find a certain analogy between hydrochloric acid and hydrogen sulphide. If he gave hydrochloric acid the formula HCl, he will give hydrogen sulphide the formula HS. Someone else might deny the analogy between these two acids and, while preserving the formula HCl for hydrochloric acid, give hydrogen sulphide a formula of different form, for example H2 S. Again, logic gives us no means of deciding this issue. In any case, if logic is impotent to compel two chemists to agree on the characteristics of chemical analogy, it does at least oblige one chemist to be self-consistent with these characteristics. Suppose, for example, that, at the beginning of a treatise, a chemist has stated the following rule: We will regard as analogies those compounds which form isomorphous crystals. He is obliged to regard permanganates and perchlorates, which are isomorphous, as analogous and to give the same formula to perchloric acid and permanganic acid. If, in the course of his treatise, we see he has given permanganic acid the formula Mn2 O7 and perchloric acid the formula ClO7 , we are in the right when we say to him: You sin against logic, you commit an absurdity. Either cease regarding isomorphism as a certain mark of chemical analogy or see to it that you give the same formula to permanganic acid and perchloric acid. You
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can choose between these two paths, but you are obliged to make a choice. Such is the only means of conviction at our disposal to settle discussions which arise about fixing chemical formulas. It seems to be very limited; but its power is, in reality, much greater than at first appears, because it is rare that anyone is self-consistent! Suppose [401] that two chemists, confronted with two compounds, would be in agreement in deciding that two compounds are analogues or asserting that they are not. Does it follow that the proportional numbers of all simple substances, and the chemical formulas of all compound substances would be fixed without room for any divergence? Not necessarily, and here a new difficulty comes to the fore which we must examine. Here are a certain number of simple substances which form compounds whose analogy is indubitable. We classify the one close to the other in the same family; for example, chlorine, bromine, iodine and fluorine.7 The condition that we have imposed to represent analogous compounds by analogous formulas fixes the proportional number of bromine, iodine and fluorine when we give a proportional number to chlorine. If, for example, we have taken 35.5 as the proportional number of chlorine, we would be obliged to take as the proportional numbers of bromine, iodine and fluorine, the weights equivalent with 35.5 for chlorine, that is, the numbers 80, 127 and 19. Here now is another family of simple substances which form compounds presenting close analogies; they are, for example, oxygen, sulphur, selenium, and tellurium. Again, if we have adopted a certain proportional number for oxygen, we are obliged to take well determined proportional numbers for sulphur, selenium, and tellurium, that is to say, the equivalent weights which correspond to the proportional number chosen for oxygen. But the choice of proportional number for oxygen is, so far, arbitrary. I can take the number 8 for oxygen, and then sulphur, selenium, and tellurium will have the proportional numbers 16, [402] 40 and 64, respectively. The formula of water would be HO and those of the acids hydrogen sulphide, hydrogen selenide and hydrogen telluride would be written HS, HSe and HTe. I can, however, take 16 as the proportional number of oxygen; then sulphur, selenium,
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and tellurium would have as proportional numbers 32, 80 and 128, respectively. The formula of water would be H2 O, and those of the acids hydrogen sulphide, hydrogen selenide and hydrogen telluride would be written H2 S, H2 Se and H2 Te. Here we have an indeterminacy. Can it be made to disappear?8 Yes, if it can be shown that there are some chemical analogies between a compound formed by substances from the chlorine family and a compound formed by substances from the oxygen family which are accepted by all chemists amongst whom this ambiguity has created a debate. For then, in order to give similar formulas to these two compounds, we will be obliged to establish a relation between the proportional number of chlorine and that of oxygen; and if the first of these numbers is given, then so is the second. And it might well be remarked that in order to thus remove the indeterminacy which we are concerned with, it is not necessary to find a large number of compounds formed from the substances of the oxygen family and a large number of compounds formed by substances from the chlorine family analogous. A single analogy, provided it is distinguished by characteristics whose value no one disputes, suffices to resolve the question. Such an analogy will be presented here. All chemists, both those who attribute to water the formula HO as well as those who attribute to it the formula H2 O, regard the isomorphism of two crystalline substances as a good sign of analogy between them. Now, alongside the fluorotungstates and the fluoronibiolates, which are isomorphous with one another, there are fluoroxytungstates and fluoroxynibiolates, which are isomorphous to one another, and also isomorphous with the preceding substances, as Marignac has shown. These various salts display the [403] closest analogies. This suffices to remove our doubt; everyone accepts that fluorine has a proportional number 19. What proportional number would it be necessary to attribute to oxygen in order that a fluoronibiolate and a fluoroxynibiolate should be represented by a similar formula? The analysis shows us that the proportional number that must be attributed to oxygen is the number 16. All ambiguity thus disappears. Sulphur, selenium and tellurium have 32, 80 and 128 as their proportional numbers; water, hydrogen sulphide, hydrogen selenide and hydro-
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gen telluride are represented by the symbols H2 O, H2 S, H2 Se and H2 Te. Carefully running through the field of chemistry, it is soon recognised that among the simple substances, some display numerous analogies between their compounds as though related very much like members of the same family, while between others, on the other hand, the affinities are very loose. But no substance, nor any group of substances, remains absolutely isolated from the other substances. Between the groups of simple substances most remote in appearance, the law of isomorphism and other physical and chemical properties establish unexpected links. We have already had occasion to cite one of the comparisons between compounds formed from two substances whose chemical role is, in general, quite different. Chlorine and manganese – profoundly dissimilar on the basis of the totality of their chemical properties – form some salts which are entirely analogous: the perchlorates and the permanganates. Chromium, a metal quite remote from sulphur, nevertheless forms chromates entirely analogous to sulphates. Chlorine and nitrogen appear to be the most dissimilar of the metalloids; however, the chlorates resemble the nitrates in more than one character, and the beautiful work of Mallard has established beyond doubt the isomorphism of these salts. [404] We have just seen that the oxyfluorides are sometimes analogous to fluorides. Just as the oxygen and hydrogen compounds of arsenic and of antimony display no analogies with the corresponding compounds of sulphur, nature offers us a sulphoarsenate of cobalt (cobaltine), a sulphoarsenate of nickel (gersdorffite) and a sulphoantimate of nickel (ullmannite) which resemble iron sulphide (pyrites) and manganese sulphide (hauerite) so much that it is hard to tell them apart. Finally, the curious isomorphism of calcite with anhydrous sodium nitrate establishes a surprising analogy between a compound formed from nitrogen and a compound formed from carbon. The study of these analogies makes it possible to fix the proportional number appropriate for each simple substance when proportional numbers agreeing with one another have been fixed – when, for example, 1 is taken as the proportional number of hydrogen.
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After the definition we have given to the word equivalent weight, the proportional numbers thus determined represent the mutual equivalent weights of various simple substances. For reasons which will be presented later, this system of equivalent weights has been called the atomic weights of the various simple substances. The name equivalent weights has, on the other hand, been given to a system of proportional numbers which were in force for a long time, but which didn’t always accord with the chemical analogies generally acknowledged. Thus, in this system, although chlorine was attributed the proportional number 35.5, oxygen was attributed the proportional number 8. Chemists who cling to this system accept that isomorphism characterises chemical analogy, and we have seen that chemical analogy thus defined required that the number 16 be taken as the proportional number of oxygen. Equally, in this system, chloric acid has [405] the formula ClO7 and manganic acid the formula Mn2 O7 . Thus, it can be seen that the proportional numbers which constitute the said system of equivalent weights cannot all be regarded as equivalent to one another, even when only the characteristics of analogy acknowledged by all chemists are invoked. There was a time when the conflict between the advocates of these two systems of proportional numbers was very lively indeed – between the atomists and the equivalentists. At the head of these two parties were to be found, in France, two Chemists of genius, Adolphe Würtz and Henri Sainte-Claire Deville. Clearly, if the advocates of equivalents had been entirely consistent with the principles which they acknowledged, and with the characteristics of chemical analogy which they recognised, they would have adopted the system of atomic weights. In this conflict, the true equivalentists were the atomists. Today, this conflict is over. The system of atomic weights is in use everywhere. Or at least, if the system of equivalents is still sometimes employed, the reasons it remains in favour have nothing to do with science. Now that this system has triumphed over the said system of equivalent weights, it would be fair to relieve it of a denomination which seems to imply a hypothesis which is, at the very least, pointless, and to restore to the atomic weights the name
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of equivalent weights which better indicates their true sense. This is what we will do in this article.
