Transforming Atomic Chemistry into an Experimental Science: The Limitations of Dalton’s Theory

Alan Chalmers



Speculations about the corpuscular structure of matter were revived in the seventeenth century by mechanical philosophers. Elsewhere (1993) I have argued, in the particular case of Robert Boyle, that atomism as formulated by those mechanical philosophers did not fit well with the focus on experimental knowledge distinctive of the seventeenth century. Boyle’s claims about the physical properties of air explored in the laboratory could be substantiated and extended by experiment in a way that the abstract claims of his mechanical atomism could not. Newton transformed the atomism of the mechanical philosophers by introducing inter-atomic forces but it remained the case that his atomism, as distinct from his mechanics, was remote from anything that could be tested experimentally. In the domain of chemistry, the path that led to Antoine Lavoisier’s pragmatic definition of an element as a substance that cannot be broken down by chemical means involved the development of an experimental chemistry independent of and not usefully informed by Newtonian or any other brand of atomism as Arnold Thackray (1970) has argued in detail. Lavoisier set chemistry on its modern path by turning away from speculations about atoms. To what extent did Dalton give a further booste to the new experimental science by bringing them back in again?

Dalton’s atomic chemistry created a link between hypotheses about atoms and experimental knowledge where others had failed insofar as the theory explained chemical laws of proportion and insofar as it provided for the first time an avenue to determining a property of atoms, their relative weight. A sensible diagnosis of the key to the success of Daltonian atomism is that the interatomic forces presumed by atomists to be responsible for chemical combination were recognised as lying beyond what could be accessed by way of experiment on macroscopic chemicals and were ignored. Instead, the theory focused solely on the more tractable problem of the relationship between atomic weights and the proportions by weight of chemical compounds.

As we shall see, such a construal of Dalton’s atomism involves the abstraction of a basic chemical atomism from the detailed physical atomism that was espoused by Dalton himself and which was a failure. This historical point aside, the truncated version of Dalton’s atomism that yields the laws of proportion yields little else that is experimentally testable beyond what is a consequence of the laws of proportion themselves. Consequently, Dalton’s chemistry did not open up an experimental programme over and above what could be pursued by tracing the consequences of the laws of proportion themselves and ignoring atoms.

Nineteenth-century chemistry did progress beyond the consequences of the laws of proportion. The key factor that made experimental progress possible was the deployment of chemical formulae, especially in organic chemistry. I will argue that this deployment of chemical formulae did not require a commitment to atomism. It is true that, from 1860 onwards, links between chemistry and physics made it increasingly possible to forge links between hypotheses about atoms and experiment. Advances in chemistry, and, in particular, the emergence of a unique set of chemical formulae, had set the scene for those developments. They were a precondition for, rather than result of, the incorporation of atomism into experimental science.

There is something of the order of 1024 atoms in a typical coin. This fact helps to remind us of the difficulty of getting to know that this is the case. Dalton turned out to be right about the existence of chemical atoms, but we should not allow this fact to lead to an overestimate of Dalton’s achievement and an underestimate of the efforts of those who modified and extended his key idea. Otherwise we will lose sight of the difficulty of gaining experimental access to atoms and fail to appreciate how much knowledge needed to be in place to make it possible.

Dalton’s Atomism

Newtonian atomists of the eighteenth century aimed to explain properties of bulk matter, such as coagulation and chemical combination, by appeal to inter-atomic forces. In the case of chemical combination the forces became known as affinities. A major problem with this approach was the gulf between the speculations about inter-atomic forces on the one hand and what could be investigated experimentally on the other. Near the end of the eighteenth century, Claude-Louis Berthollet, himself a Newtonian atomist, spelt out the futility of trying to derive inter-atomic affinities from experiments on chemical combination in the laboratory because an atomist must recognize that any net attraction or repulsion measurable at the macroscopic level is a function of the state, temperature and masses of the combining substances and arises from unknown arrangements of large numbers of atoms.1 These problems could be supposed to be at a minimum in the case of the physical properties of gases, where an atomist could assume the atoms to be sufficiently far apart for forces of coagulation and chemical affinities to be ignored. (As it happened, the first atomic theory to gain significant empirical support, the kinetic theory of gases, made headway by ignoring inter-atomic forces altogether and admitting only the impulsive forces experienced by colliding atoms.)

Dalton’s atomism emerged out of what was in key respects a Newtonian atomistic theory of gases. The details of the path that led Dalton to his theory have been much studied and debated.2 Here I extract some of the uncontroversial features.