II ON CHEMICAL SUBSTITUTION
We9 have just seen how chemists have brought a confused and indefinable notion, the notion of chemical analogy, into correspondence with a representation of a mathematical clarity, [406] the chemical formula or, to speak more precisely, the crude chemical formula. We will now witness the development of a new notion, that of chemical substitution. At first intimately tied to the notion of chemical analogy, it has gradually been separated from it until it has become absolutely independent. Like chemical analogy, it is one of the confused, indefinable notions which are noticed but not proved. Like chemical analogy, it will be represented by a symbol endowed with a mathematical clarity, by a certain arrangement of signs which constitute the developed chemical formula or formula of constitution. When a zinc plate is immersed in a solution of copper sulphate, the copper is precipitated and the copper sulphate contained in the solution is replaced by zinc sulphate. This substitution of one metal by another in a salt solution is the oldest known phenomenon of substitution. For chemists of the last century and the beginning of this century, these phenomena of substitution were the signs of chemical analogy. Zinc was a substance analogous to copper, which it substitutes in copper sulphate yielding a substance analogous to this latter salt. The substitution of one substance by another in a chemical compound was thus regarded as a mark of chemical analogy, both between the substances which substitute one another and the compounds which are derived from one another by this substitution. The weights of the two substances which are susceptible to substitution of the one by the other should stand to one another as the equivalent weights of these two substances. Two compounds, the one of which is derived from the other by substitution, must be repre-
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sented by similar formulas. Thus, in the example that we have just cited, 32.50 grammes of zinc replaces 31.75 grammes of copper. The equivalent numbers of zinc and copper must therefore stand to one another as 32.50 and 31.75. [407] Copper and zinc sulphates must be represented by analogous formulas. Progress in chemistry has modified this view. The fact that one of two compounds is derived from the other by substitution is no longer regarded as a mark of chemical analogy between these chemical compounds. The weights of two substances one of which substitutes the other are not always proportional to the equivalent weights adopted today, that is to say, to atomic weights. Thus, a strip of copper immersed in a solution of silver nitrate precipitates the silver and yields copper nitrate. 31.75 grammes of copper substitutes 108 grammes of silver. For a long time it was accepted that the equivalent weights of copper and silver stand in the ratio of the numbers 31.75 and 108; silver nitrate was regarded as analogous to copper nitrate, and the two salts were given similar formulas, AgNO6 , CuNO6 . Silver nitrate is today no longer regarded as analogous to cupric nitrate obtained in the preceding experiment; the salts of silver are regarded as analogous to cuprous salts each containing twice the amount of copper as the corresponding cupric salts. Silver nitrate and cupric nitrate are no longer represented by similar formulas. The one is given the formula AgNO3 , and the other the formula CuN2 O6 . The equivalent numbers (atomic weights) adopted today for copper and silver do not stand in the ratio of the numbers 31.75 and 108, but in the ratio of the numbers 63.50 and 108. This separation between the notion of substitution and the notion of chemical analogy was the result of slow progress. We will briefly outline the history of this development.10 The [408] first step towards separating the idea of chemical substitution from the idea of chemical analogy consisted in showing that two elements to which chemists attributed roles so absolutely different that they were placed at two opposite extremities of the chemical classification, chlorine and hydrogen, were susceptible of substitution of the one by the other. This discovery, one of the most surprising and most fruitful to be made in chemistry, was due to Dumas.
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In the course of passing a current of chlorine through alcohol, Liebig obtained a liquid giving off fumes in the air which he named chloral, a name which, without prejudging the composition of the compound, recalls the circumstances of its formation. In 1834, Dumas returned to the study of this reaction and determined exactly the composition of chloral. The result of this determination was that chloral differs from alcohol in having five equivalents11 less of hydrogen and three equivalents more of chlorine. It required the genius of Dumas to grasp in this single result the notion of the phenomenon of substitution because this phenomenon was masked, concealed by a further phenomenon. Dumas drew the following law from the fact which he studied by a bold induction: When a substance can be regarded as a hydrate – and this is precisely the case with alcohol – the chlorine begins by taking away two equivalents of hydrogen without being combined in the compound which results from this reaction. If the action of the chlorine continues to take effect on the dehydrogenated12 substance thus obtained, the chlorine displaces the remaining hydrogen, in order to substitute it equivalent for equivalent, just as zinc replaces the copper in copper sulphate. If instead of taking a hydrated substance, an anhydrous substance had been taken, then the phenomenon of substitution takes place immediately. It [409] is difficult today to conceive exactly how audacious Dumas had to be to take such a stance. At this time, the electrochemical theory of Berzelius reigned uncontested; chemical combination was a manifestation of the attraction that positive electricity exerts on negative electricity. Among simple substances, some are positively electrified: they are the metals – and the others are negatively electrified; these are the metalloids. Where in a combination, the positive electricity of a metal is attracted by a force which keeps the metal within the combination, another metal, also charged with positive electricity, could be attracted more strongly; it would displace the first metal, and take its place. But where an attraction keeps in place the positive electricity of hydrogen, the negative electricity of chlorine can only be repelled. It is therefore impossible that chlorine would come to occupy the place of hydrogen in a combination. The substitution of one of these elements by the other is an absurdity.
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Following Dumas’s struggle with the reigning theory, a chemist, Laurent, who was inclined to take the logical consequences of an idea to their ultimate conclusion became interested. Taking the denial of electrochemical ideas even further than Dumas, he maintains that not only is chlorine able to substitute hydrogen equivalent for equivalent; what is more, the compounds which are transformed from one to another by similar substitutions are analogues of one another. He based this claim on a comparison of chlorine derivatives of naphthaline with hydrogen carbide which had given rise to them. Supported by Laurent’s idea, Dumas presented an incontestable argument in 1839: the discovery of trichloroacetic acid. A small quantity of crystallisable acetic acid is introduced into a flask filled with dry chlorine and exposed to [410] sunlight. After a certain time, the walls of the glass are covered with crystals. These crystals are shown upon analysis to have a composition which differs from that of acetic acid by having three equivalents less of hydrogen and three equivalents more of chlorine. Like acetic acid, the substance which forms these crystals is a monobasic acid. It neutralises bases forming salts whose constitution and properties completely resemble the constitution and properties of the corresponding acetates. In a word, it is impossible to find two substances more alike than acetic acid and trichloroacetic acid, which are derived from one another by [411] substitution of three equivalents of chlorine for three equivalents of hydrogen, despite the radical difference in the electrochemical properties of the elements which substitute for one another. In 1844 Melsens completed the beautiful discovery of Dumas. He showed that, just as chlorine can replace the hydrogen in acetic acid, so can hydrogen freed from contact with a sodium amalgam substitute for the chlorine in trichloroacetic acid and reproduce acetic acid by an inverse substitution. Thus it was shown that two elements, no matter how different in view of the totality of their chemical properties, could substitute for one another in a combination without notably changing the properties of this combination, just as two metals can replace one another without profoundly changing the properties of the salt within which this substitution takes place.
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The idea of substitution, at first intimately connected with the idea of the existence of a chemical analogy, both between the simple substances which replace one another and between the compound substances derived from one another by substitution, took a first step in the direction of progress. The analogy of simple substances which are replaced was no longer required by chemists as a necessary condition for regarding the replacement as substitution. It remained to take a new step, and count the idea of substitution totally independent of any analogy between the two compounds derived from one another by substitution. This step was due to Regnault. Based on studies of the chlorine derivatives of chlorohydric ether and Dutch liquid oil, he extended the notion of substitution to the point of regarding as derivatives by substitution substances whose chemical properties were profoundly different. The notion of chemical substitution was thus constituted as a new notion, independent of the notion of chemical analogy which had previously been the only way of building chemical formulas. The two notions are distinct, but have a characteristic in common. Chemical substitution can no more be defined than can chemical analogy. Thus, when two chemists dispute concerning the same reaction whether it is to be seen as a substitution or not, it is not possible to throw the one or the other back onto a contradiction by a sequence of syllogisms. When, for example, Dumas suggested that trichloroacetic acid is derived from acetic acid by the substitution of chlorine for hydrogen, Berzelius refused to accept the idea. He regarded trichloroacetic acid as a compound with a totally different character to acetic acid. Certainly, this resistance might be regarded as unwise; it might be objected that the Swedish chemist’s theory is strange and sterile, whereas Dumas’s view is natural and fruitful. But can it be said to be absurd, as a geometer who professes a false theorem can be said to be absurd? No; that would exceed the rights of logic. His [412] obstinacy might be puerile and unreasonable, but it is not contradictory. We have seen that the first action of chlorine on alcohol consists, according to Dumas, in taking away two equivalents of hydrogen. A compound is formed, discovered by Liebig who called it alcool deshydrogenatum or, abbreviated, aldehyde. Neither Liebig
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nor Dumas were certain whether to regard aldehyde as a derivative by substitution of alcohol. What substance in fact replaced the hydrogen taken away? None. Today, chemists regard aldehyde as a derivative of alcohol by substitution of one equivalent of oxygen for two substances, H and OH. They have been able to put forward many plausible reasons in support of the constitution that they attribute to aldehyde; but no one can conclude that the view of Liebig is absurd.
III ON CHEMICAL TYPES
Two compounds, the one derived from the other by substitution of one element for another, are not necessarily endowed with the same chemical function; they are not necessarily analogues. To designate the character of the relation, distinct from analogy, in which they stand, Dumas proposed that the expression chemical type be used to denote the characteristic, distinct from analogy and chemical function, which relates two substances derived the one from the other by substitution. All compounds derived, immediately or mediately, from one another by some route of substitution of one element by another belong to the same chemical type. But should the notion of type be limited to compounds which are derived from one another by the substitution of one simple substance by another simple substance, for example, by the substitution of chlorine for hydrogen? Evidently not; chemical facts, already classic during the epoch when Dumas created [413] the notion of chemical type, showed that such a restriction on this notion was not possible. Gay-Lussac studied the combinations of cyanogen. This compound gas, formed from carbon and nitrogen united in equivalent proportions, acts in a range of circumstances as a simple substance, chlorine. It forms combinations with metals which often have close analogies with chlorides. The formulas of these substances become similar if the complex whole CN which constitutes cyanogen is represented by a single symbol, Cy. For example, potassium chloride is represented by the formula KCl, and potassium cyanide could be represented by the formula KCy.