An atomistic theory of gases took shape in the context of one of Dalton’s early research preoccupations, namely, meteorology. In 1793 we find him insisting that the absorption and precipitation of water vapour by the atmosphere is a physical rather than a chemical process. The fact that the amount of water vapour that can be absorbed by a given volume of air at a fixed temperature is independent of the pressure of the air in that volume told against the prevailing idea that the absorption was due to some chemical affinity between air and water. Dalton’s understanding, atomistic from the start, was of atoms of water interspersed amongst other atoms composing air and acting independently of them. The idea that each gas in a volume makes its contribution to the total pressure independent of the other gases in the mixture was soon confirmed experimentally and has survived as ‘Dalton’s law of partial pressures’. Dalton developed his atomistic understanding by adapting Newton’s observation, in the Principia (Book II, Proposition 23) that a gas made up of a static array of atoms repelling each other with a force inversely proportional to their separation will obey Boyle’s law, notwithstanding the problems with this conjecture that Newton himself had already discerned.3 Dalton speculated that the atoms of each gas repel atoms of like kind with a force inversely proportional to their separation whilst exerting no force on atoms of other gases. This explained both the law of partial pressures and also why the gases in the atmosphere remain a homogeneous mixture rather than separating out with the more dense gases settling in layers below the less dense.

Dalton soon extended his research to consider the solubility of gases in liquids, and here he was able to join forces with William Henry, who had done experimental work in the area. Dalton, faced with the question of why some gases dissolve more readily in a given liquid than others, invoked the weight of the atoms of the respective gases as the likely cause of the difference. In the 1805 paper where these ideas were developed, Dalton (1805, p. 206) observed,

An enquiry into the relative weights of the ultimate particles of bodies is a subject, as far as I know, entirely new: I have lately been prosecuting this enquiry with remarkable success. The principle cannot be entered upon in this paper; but I shall just subjoin the results, as far as they appear to be ascertained by my experiments.

Entries in Dalton’s notebooks of 1803, now lost but referred to by Henry E. Roscoe and Arthur Harden (1826, pp. 26-9), imply that the atomic weights ‘subjoined’ to the 1805 paper were arrived at via Dalton’s chemical atomism.

Alongside these studies of the behaviour of gases and integrated into them were Dalton’s views on the nature of heat. His acceptance of the caloric theory of heat put him in the majority in the first decade of the nineteenth century, but what was peculiar to Dalton’s treatment was the extent to which he took a strong view on the materiality of caloric and the way in which he integrated that fluid into his atomic theory. An early version of these views appeared in a five page note ‘On heat’, an entry in Dalton’s notebook dated May 23, 1806. (Roscoe and Harden, 1896, p. 71, italics in original)

According to this view of the subject, every atom has an atmosphere of heat around it, in the same manner as the earth or any other planet has an atmosphere of air surrounding it, which cannot certainly be said to be held by chemical affinity, but by a species of attraction of a very different kind. Every species of atoms or ultimate particles of bodies will be found to have their peculiar powers of attraction for heat, by which a greater or less quantity of heat will be conglomerated around them in like circumstances: this gives rise to what has been called the different capacities of bodies for heat or their specific heat.

Whatever its initial attraction, Dalton’s efforts to pursue his physical atomism soon ran into serious trouble, and his attempts to square it with threatening experimental results had the effect of it losing whatever coherence it had. For example, Dalton’s attempts to give an account of the specific heats of gases, which, as can be inferred from the quotation from Dalton reproduced above, focused on the atmospheres of caloric surrounding atoms of a gas, met with no significant support from experiment. The same can be said of Dalton’s attempt to link the solubility of gases in liquids to atomic weights. There was a fundamental tension in Dalton’s theory concerning the cause of the expansion of gases. The caloric theory attributed expansion of a substance to an addition of caloric, which, for an atomist, insinuated itself between atoms and pushed them further apart. Yet Dalton explained vapours in terms of 1/r repulsions between like atoms. Dalton (1910, p. 548, italics in original) did respond to this difficulty by attempting to explain the even distribution that a mixture of gases settles into by appeal to caloric. His account involved the assumption that ‘every species of pure elastic fluid has its particles globular and all of a size; but that no two species agree in the size of their particles, the pressure and temperature being the same’. The rough idea seems to be that where unlike atoms meet, there is a discontinuity in the state of caloric, because of the difference in size, and that the forces arising from this discontinuity give rise to the motions that result in the uniform mixing of the gases. It is difficult to disagree with Roscoe and Harden (1896, p. 23) when they remark that this idea ‘does not appear to have been very carefully thought out, and although the conditions of equilibrium would certainly be disturbed, it is doubtful whether the intestine motion of which Dalton speaks would have been set up in a vessel filled with atoms’. Dalton expanded on his idea and illustrated it with diagrams in Part 2 of his New System of Chemical Philosophy published in 1810. Whilst these diagrams do exhibit the discontinuities arising from differing particle size, they did not help Dalton to show what he needed to show, namely, that the result of the discontinuities is a homogeneous mixture of gases and a force varying as 1/r between like atoms. It should also be noted that Dalton’s assumption that the atoms of unlike substances differ in size had no independent support and Dalton himself violated the condition on a number of occasions.