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Salts of ammonia are entirely analogous, in virtue of their chemical properties, to the salts formed by potassium and sodium. They are often isomorphic. Their formulas should be alike if the group NH4 , to which Ampère drew the attention of chemists and which Berzelius called ammonium, was replaced by a single symbol, Am. It can be said that this compound group functions as an element,13 like an alkaline metal. The replacement of chlorine by cyanogen, and of potassium or sodium by ammonium, preserves the chemical analogy between the compounds that the replacement transforms from one to the other. Isn’t it natural to say that a parallel replacement equally preserves chemical type when it constitutes a substitution, even a substitution of a simple substance by a compound group – by the group CN for the element Cl, by the group NH4 for the element K or the element Na? Dumas therefore widened the notion of chemical type by allowing that the type is conserved not only by substitution of an element by another, but also by the substitution with a group of elements by an element or a group of elements. Dumas proved the legitimacy of this extension [414] with the observation that by the action of nitric acid on a large number of organic substances, the group NO2 replaces hydrogen exactly like chlorine does. This generalisation of the notion of type was soon to receive a striking confirmation by the discovery of ammonia-based compounds by Ad. Würtz in 1849. On treating cyanic acid with potash, ammonia is obtained. Treating ether cyanide in the same way with potash, Würtz obtained a volatile liquid endowed with a piquant odour analogous to that of ammonia, turning litmus blue, combining directly with hydroacids to form salts very like salts of ammonia, and combining with oxyacids with the elimination of water to form yet more combinations highly analogous to corresponding ammonium salts. Würtz regarded this base as ammonia NH3 in which an equivalent of hydrogen is displaced and replaced by a complex group formed of hydrogen and carbon, the group C2 H5 , to which chemists have given the name ethyl. He called this base ethylamine. The ethyl group is not the only group formed of carbon and hydrogen which can replace an equivalent of hydrogen in ammonia.
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By a procedure analogous to that by which he prepared ethylamine, Würtz obtained a host of other analogous bases: methylamine, which is ammonia with the group CH3 , which he called methyl, replacing an equivalent of hydrogen; propylamine, where the group propyl C3 H7 replaced an equivalent of hydrogen, etc. . . . All these bases belong to the same type, the ammonia type, whose importance was thus made clear. At the first attempt, Würtz made a considerable extension of this type, [415] attaching to the group of ammonia substitutes most of the volatile alkaloids which constitute organic chemistry. Hofmann’s work, coming directly after Würtz’s, contributed considerably to making the notion of the ammonia type precise and to corroborating the theory of chemical types. Reacting ammonia NH3 with hydroiodic acid yields a compound which is ammonium iodide NH4 I. The action of a base on this substance regenerates the ammonia. If, on the other hand, ammonia is treated, in the way Mr. Hofmann did in 1850, with ether hydroiodide whose formula is C2 H5 I, a salt is obtained which stands to the ethylamine of Würtz as ammonium iodide does to ammonia. It is ammonium iodide with hydrogen replaced by the group C2 H5 , therefore having the formula N(C2 H5 )H3 I, and is ethylammonium iodide. Treating this substance with a base yields the ethylamine of Würtz. The action of ether hydroiodide on ammonia does not only produce ethylammonium iodide, however. A salt derived from ammonium iodide by substitution of two equivalents of hydrogen by two C2 H5 groups is also produced. It is the iodide of diethylammonium with a formula N(C2 H5 )2 H2 I. Treated with a base, this iodide yields a substance analogous to ethylamine, but which is derived from ammonia by the substitution of two groups C2 H5 for two equivalents of hydrogen. This is diethylamine with formula N(C2 H5 )2 H. Again, the same reactions yield an iodide of triethylammonium, N(C2 H5 )3 HI, and a triethylamine, N(C2 H5 )3 , which derive, respectively, from ammonium iodide and ammonia by the substitution of three C2 H5 groups for three equivalents of hydrogen. Not only did these researches enrich the ammonia type [416] by the discovery of the amines twice and three times substituted;
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they revealed a series of combinations belonging to another group, the type hydroiodide of ammonia or ammonium iodide, NH4 I. We have seen how the action of ether hydroiodide on ammonia forms substances deriving from it by substitution of one, two or three equivalents of hydrogen14 by one, two or three ethyl groups. But what is more, this same action produces a substance in which the four equivalents of hydrogen in ammonium iodide are replaced by four ethyl groups, namely tetraethylammonium iodide, N(C2 H5 )4 I. Gerhardt introduced a new extension of the ammonia type by attaching substances which form the class of amides. Amides were studied by Dumas, who envisaged them as dehydrated salts of ammonia. If, for example, the elements of water, H2 O, are removed from acetate of ammonia, acetamide is obtained. Here is how Gerhardt related the amide substances discovered by Würtz: What is the ethyl group which we have seen replaces an equivalent of hydrogen in ammonia to form ethylamine? It is what remains when one equivalent of oxygen and one equivalent of hydrogen are removed from alcohol, whose formula is C2 H6 O. Alcohol is therefore ethyl C2 H5 plus hydroxyl OH. Take in the same way acetic acid, with formula C2 H4 O2 , and remove the group hydroxyl OH. A group remains with the formula C2 H3 O, a group which Gerhardt named acetyl. Now for Gerhardt, acetamide is the substance N(C2 H3 O)H2 which is derived from ammonia by substitution of one equivalent of hydrogen by the acetyl group. More generally, if one equivalent of hydrogen in ammonia is replaced by a group which, when united with OH, forms an alcohol, we have an amine. If it is replaced by a group which, when united with OH, forms an acid, we have an amide. This [417] idea of Gerhardt’s was later to find a powerful confirmation in the discovery of the alkylamides. An equivalent of hydrogen in ammonia is replaced by the remainder of an alcohol, for example by the ethyl group, and another equivalent of hydrogen by the remainder of an acid, for example the group acetyl, and the result is a substance whose properties are intermediate between or, rather, are akin to, those of ethylamine and those of acetamide. It is an alkylamide.
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By attaching amides to the ammonia type, Gerhardt illuminated well the fundamental principle on which we have insisted: that various substances do not need to be analogues in order to belong to the same type. In fact, while amines are bases which offer close analogies with ammonia, it is by no means the case that amides share the alkaline properties of ammonia. At the time when the work of Würtz and Hofmann created a host of compounds, some belonging to the ammonia type, others to the ammonium iodide type, work no less famous of Williamson’s concerning the formation of ether by the action of sulphuric acid on alcohol was to emphasise the importance of another type, the water type. Williamson showed in 1851 that the properties of alcohol and ether are easily interpreted if alcohol is regarded as water H2 O in which an equivalent of hydrogen is replaced by the ethyl group, and ether is regarded as water in which two equivalents of hydrogen have been replaced by two ethyl groups. So alcohol might be represented by the formula (C2 H5 )HO and ether by the formula (C2 H5 )2 O. In support of this view, numerous proofs can be given. One cannot do better, it seems to me, than to cite the most striking which consists of treating sodium [418] ethoxide with the iodide of an alcoholic radical, for example with methyl iodide. The substance thereby obtained is analogous to ether and called a mixed ether; it is water in which one equivalent of hydrogen has been replaced by the ethyl group, C2 H5 , and the other equivalent of hydrogen by the methyl group, CH3 . The formula of this substance is therefore (C2 H5 )(CH3 )O. Williamson wasn’t satisfied with creating the water type by adding to it alcohol, ether and the mixed ethers; he put in a large group of acids, bases and salts from the chemistry of minerals. Nitric acid is water in which an equivalent of hydrogen has been replaced by the group NO2 . Potash is water in which an equivalent of hydrogen has been replaced by an equivalent of potassium. Silver oxide is water in which two equivalents of hydrogen have been substituted for two equivalents of silver. Silver nitrate is water in which one equivalent of hydrogen has been replaced by a nitryl group, while the other equivalent of hydrogen has been replaced by an equivalent of silver. This takes us back to ideas Davy and Dulong had
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put forward regarding the constitution of salts – ideas which Liebig and Wöhler have clearly formulated in the course of studying the combinations of benzoic acid. The water type was soon enriched by Gerhardt with a new category of substance, the possibility of which Williamson had conceived. What, for Williamson, is alcohol? It is water in which an equivalent of hydrogen has been replaced by the ethyl group. What is ether? It is water in which two equivalents of hydrogen have been replaced by two ethyl groups. What is acetic acid? It is water where one equivalent of hydrogen has been replaced by an acetyl group, C2 H3 O. Cannot, therefore, a substance which stands to acetic acid as ether stands to alcohol, be conceived as a substance which stands to water where two equivalents of hydrogen would [419] be replaced by two acetyl groups, and which would have the formula (C2 H3 O)2 O? The realisation of this substance was provoked by an unexpected discovery. In 1850, all chemists believed, with Gerhardt, that monobasic acids cannot exist in the anhydrous state. All known anhydrides were associated with polybasic acids. Now, reacting dry chlorine with dry silver nitrate, Henri Sainte-Claire Deville produced anhydrous nitric acid. Confronted by this fact, Gerhardt didn’t hesitate to abandon his old ideas. He sought to interpret Sainte-Claire Deville’s discovery. For him, the nitric anhydride stands to nitric acid as ether stands to alcohol: it is water whose two equivalents of hydrogen have been replaced by two groups NO2 . Its formula is (NO2 )2 O. In 1851, Gerhardt based on this interpretation a strictly general method for producing anhydrides of monobasic acids. Should, for example, acetic acid anhydride be required, then react silver acetate with acetyl chloride. What is produced is the substance whose existence was predicted by Williamson. Gerhardt was not satisfied with enlarging the water type by adding the class of monobasic anhydrides; he defined new types, such as the hydrochloric acid type. Water contains two equivalents of hydrogen. It might happen that just one of these equivalents is replaced by an element, as in potash, or by a group of elements, as in nitric acid, alcohol and acetic acid. It is also possible that both equivalents of hydrogen are simultaneously
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replaced, either by two elements, as in silver oxide; or by an element and a group of elements, as in silver nitrate, potassium acetate, and sodium ethoxide; or by two different groups, as in acetic ether and in the mixed [420] ethers; or, finally, by two identical groups, as in ether, nitric anhydride and acetic anhydride. Nothing of the kind is to be found in hydrochloric acid. It contains only a single equivalent of hydrogen which, in substitution phenomena, is always replaced at one go by another element or by a group of elements. If this equivalent of hydrogen is replaced by an equivalent of sodium, then we have sodium chloride; if by the group NH4 , then we have ammonium chloride; if by the group C2 H5 , then we have ethyl chloride; if by the group C2 H2 O, then we have acetyl chloride. Hydrochloric acid, water, ammonia and ammonium iodide are, after Gerhardt, the principal types under which all chemical combinations came to be regimented. The nomenclature is, however, far from being complete. It is noteworthy that there is one type that Gerhardt doesn’t mention and which has, however, taken on a major importance since Kékulé has taught us to see nearly all organic combinations as derived from it, namely the methane type, constituted by hydrogen protocarbon CH4 . Mineral chemistry provides us with still more types. We leave them aside, thinking that the preceding suffices to give a clear idea of the notion of chemical types and the way in which it has developed. We are impatient to take up a new notion, rich in consequences. We wish to speak about the notion of a condensed type.
IV ON CONDENSED TYPES
Williamson [421] had related monobasic acids to the water type; they were represented as water in which one equivalent of hydrogen has been replaced by a certain group of elements, by an acid radical. Thus, nitric acid was water in which an equivalent of hydrogen has been replaced by the group NO2 . Acetic acid is water in which an equivalent of hydrogen has been replaced by the group C2 H3 O. Such substitution involves the replacement of one of the two equivalents
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of hydrogen contained in water. The other can, in turn, be replaced by a metal such as potassium, sodium or silver; salts are formed in this way. In this case, an acid contains only a single equivalent of hydrogen which a metal can replace to form a salt. So a given acid and a given metal can only form a single salt. But this is not always the case. Take sulphuric acid and make it react with potash. It forms two different salts, according to the circumstances. One of these salts contains one equivalent of hydrogen and one equivalent of potassium; the other contains two equivalents of potassium and contains no hydrogen. It is this that leads us to say that sulphuric acid is a dibasic acid. Similarly, ordinary phosphoric acid can yield three different salts with potassium. One of these salts contains an equivalent of potassium and two equivalents of hydrogen; another contains two equivalents of potassium and one equivalent of hydrogen; and finally a third contains three equivalents of potassium and no hydrogen. Ordinary phosphoric acid is a tribasic acid. But how can acids such as sulphuric and phosphoric acid belong to the water type? How can we understand the circumstance that after a first substitution, which removes an equivalent of hydrogen from water, there remains yet two or three equivalents of hydrogen in the water replaceable by a metal? It seems that this would be very difficult, if not impossible. Williamson resolved the difficulty. How have we conceived the formation of a monobasic acid, nitric acid for example? We have supposed [422] that water H2 O loses an equivalent of hydrogen and that this equivalent of hydrogen is replaced by the group NO2 . Let us now take the formula of water H2 O not once, but twice. From each of these formulas let us remove an equivalent of hydrogen, which will give us two hydroxyl groups OH; for the two equivalents of hydrogen removed the group SO2 is substituted a single time. We have a compound (SO2 )(OH)2 whose composition will be that of sulphuric acid. There will be two equivalents of hydrogen in this compound coming from water from where we derived it, two equivalents of hydrogen entirely analogous to the single equivalent contained in nitric acid. The existence of these two equivalents of hydrogen shows the double basicity of sulphuric acid.
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Similarly, phosphoric acid is obtained by taking the formula of water H2 O three times, removing one equivalent of hydrogen from each of these H2 O groups and substituting these three equivalents of hydrogen with a single group PO.15 The formula (PO)(OH)3 of the compound thereby obtained clearly shows the triple basicity of phosphoric acid. Thus the polybasic acids belong to the water type, although to the water type several times condensed, thanks to the intervention of a group of elements susceptible of alone substituting for several equivalents of hydrogen removed from several different H2 O groups. The dibasic acids are thus associated with the water type twice condensed; two hydroxyl groups OH are tied together by a single group. The tribasic acids are associated with the water type condensed three times; three hydroxyl groups OH are tied together by a single group. “Mr. Williamson has written that in two lines;16 but how rich in developments this simple statement was!” [423] Williamson’s idea, issuing from the notion of basicity, was soon to lead to one of the greatest discoveries which have been made in chemistry: we wish to speak about the discovery of glycol. In 1854 Berthelot concluded an important work on the ethers of glycerine with the following words: “These facts show us that glycerine presents, vis-à-vis alcohol, precisely the same relation that phosphoric acid presents vis-à-vis nitric acid. In fact, while nitric acid only produces one series of salts, phosphoric acid produces three: the ordinary phosphates, the pyrophosphates and the metaphosphates . . . Similarly, while alcohol only produces a single series of neutral ethers, glycerine gives rise to three distinct series of neutral combinations.” The facts observed by Berthelot were exact; the interpretation that he proposed was erroneous. The three series of ethers of glycerine derive from one and the same glycerine, and not three different glycerines, comparable to orthophosphoric, pyrophosphoric and metaphosphoric acid. These three series of ethers are comparable, not with orthophosphates, pyrophosphates and metaphosphates, but with acidic orthophosphates, neutral orthophosphates and basic orthophosphates. Orthophosphoric acid, we have seen,
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is formed from three hydroxyl groups OH joined together by the PO group. If in one of the OH groups an equivalent of hydrogen is replaced by an equivalent of potassium, the result is the acidic orthophosphate of potassium; if in two of these groups, the neutral orthophosphate of potassium; if in three of these groups, the basic orthophosphate of potassium. Similarly, glycerine belongs to the water type three times condensed; it is formed from three hydroxyl groups OH tied together by the group C3 H5 . In each of these hydroxyl groups, hydrogen can be replaced by an alcoholic group, for example by [424] ethyl C2 H5 . Depending on whether such a substitution is effected in one, two or three of these groups, we will obtain three different ethers. This was the interpretation that A. Würtz proposed in 1855 of the facts observed by Berthelot. Alcohol and glycerine are comparable to nitric acid and phosphoric acid. Alcohol is a single alcohol as nitric acid is a single acid. Glycerine is a triple alcohol as phosphoric acid is a triple acid. In order to confirm this view, it was necessary to form a substance which would stand to alcohol as sulphuric acid stands to nitric acid, and would be a double alcohol as sulphuric acid is a double acid. Würtz sought to form this substance, intermediate between alcohol and glycerine, and succeeded; it is glycol, discovered in 1856. In what way should we proceed to obtain a substance which is a double alcohol based on Williamson’s ideas on the constitution of polybasic acids and Würtz’s on the constitution of glycerine? We should look for a group composed of carbon and hydrogen which is capable of substituting for two equivalents of hydrogen and tying together two OH groups. Now there exists a substance, composed of carbon and hydrogen, which seems to present the required characteristics, namely the gas ethylene, whose composition is represented by the formula C2 H4 . This substance combines with two equivalents of chlorine to form a liquid oil well known under the name Dutch liquid oil. Dutch liquid oil can be regarded as hydrochloric acid twice condensed by substitution of ethylene for two equivalents of hydrogen. The ethylene group therefore looks like one of the groups, analogous to SO2 , which can substitute for two equivalents of hydrogen.
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Let us therefore take ethylene as our point of departure. Combining it with bromine or iodine yields [425] the bromide or iodide of Dutch liquid oil; if this is saponified with silver oxide, the substance C2 H4 (OH)2 is obtained. This is the substance which is a double alcohol, intermediate between alcohol and glycerine, sought by Würtz; it is glycol.
V ON VALENCY
From the point of view of the science of chemistry, the discovery of a substance has no interest if it is not the occasion of the demolition of a false theory, the confirmation of a correct theory, or the introduction of a new conception. The importance of a new fact is measured by the evolution that the knowledge of this fact imprints on ideas. In the light of this rule, there are, in chemistry, few substances whose discovery has been so important as that of glycol. The modern chemical notation hangs on it – to what extent we will now examine. The discovery of glycol made everyone appreciate the characteristic possessed by certain groups, such as ethylene, of replacing two equivalents of hydrogen taken either from two different HCl’s or from two different H2 O’s, and tying together the remaining two equivalents of chlorine or the two remaining OH groups. This characteristic, already indicated by Williamson as belonging to the SO2 group and as explaining the double basicity of sulphuric acid, profoundly distinguished these groups from groups such as NO2 , C2 H5 and C2 H2 O which can only substitute for one equivalent of hydrogen either from hydrochloric acid or water. The latter substitutions generate products belonging to the same group from which they come, of the hydrochloric acid type or the water type. On the other hand, substitutions of the former kind generate products which do not belong [426] to the same type from which they came, but to a twice condensed type – the doubly condensed hydrochloric acid type or the doubly condensed water type. Picking up again, under a more precise form, an expression already employed by Milon and by Malaguti, Würtz called the first groups monatomic groups,
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and the second diatomic groups. Later, he proposed to replace these terms by univalent and bivalent groups, respectively. Adopting these latter expressions, we therefore say that NO2 , C2 H5 and C2 H2 O are univalent groups, and that SO2 and C2 H4 are bivalent groups. The PO group which we encountered in studying phosphoric acid and the group C3 H5 which we have cited in connection with glycerine possesses the property of being able to substitute for three different equivalents of hydrogen taken from three different HCl’s or three different H2 O’s. They therefore yield combinations which belong not to the hydrochloric acid type, or to the water type, but to the triply condensed hydrochloric acid type or the triply condensed water type. The group PO and the group C3 H5 in phosphoric acid and in glycerine are therefore trivalent groups. Let [427] us pursue the consequences of these ideas. How did Williamson come to compare the water type with the doubly condensed water type? He considered nitric acid which contained a single equivalent of hydrogen replaceable by an alkaline metal and which produces a single series of salts. He considered sulphuric acid which contained two equivalents of hydrogen replaceable by an alkaline metal, and which produces two series of salts according as one or two equivalents of hydrogen are replaced by the metal. From this comparison the idea was born that, just as nitric acid was derived from water, so sulphuric acid was derived from the water type twice condensed. Let us now compare the action of water on metals with the action of hydrochloric acid. Hydrochloric acid contains a single equivalent of hydrogen which can be substituted by an equivalent of a metal such as potassium or sodium. On reacting with these metals, a single series of salts is formed – potassium or sodium chloride. Water, on the other hand, contains two equivalents of hydrogen each of which can be replaced by a metal such as potassium, sodium or silver. If a single equivalent of hydrogen is replaced by a metal, a first series of compounds is obtained, the hydroxides such as potash or soda. If two equivalents of hydrogen are replaced by two equivalents of metal, a second series of compounds is obtained, the oxyanhydrides such as silver oxide.
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Isn’t this comparison between hydrochloric acid and water entirely analogous to that which exists between a monobasic acid and a dibasic acid? Are we not naturally led to regard water as belonging to the doubly condensed hydrochloric acid type, as deriving from two HCl groups by substitution of a single equivalent of oxygen for two equivalents of chlorine? Are we not authorized to say that in hydrochloric acid, chlorine is a univalent element, and that oxygen is a bivalent element? Similarly, ammonia might be regarded as belonging to the triply condensed hydrochloric acid group. It is derived from three HCl groups by substitution of one equivalent of ammonia [sic.]17 for three equivalents of chlorine. In ammonia, nitrogen is a trivalent element. Methane might be regarded as belonging to the quadruply condensed hydrochloric acid type. An equivalent of carbon is substituted for four equivalents of chlorine taken from four different HCl’s. In methane, carbon is a quadrivalent element. Ammonium iodide might be regarded as derived, [428] by substitution of an equivalent of iodine for an equivalent of hydrogen, from the ideal substance NH5 , which is ammonium hydride. Ammonium hydride might be associated with the five times condensed hydrochloric acid group. Take five different HCl’s; substitute the five equivalents of chlorine it contains with a single equivalent of nitrogen, and you will have ammonium hydride. In this substance, in ammonium iodide, and in ammonium hydrochlorate, nitrogen is a quintivalent element. All the types of which we have spoken are thus found to be reduced either to the hydrochloric acid type or the one, two, three, four or five times condensed hydrochloric acid type. There are still other types which can all be reduced to the hydrochloric acid type condensed a certain number of times. This said, let us consider any chemical type formed by the union of two elements or two groups of elements a and b. If it is the hydrochloric acid type, a will be Cl and b will be H. If it is the water type, a will be O and b will be H2 ; etc. . . . If the type corresponds to the hydrochloric acid type condensed n times, each of the two groups a and b is said to be n-valent in the compound a b, or, when united in forming the compound a b, each of the two groups a and b
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exchange n valencies with one another, and the formula of the compound is written by drawing n lines between the two groups a and b. Thus, in hydrochloric acid, one equivalent of hydrogen exchanges one valency with one equivalent of chlorine, and the formula for hydrochloric acid is written H–Cl. In water, an equivalent of oxygen exchanges two valencies with two equivalents of hydrogen, and the formula for water is written H2 = O. In ammonia, an equivalent of nitrogen exchanges three valencies with three equivalents of hydrogen, and the formula for ammonia is written N ≡ H3 . In methane, an equivalent of carbon exchanges four valencies with four equivalents of hydrogen, and the formula for methane [429] — H4 . In ammonium iodide, an equivalent of nitrogen is written C ≡ exchanges five valencies with five equivalents of hydrogen, and the — — 4 formula for ammonium iodide is written N ≡ H I. That oxygen, nitrogen, carbon and nitrogen again have replaced the chlorine of two, three, four and five HCl groups is represented still more clearly by writing
Each line marks the place of one equivalent of chlorine replaced by substitution and indicates the equivalent of hydrogen that was united with it. Let us now consider a combination belonging to the type a b; it is formed by the substitution of an element or a group of elements A for the group a, and an element or a group of elements B for the group b. Again, the two groups A and B are said to exchange n valencies in the compounds AB, and the formula for the compound is written by putting n lines between the symbols A and B. Take, for example, triethylphosphine; it is a substance derived from ammonia by substitution of one equivalent of phosphorus for one equivalent of nitrogen and three ethyl groups C2 H5 for three equivalents of hydrogen. One equivalent of phosphorus is therefore said to exchange three valencies with the group (C2 H5 )3 .
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The formula of trimethylphosphine is written:
Clearly, the type to which a combination belongs is now represented by the number of valencies that are exchanged [430] between the two parts whose union is assumed to form this combination. This method of representation immediately presents a first advantage. Consider the ammonium type. A certain number of combinations are put into this type, for example phosphorus protochloride, that can be derived from ammonia by substitution of an equivalent of phosphorus for an equivalent of nitrogen and three equivalents of chlorine for three equivalents of hydrogen. But evidently, each of the combinations that we have considered as being of the ammonia type can, in turn, be taken as the combination type from which all the others may be derived by substitution. For example, we can take the phosphorus protochloride type, and say that ammonia is derived by substitution of one equivalent of nitrogen for one equivalent of phosphorus and of three equivalents of hydrogen for three equivalents of chlorine. There is thus something very arbitrary in the operation consisting of choosing, from all the combinations belonging to a given type, one which serves to personify the type. The arbitrary importance given to one combination among all those deriving from the same group is avoided by the valency notation. All combinations belonging to the same type are now marked with the same characteristic, without having to make any play a particular role. And this common characteristic is precisely what is considered essential for the type, namely the condensation to which it is necessary to subject the hydrochloric acid type in order to derive the type in question.
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But the introduction of the notion of valency has yet other, considerably more important, advantages; we will examine what these advantages are.
VI ON THE DEVELOPED, OR CONSTITUTIONAL, FORMULA
There [431] is something arbitrary and indeterminate in the operation by which a combination is related to a given type because the same compound may be related to several different types. Consider methylamine, for example. It can be regarded as ammonia in which an equivalent of hydrogen has been replaced by a methyl group CH3 , and it is then put into the ammonia type. It can also be regarded as methane in which an equivalent of hydrogen has been replaced by the group NH2 , and it is then put into the methane type. Take a slightly more complicated case, methylammonium iodide. This can be regarded as ammonium iodide in which an equivalent of hydrogen has been replaced by the methyl group, and it is put into the ammonium iodide type. It can be seen as methane in which an equivalent of hydrogen has been replaced by the group NH3 I; we put it into the methane type. Finally, it can be considered as hydroiodic acid in which an equivalent of hydrogen has been replaced by methylammonium NH3 (CH3 ); we put it in the hydrochloric acid type. Take yet another example, potassium nitrate. We can regard this substance as water where one equivalent of hydrogen has been replaced by potassium, and the other by the group NO3 ; we put it in the water type. We may regard it as potassium chloride where the chlorine has been replaced by the group NO3 , and we therefore put it in the hydrochloric acid type. [432] We might regard it as ammonium iodide where four equivalents of hydrogen have been replaced by two of oxygen and where the fifth has been replaced by the group OK, and it is now related to the ammonium hydride type. All substances would give rise to considerations analogous to those we have just developed with particular examples. Thought can split every substance into elements or groups of elements in various
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ways, and these various ways of cutting it up will, in general, lead to derivations from different types. From among these various ways of envisaging a compound it is necessary to choose one which determines the type to which it would belong. But this choice is not without drawbacks. In fact, each of the ways in which a compound can be assigned to a type has the advantage of illuminating certain relations that the compound has with other substances, but also has the disadvantage of casting a shadow over certain other relations. Take, for example, methylammonium hydroiodide. In linking it to the ammonium hydride type, we bring out its relations with ammonia, but we conceal its links with methane and with methyl alcohol. In linking it with methane, we bring out the latter relations, but conceal its analogies with the alkaline salts. It is here that the new notation based on the notion of exchange of valency comes into play. It gives us the means of avoiding the arbitrary and defective choice between the various types to which a compound might be linked. What, in fact, makes a compound eligible for a determinate type? It is the taking of one particular element or group of elements which belongs to the compound, and saying how this element or group of elements exchanges valencies with the remainder of the compound and how the exchanges are brought [433] about. When, for example, I say that potassium nitrate belongs to the water type, where one equivalent of hydrogen is replaced by an equivalent of potassium and the other by the group NO2 , I say that potassium nitrate contains an equivalent of bivalent oxygen which exchanges one valency with potassium and another valency with the group NO2 . When I regard the substance as derived from ammonium iodide by substitution of the group OK for an equivalent of iodine and two equivalents of oxygen for four equivalents of hydrogen, I say that, in potassium nitrate, nitrogen is a quintivalent element which exchanges one valency with the group OK and the other four with two equivalents of oxygen. When I link potassium nitrate with the hydrochloric acid type, I intend to express that the salt contains an equivalent of univalent potassium which exchanges its single valency with the group NO3 .
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But doesn’t what has just been said immediately suggest the following idea: making clear the number of valencies of each of the elements which figure in the compound and the way in which these valencies are exchanged with one another? Thus, for potassium nitrate, we note that nitrogen is quintivalent in this compound, that each of the equivalents of oxygen is bivalent and potassium is univalent; moreover, two of these equivalents of oxygen each exchange two valencies with two valencies of nitrogen; and the third equivalent of oxygen exchanges one of its valencies with the fifth of nitrogen’s valencies and the other with the single valency of potassium. Potassium nitrate will therefore be represented by the following symbol:
This [434] symbol doesn’t link potassium nitrate with any type in particular, but it makes immediately clear all the types to which potassium nitrate might belong. The various ways of envisaging potassium nitrate lead, in fact, to writing the salt as
if it is to be linked to the water type, or writing it as
if it is to be linked with the ammonium hydride type, or writing it as
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if it is to be linked with the hydrochloric acid type. And it is easily seen that all that can be expressed by each of these formulas is completely expressed by the formula that we wrote first. This formula will be called the developed formula or the constitutional formula of potassium nitrate.18 For further clarity, let us consider some other examples of developed formulas. We have seen that methylamine may be regarded as of the ammonia type, which leads to the representation by the formula
We have also seen that it can be assigned to the methane type, [435] which leads to the representation by the formula
All that is expressed in these two formulas can be found in the symbol
which is the developed formula of methylamine. We have seen that the hydroiodide of methylamine can be put in the ammonium hydride type, which leads to the formula19
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or in the methane type, which leads to the formula
or in the hydrochloric acid type, which leads to the formula
All [436] that is expressed in these various formulas is to be found in the developed formula
The developed formula of a substance thus displays all the types to which the substance might be assigned. From this, there follows a first consequence: When20 the formula of a compound is known, it is immediately apparent which substances it can give rise to by way of substitution, so the reactions to which the substance will give rise can be classified, and sometimes predicted. Moreover, comparing the developed formulas of a given substance with others shows by which substitutions it would be possible to pass from the one to the other. Now, progress in science has in many cases equipped chemistry with appropriate methods for effecting a given substitution. Consequently, when the constitutional formula of a substance is known, one will often be in a position to reproduce a substance by means
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of other substances already to hand, in other words, to effect a synthesis. This ability of a developed formula to indicate the route by which it is possible to synthesise a given substance is one of the great and admirable accomplishments of modern chemical notation. It has led to innumerable discoveries and enriches industry each day with new products. To give examples of such syntheses would be more appropriate in a detailed study of chemistry than the dimensions of this article and the programme of the Revue would allow. Suffice it to mention just two syntheses from among the more remarkable [437] in the way they were predicted and sought after: the synthesis of acetic acid by Grimaux and Adam, and the synthesis of indigo by Bäyer. But let us leave aside the practical import of the developed formula, its fecundity manifests itself in such a way that it would be puerile to delay demonstrating it. There is another consequence, now a theoretical one, to which the new notation leads us, and it is to this consequence that we would now wish to draw the reader’s attention. Two substances might have the same crude formula but different developed formulas. They would then be two distinct substances, although of the same composition. To obtain them, different reactions, different substitutions, are required. Such substances are isomers of one another. The isomerism between two substances can itself be of two different kinds. Take the two substances whose developed formulas are:
the first of which is propionaldehyde, while the second is acetone. When the former is submitted to the action of an oxidant, the hydrogen that is linked to the equivalent of carbon which already carries an equivalent of oxygen will be replaced by the group OH and we obtain a substance whose developed formula will be
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this [438] substance contains the group OCOH characteristic of the organic acids. This is an acid, proprionic acid. When acetone is submitted in the same way to an oxidant, nothing similar is produced because no equivalent of hydrogen is directly united with the equivalent of carbon which is connected with oxygen. Thus acetone submitted to the action of an oxidant divides into acetic acid and formic acid. This is a first example of isomerism. Between the two isomers there is a difference of chemical function; in the same circumstances, they undergo different chemical reactions. Here now is a completely different case of isomerism, where two compounds formed from the same elements, but arranged in different fashion, can always undergo similar substitution. So in chemically similar conditions, the two compounds undergo similar reactions; however, the products resulting from these similar reactions will not be identical substances, but isomeric substances like the original reactants. Striking examples of this isomerism of position are provided by the derivatives of benzene. The study of these examples would, unfortunately, require too extensive a preliminary discussion for it to be possible to develop here. This representation of isomeric substances, and particularly of position isomers, is one of the most beautiful consequences of the employment of constitutional formulas. We have just sketched the principles of the notation with which chemists represent and classify the innumerable compounds which they have studied. We have seen that the foundations of this notation were constituted by the two ideas of chemical analogy and chemical substitution. Neither of these ideas is susceptible of a definition in the way [439] these are given in geometry. So discussions between chemists cannot be cut short by a series of syllogisms resulting in a reductio ad absurdum. Chemical analogy found a representation in the crude formula, a structure built from the equivalent weights of the various elements. To represent the way in which various substances can be derived
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from one another by substitutions, it is necessary to appeal to the developed formula, an arrangement where atomic weights of the elements figure together with the number of valencies they exchange with one another. Such are the fundamental notions on which rests what is called atomic notation.
VII ON ATOMISTIC HYPOTHESES
We have traced the principles on which atomic notation rests and we have not made any use of the word atom. Twice have words derived from it been encountered under our pen. The first was the word atomic weight; the second was the word atomicity; but we have rejected these, and replaced the one by the word equivalent weight, and the other by the word valency. Although we have invoked neither the name nor the idea of the atom in the theory we have just developed, however, it is in fact by way of hypotheses about the atomic constitution of material that this theory is constituted. Consider a simple body, for example a piece of copper. It seems to us as though it continuously fills a certain volume. This volume is divisible in thought into two parts, these into two others, these resulting parts [440] again into two, and so on to infinity. We see nothing which hinders each of these volumes, however small, that we obtain in this way, from being a piece of copper like that we imagine, as being continuously filled with copper. For some schools of philosophy it is certain, even evident, that a body is infinitely divisible. Descartes, for example, who identified material and geometric extension, could not deny material the infinite divisibility which incontestably belongs to geometric extension. For other schools of philosophy it is no less certain, no less evident, that it cannot be so: admitting that material is infinitely divisible is an absurdity. The continuity that we think we encounter in our fragment of copper is, according to these philosophers, an illusion. Our piece of copper is formed of elements that we call atoms; these
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elements are separate from one another in such a way that a volume with dimensions accessible to our means of experience encloses a very considerable, yet finite, number. The division of the volume occupied by our piece of copper can therefore be pressed quite far in order that each of the partial volumes obtained contain a single atom. Having arrived at this term, we will be able to press further the ideal division of the volume occupied by copper, but not the physical division of copper. The element that we have isolated is now indivisible. What is this element, and why is it indivisible? The various metaphysical doctrines resolve this question in different ways. For one of them, this ultimate element of material is not extended; it is a true point, entirely devoid of dimension. It is a simple being which is not composed of parts and consequently not capable of being divided. For [441] the others, this ultimate element of matter occupies a certain extension, but this character of being extended, of having a shape, doesn’t prevent it being constituted by a unique being which is not capable of division, that is to say of becoming two beings. Let us mention yet a third solution, that of the vortex atoms of W. Thomson, a peculiar synthesis of the Cartesian theory of matter and the atomic theories, too complicated for us to be able to provide an exposition of it here without disproportionately extending this article. Now consider two simple substances, for example copper and sulphur, and combine them. What do you see? Two different substances, continuously filling two different volumes, are transformed into a third substance continuously filling a volume and possessing properties which are no longer those of sulphur nor those of copper. In other words, there is no longer any sulphur or copper; there is only copper sulphide. All these immediate results of observation are, for the atomists, nothing but illusion. When sulphur and copper combine, neither the copper nor the sulphur cease to exist; their atoms are imperishable. The atoms of sulphur and those of copper simply become arranged besides one another, grouped in a certain way. This grouping is given the name molecule. The nature and number of atoms juxta-
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posed to form a molecule are characteristic of the properties of the compound. From that, as Dalton showed, it is easy to deduce the fundamental laws of chemistry. Each atom has invariable mass. No atom is destroyed in the act of combination, [442] and nor is any created. Consequently, the mass of the compound is equal to the sum of the masses from which it was produced. In a determinate compound of two substances, the molecule is always formed from a determinate number of atoms of the first substance and a determinate number of atoms of the second. Consequently, the masses of the two substances which unite to form a determinate compound always stand to one another in a determinate ratio; this is the law of definite proportions. The same two substances can form different compounds. But the molecule of each compound always contains an integral number, generally simple, of atoms of the first substance, and an integral number, generally simple, of atoms of the second substance. From this the law of multiple proportions follows immediately. In other words, when two substances combine, the combining masses stand as the masses of the atoms of the two substances, or as the products of these masses with generally simple integral numbers. What is the cause of chemical analogy between two different substances? A similar grouping with the same number of atoms of different nature. So the molecules of two analogous compounds will be similar structures built from dissimilar materials. This similarity of shape and structure of the molecule is translated outwardly by the shape of crystalline polyhedra. From this we have the law of isomorphism which Mitscherlich stated in the following phrase, entirely impregnated with the ideas that we are at present dealing with: The same number of atoms, combined in the same way, produce the same crystalline shape; and the same crystalline shape is independent of the chemical nature of the atoms and is determined only by the number and relative position of the atoms.
What, [443] then, is the equivalent weight of a simple substance? It is the ratio of the mass of the atom of the substance to the mass of the hydrogen atom. For example, the equivalent weight of oxygen is 16, because the mass of the oxygen atom is 16 times as large as the
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mass of a hydrogen atom. From this we have that the name atomic weight is employed to designate the equivalent weight. What is the chemical formula of a compound? It is the indication of the number and nature of the atoms grouped together to form a molecule of the compound. Thus, the name molecule is steadfastly given to this formula. HCl is said to represent a molecule of hydrochloric acid, and H2 O to represent a water molecule. The sum of the equivalent weights brought together in the same chemical formula represents the ratio of the mass of this molecule to the mass of a hydrogen atom, and it is therefore given the name molecular weight. Thus, 36.5 is the molecular weight of hydrochloric acid, and 18 the molecular weight of water. This is Dalton’s atomic hypothesis. It agrees well with the primary laws and the primary notions of chemistry. The concern now is to complete it so that it entirely embraces that branch of chemistry that Dumas created when he conceived the notion of substitution. Each atom possesses one or more atomicities. Atomicity is that by which an atom can attach itself to another atom or, rather, in order that two atoms be united, it is necessary that a certain number of atomicities of the first are joined, one by one, with an equal number of atomicities of the second. There are atoms which possess only one atomicity; these are the atoms of chlorine, iodine, hydrogen, potassium, etc. . . . Evidently, each of these atoms can unite with only one atom of the same class. When [444] such a union is effected by soldering of the unique atomicity of one of these atoms with the unique atomicity of another, the two atomicities no longer present any free atomicity. The compound cannot be united with a new atom; it is saturated. There are atoms which possess two atomicities: oxygen and calcium fall into this category. The oxygen atom can unite with two atoms of hydrogen, each one of which, by virtue of its unique atomicity, saturates one of the atomicities of the oxygen atom, and the calcium atom can combine with two atoms of chlorine, thus forming water and calcium chloride. But an atom of oxygen combines with a single atom of calcium because each of them, having two atomicities to saturate, will need only the two atomicities of the other.
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When an atom of hydrogen occurs in a compound body, its unique atomicity saturates one of the atomicities of the remainder of the compound. Chlorine, which also exhibits just one atomicity, will be equally disposed to saturate this single atomicity in the course of saturating itself. An atom of chlorine and an atom of hydrogen will, therefore, be able to substitute for one another in the same molecular structure. On the other hand, if an oxygen atom, which has two atomicities to saturate, is to be placed in a molecular structure, it is necessary that the part of the structure which it displaces releases two atomicities. If the introduction of an oxygen atom is to be possible, it is not enough to remove a single hydrogen atom or a single chlorine atom from the molecular structure. That operation only extricates a single atomicity. It is necessary to remove two atoms of oxygen [sic.]21 or two atoms of chlorine. Oxygen possesses that property that a single one of its atoms is substituted for two atoms of hydrogen or two atoms of chlorine. These examples suffice to show how the phenomena of substitution are accounted for in the theory of the atomic constitution of matter. [445] What we have called the number of valencies of an element is the number of atomicities possessed by the atom of the elementary substance. The characteristics which are represented by the exchange of valencies in developed formulas represent in reality the way in which the atomicities of various atoms grouped together in the molecules are saturated by one another. All that we have just said is very general. We have spoken of atomicities possessed by an atom without making precise the intimate nature of these atomicities. It is, in fact, easier to describe how the atomic school interposes atomicity in the phenomena of substitution than to ascertain how it explains this peculiar property of the atom. The majority of the chemists in this school avoid all enquiry into the nature of this I know not what which can solder together two atoms, and which has perhaps the defect of over-resembling the classical hooks of the Lucrecian atoms. Let us hear, for example, Würtz22 the veritable creator of the notion of valency: The capacity for combination23 is not synonymous with affinity. The energy with which a body combines with another body is independent of the faculty which it possesses of attracting one or more atoms.
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The first is affinity, the second is atomicity: both are manifestations of the chemical force. Affinity is measured by the quantity of living force which is transformed by the effect of the combination and which is manifested as heat. Atomicity is measured by the number of atoms of hydrogen or of an analogous element that a given substance can fix. The atoms of chlorine and those of hydrogen are so constituted that an atom of the first kind always attracts an atom of the second. The force with which it attracts it is the affinity; [446] the quality of being satisfied with a single atom is the atomicity. Under the latter relation, the atoms of chlorine and hydrogen are the same: an atom of the one kind fixes only one atom of the other. The force residing in them is a powerful but simple force. The force which resides in an oxygen atom is powerful too, but of a more complex nature because it succeeds in annexing two atoms of hydrogen when an atom of chlorine can only attract one. Thus we see in the force which attracts the atoms of a substance towards the atoms of another substance two distinct things, namely: 1st. its intensity; 2nd. its simple or multiple action. These two manifestations of the chemical force are independent of one another. In fact, the energy of affinity does not give a measure of the degree of atomicity. Chlorine attracts hydrogen with more force than it does carbon; nevertheless, an atom of carbon can unite with four atoms of hydrogen, while an atom of chlorine can only unite with a single atom of hydrogen. Atomicity is therefore the peculiar property of an atom of attracting a greater or lesser number of other atoms. It is its value or, so to say, its capacity of combination.
Not all chemists have imitated the prudent reserve of A. Würtz. In an interesting little book,24 which we will soon have to speak about to the readers of the Revue,25 Father A. Leray supposes that the chemical atom has the shape of a polyhedron. Two atoms which combine cling to one another by two equal or unequal faces. The valency of an atom, of oxygen for example, in relation to another atom, of hydrogen for example, is the number of faces of the first which exhibit a shape and extension such that a face [447] of the second can come and cling to it in a stable fashion. J. J. Thomson has also tried, with his hypothesis of vortex atoms,26 to give an explanation of chemical combination which accounts for the facts of substitution represented by the notion of valency. Let us also mention in passing that this explanation is not adequate for all the points which the chemists hold on the subject of the valencies of the various elements.
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But these various explanations of the valency of atoms run up against several difficulties that we must examine. In the first place,27 the number of valencies possessed by an element in a determinate compound is well defined. Thus, chlorine and iodine are univalent in hydrochloric acid and hydroiodic acid; nitrogen is trivalent in ammonia; and carbon is quadrivalent in methane. But it shouldn’t be concluded that the number of valencies of an element is entirely determined, absolutely, in abstraction from compounds in which the element is tied up and of the way in which it is bound. The number of valencies of an element can change according as the element is part of one compound or another. Iodine, univalent in hydroiodic acid, is trivalent in iodine chloride; nitrogen, trivalent in ammonia, is quintivalent in ammonium hydrochlorate; carbon, quadrivalent in methane and in carbonic acid, is bivalent in carbon monoxide. Moreover, when two equivalents of the same element occur in the same combination, they may do so with different valency numbers. In ammonium nitrite, for example, the equivalent of nitrogen which comes from ammonia is quintivalent and that [448] which comes from nitrous acid is trivalent. Ethylcarbylamine contains two equivalents of quadrivalent carbon and one equivalent of carbon which exhibits only two valencies. This variation in the number of valencies of an element with the combination in which it occurs is therefore an undeniable fact. It is not without a little embarrassment that chemists have envisaged valency or atomicity as an elementary property of the atom. Take, for example, the nitrogen atom. It should exhibit trivalency or quintivalency according to the circumstances. Whatever the desired interpretation that might be given to valency or atomicity, nitrogen must in any case exhibit first of all three atomicities, which we call atomicities of the first order, and which are those fixed by three atoms of hydrogen in ammonia. Then, it exhibits two other atomicities, which might be called atomicities of the second order, and it is these which fix the elements of hydrochloric acid in the formation of ammonium hydrochlorate. An atomicity of the second order of the nitrogen atom could not arise from the same cause, or act in the same manner and in the same proportions as, an atomicity of the first order. For otherwise, if the five atomicities were absolutely identical, reasons of symmetry
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would render absurd the existence of compounds such as ammonia where three of these atomicities would be satisfied while the other two would be free. We must therefore accept that there is an essential difference between an atomicity of the first order of a nitrogen atom and an atomicity of the second order of the same atom, whatever the origin and nature of this difference might be. If, for example, we adopt the explanation given by Father A. Leray, it will be necessary for us to suppose that the faces of [449] the nitrogen atom corresponding to three atomicities of the first order do not have the same shape or the same size as the faces corresponding to the two atomicities of the second order; this, it seems, is the view of Father A. Leray. Now, is this essential, intrinsic, distinction admissible that we have been obliged to establish between atomicities of the first order and atomicities of the second order as soon as we wish to regard these atomicities as properties of the nitrogen atom? Take ethylamine, in which the ethyl group C2 H5 is fixed by an atomicity of the first order of the nitrogen atom. If this substance is combined with hydroiodic acid, its elements will be fixed by atomicities of the second order, and we obtain the hydroiodate of ethylamine. Now take ammonia, in which nitrogen’s three atomicities of the first order are saturated by three hydrogen atoms. If it is combined with ethyl iodide, iodine will be saturated by one of the atomicities of the second order and the ethyl group will be fixed by the other and we thus obtain a substance whose composition is the same as in the preceding example. These two substances of the same composition are formed in different ways. In the one, the ethyl group is fixed by an atomicity of the first order and in the other by an atomicity of the second order. Since these two atomicities of different kinds cannot be identical, the two compounds cannot be identical either, they should be two isomeric substances. But experiment shows that these two compounds are not two different isomers, but one and the same substance. Facts of this kind – and they are numerous – are difficult to explain on the view that isolated atoms possess a determinate number of atomicities, whatever the property might be in virtue of which
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[450] these atomicities might be explained.28 The difficulty disappears if the notion of valency is introduced as we have done above. The questions of whether the nitrogen atom has three or five valencies, and whether these valencies are similar or not, don’t arise. The nitrogen atom, taken in isolation, away from all compounds, doesn’t have a valency; the word doesn’t even have any sense applied to it. It [the nitrogen atom] only possesses valencies when it is bound in a compound, and in this compound it has either three or five according as the compound is related to the hydrochloric acid type three times condensed or to the hydrochloric acid type five times condensed. And whether it has three or five of them, the three or five valencies are, by definition, identical with one another. Now let us tackle the examination of another kind of difficulty which confronts the atomic hypotheses. If valencies represent that by which atoms are joined with one another in a chemical molecule, two chemical molecules should, if analogous, be formed from atoms placed in the same way and exchanging valencies between them in similar fashion. This similarity in the way in which valencies nail the one with the other will be the cause of isomorphism since, according to Mitscherlich, the same number of atoms, grouped in the same way, produce the same crystalline shape. Let us compare, then, sodium nitrate and calcium carbonate, and write the developed formulas of these two substances:
Can [451] two more differently drawn formulas be imagined? And if the formulas sketched bear any relation to the way in which the atoms are linked with one another in the molecule, can two molecules with a more different structure be imagined? Nevertheless, not only has sodium nitrate the same perceptible crystalline shape as calcium carbonate; if a rhombohedron of Island spar is immersed in a saturated solution of sodium nitrate, the rhombohedra of sodium nitrate are deposited on its surface and with the same orientation. Calcium carbonate and sodium nitrate are isomorphous.
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Again, let us compare potassium nitrate with potassium chlorate, writing their developed formulas as:
Certainly, these formulas are very different and, if the formulas represent to any degree the structure of the molecule, then the molecules must be very different. Chlorates are analogous to nitrates, however, and the works of Mallard leave no room for doubt about the isomorphism of these two kinds of salts. Here, then, are new difficulties. From what do they result? If the developed formula is regarded as representing the arrangement of chemical atoms in the molecules, it is difficult not to attribute to these molecules a structure like that of a developed formula and not to accept that the molecules analogous from the chemical point of view have an analogous structure. So the chemical analogy of two compounds should be represented by a similarity in the developed formulas. On the contrary, we have seen how the notion of valency [452] springs from the notion of substitution, a notion absolutely distinct from and independent of the notion of chemical analogy. So it is the crude formula and the crude formula alone which should express chemical analogy; two chemically analogous compounds must have similar crude formulas; but these crude formulas need not be developed in the same way. It is apparent that the atomic notation as ordinarily explained faces certain difficulties which have their source in experience. The cause of all these difficulties is the link established between this notation and the atomic hypotheses about the constitution of matter. But this link is not indissoluble. Let us untie it; let us take chemical notation for what it is in reality: an appropriate method for classifying chemical compounds. Let us show that, like any method of classification, it rests on certain notions, the notion of chemical analogy and the notion of chemical substitution, which are not susceptible of being defined as geometric concepts are, but which, as with the ideas employed by naturalists, are acquired by the comparison and illumination of examples. We see disappear forthwith the
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difficulties that have given rise to the presumptuous desire to take a classification as an explanation. Furthermore, we thereby avoid all the metaphysical objections that the philosopher can address to the atomic theories of the constitution of matter. Our chemical theory becomes independent, both in its principles and in its methods, of the solutions given by the various schools of philosophy to the problems raised by the nature of substances. It seems that the exposition of ideas in this article could have avoided the passionate but sterile discussions if they had been generally accepted twenty-five [453] years ago. They seem, in fact, totally imbued with the principles taught by a chemist regarded in this epoch as the most potent adversary of the atomic theory, H. Sainte-Claire Deville. In his admirable Leçons sur l’affinité,29 which ought to be read and pondered by all those who really wish to know the method and import of the physical sciences, Deville loudly proclaims that chemistry is a natural science and that its theories are the methods of classification: “It should not be forgotten that chemistry is a natural science”. We study, we observe, we experiment with matter as it is constituted.30 Stones, minerals, the elements of organised beings and all that is found around us on the earth is offered to us as an unlimited object of work without end. Whatever we might do, whatever the contemporary fashion of abstraction might be, we must employ the methods utilised in the natural sciences in order to arrive at the discovery of the truth. Let us establish analogies, state resemblances and differences of any order, and little by little do the work of a classification which will for a long time, perhaps forever, be incomplete. Let us experiment constantly to prove the legitimacy of the principles which guide us or to establish their imperfection or their inexactitude. But let us never trust hypotheses for an instant, and in particular let us never attribute a body and a reality to the abstractions that the weakness of our nature imposes on us. I will explain myself. All the hypotheses accepted today will necessarily disappear from science. I make no exception, even in favour of the theory of waves, an admirable conception of the human mind, where the hypothesis of the luminous ether still leaves much to be desired ...
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It [454] is the same in chemistry. – The hypothesis of atoms, the abstraction of affinity, and the forces of all kinds that are made to preside over all the reactions of the substances we study, are the pure inventions of our minds: names of which we make substance, names for which we attribute a reality. – Happily, all these hypotheses, all these abstractions, are not indispensable. We will study chemical phenomena, we will establish their similarities and differences; we will experiment to establish a revisionary classification, and we will thereby constitute a science all parts of which will escape all critique.
Still today it is to be feared that these principles have not penetrated enough, and that many researchers would see in the schemas of the atomic notation a picture of the way in which atoms are grouped in compounds. This is why we have believed it useful to emphasise, as precisely as we have been able, the origin and the sense of the abstractions that are called atomic weight, valency and chemical formula because, from these abstractions, it can justly be said with H. Sainte-Claire Deville: “They are harmful when their origin and their entry into science is forgotten, and they lead us to that scientific mysticism of which chemistry provides, at the moment, a dangerous example”.
NOTES 1. Princeton, NJ: Princeton University Press, 1954. Translation by Philip Wiener of La théorie physique: son objet – sa structure, 2nd ed. 1914, Paris: Marcel Rivière & Cie. 2. Paris: C. Naud, 1902; reprinted Paris: Fayard, 1985. Originally published as a series of articles in 1900 in the Revue de philosophie. 3. [“Quelques réflexions au sujet des théories physique”, Revue des questions scientifiques, 31 (1892), 139–177. This is translated in Essays in the History and Philosophy of Science, translated and edited by Roger Ariew and Peter Barker, Hackett, Indianapolis, IN and Cambridge, 1996.] 4. [“pour ceux qu’une longe initiation n’a pas familiarisés avec les symboles qui composent la langue géometrique”; presumably the intended meaning is that the symbols of the geometrical language are not familiar to those who haven’t undergone a long initiation in the discipline.] 5. [Duhem’s use of the symbol “Az”, corresponding to the French “azote”, has been systematically changed to “N”.] 6. [This and the following eight paragraphs were incorporated almost verbatim into Ch. 3 of Part 2 of Le mixte et la combinaison chimique (pp. 76–78).] 7. [Fluorine is placed at the beginning of the list throughout the corresponding paragraph in Le mixte et la combinaison chimique.]
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8. [The text of Le mixte et la combinaison chimique is different from this point.] 9. [Beginning with Ch. 4 of Part 2, the text of Le mixte et la combinaison chimique is clearly based on the present article from this point.] 10. The reader curious to know more of the details of this history will read with interest the admirable Préface written by Würtz at the beginning of the Dictionnaire de Chimie; it is one of the most beautiful pieces which exists on the history of science. See also, by the same author, Introduction à l’étude de la Chimie. Paris: Masson, 1885. [This note is absent in Le mixte et la combinaison chimique.] 11. We recall that we uniformly substitute, as we have proposed to do, the word equivalent weight for the word atom or atomic weight generally employed today. [In Le mixte et la combinaison chimique (p. 91) Duhem adds “The advantage of this substitution will soon be seen”.] 12. [In Le mixte et la combinaison chimique, “partially dehydrogenated”.] 13. [Here “élément”; in Le mixte et la combinaison chimique, “corps simple”.] 14. [In Le mixte et la combinaison chimique, “hydrogen” is changed for “ammonia”, but this alteration is presumably a mistake, however surprising.] 15. [The symbol “Ph” used throughout this article for phosphorus is systematically changed to the modern “P” in Le mixte et la combinaison chimique, and this modern notation is followed in the translation.] 16. A. Würtz, La Théorie atomique, p. 145. 17. [In Le mixte et la combinaison chimique “ammonia” is changed to “nitrogen”.] 18. [Here “du nitrate de potasse”; in Le mixte et la combinaison chimique “de l’azote de potassium”. For roughly the next two pages of the present text there is no corresponding passage in Le mixte et la combinaison chimique.] 19. [Presumably one of the H’s directly linked to the N should be I.] 20. [From this point, the text again resembles that of Le mixte et la combinaison chimique, p. 120f.] 21. [Presumably “hydrogen” is intended.] 22. Würtz. Dictionnaire de chimie, art. Atomicité. Throughout his book on the Théorie atomique (pp. 164 ff.) Würtz expresses himself in terms of analogies. 23. [There is a footnote reference in the original text at this point, but with the same number as the previous one, and there is no other footnote at the foot of the page.] 24. Father A. Leray, Complément de l’Essai sur la synthèse des forces physiques, p. 105 (Paris, 1892). 25. [Pierre Duhem, “Une Nouvelle Théorie du Monde Inorganique”, Revue des questions scientifiques, 33 (1893), 90–133.] 26. A complete exposition of work concerned with the hypothesis of vortex atoms is to be found in an interesting, but unfortunately unfinished, work of Marcel Brillouin: Recherches récentes sur diverses questions d’hydrodynamique (Paris, 1891). 27. [The text of Le mixte et la combinaison chimique resembles that of the present article from this point.]
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28. [From this point the text of Le mixte et la combinaison chimique is different.] 29. H. Sainte-Claire Deville. Leçons sur l’affinité, delivered before the Chemical Society on 28 February and 6 March, 1867 (Leçons de la Société chimique de Paris, Paris 1869). 30. [elle est faite.]
Paul Needham Department of Philosophy University of Stockholm Stockholm 10691, Sweden E-mail:
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