Dalton’s attempts to build on the early successes of his atomic theory of gases were unsuccessful. This is not surprising from a modern point of view given that Dalton worked with a static model of the arrangement of atoms in a gas and utilized a quite specific and detailed version of the caloric theory. According to an authority on the caloric theory, it does not require a modern vantage point to appreciate the shortcomings of Dalton’s theory. Robert Fox (1968, p. 197) concludes an analysis and appraisal of Dalton’s caloric theory with the observation that ‘to his contemporaries, whether in 1800 or 1842, Dalton’s work on the theory of heat must have seemed almost as wrong-headed and irrelevant to current problems as it does to us now’.

Dalton’s Atomic Chemistry

Dalton’s chemical atomism emerged out of his theory of gases because he saw in it the possibility of opening up an avenue for gaining experimental access to the relative weights of atoms. The bare bones of his theory appeared in the closing pages of Part I of A New System of Chemical Philosophy (1808) and can be separated from his physical atomic theory as his contemporary chemists soon learnt to do but which Dalton himself did not do.

Dalton was able to take Lavoisier’s notion of a chemical element for granted, together with the fact that the weight of each element is conserved in chemical reactions. As is well known, Dalton proposed that each element is composed of its characteristic atoms, the atoms of each element being identical, in weight and every other particular, and different from the atoms of any other element. The least parts of compounds, called ‘compound atoms’ by Dalton, are made up of a definite number of atoms of each of the elements that compose it with the compound atoms of a given compound again being identical to each other. These assumptions are sufficient to yield three laws of proportion relating the relative weights of elements in a compound as measured in the laboratory, the laws of constant, equivalent and multiple proportions. The first of these was already recognised as an experimental law by the time Dalton published his theory, but the third was novel and the second also had elements of novelty about it. The novelty was soon to be confirmed by a range of experiments. Dalton’s account of his theory concluded with his celebrated diagrams showing the composition of compound atoms as made up of atoms of elements represented as circles carrying signs to distinguish one element from another.

The composition of compounds and hence the relative weights of atoms were underdetermined by measurements of the relative weights of elements in a compound as Dalton was well aware. For instance, if a compound atom of water consists of one atom of hydrogen and one atom of oxygen, as Dalton in fact supposed, then the experimental fact that the weight of oxygen in water is eight times the weight of the hydrogen implies that the atomic weight of oxygen relative to hydrogen is 8, whereas it is 16 if the composition of water is two atoms of hydrogen for each atom of oxygen. Dalton broke the circle with a simplicity rule stemming from his physical assumption that atoms of like gases repel each other. Keeping the number of simple atoms of like kind in compound atoms to a minimum maximises the stability of the compound. Dalton accordingly proposed that compound atoms should contain the least number of simple atoms consistent with the measured combining weights. Apart from the question of the truth of this assumption (which was not destined to be of great help in organic chemistry) there was the problem of its ambiguity. For example, it did not of itself help to decide which of the two common oxides of carbon is binary and which tertiary.

The point that Dalton’s atomism had in its favour was that it explained the laws of proportion. Paul Needham (2004) has recently argued that not even this much can be said for Dalton’s chemistry. He denies that Dalton’s atomism did explain why substances combine in constant proportions. There is a sense in which Needham is right. Dalton’s theory does not explain why substances combine in constant proportions. It does not explain why substances combine at all! On the other hand, given that they do combine, then Dalton’s assumptions about atomic constitution do explain why they do so in constant proportions. Needham sees the lack of an explanation of chemical affinity as a serious shortcoming of Dalton’s theory whereas, I suggest and as we shall see, it became a mark of its strength when suitably interpreted and extended by others. The demand that a science explain everything in its domain leads to an infinite regress. It is not sensible to criticise modern electron theory because it does not explain the charge on the electron. Explanatory goals in science should be geared to what is realistic given the theoretical and experimental resources. Newton was wise to refrain from explaining gravity because there was no promising path towards achieving such an explanation and because there were many opportunities to explain many phenomena by taking gravity for granted. Berthollet had already pinpointed the futility of attempting to access inter-atomic force laws empirically. Dalton was wise to avoid them in his chemistry and on shaky ground when he retained them in his physics of gases.

Unlike Needham, I claim Dalton was wise to steer clear of hypotheses about forces of chemical affinity and did succeed in explaining the laws of proportion. Nevertheless, the extent to which this latter fact did indeed constitute a case in favour of Dalton’s atomism requires considerable qualification. Dalton’s atomic theory did explain laws of proportion, but was it the right explanation? The fact that there was no alternative explanation on offer at the time tells in favour of Dalton. But let us recall that by the mid-nineteenth century the only explanation on offer of known optical phenomena, including the recognition that light reaches us from distant stars, was that light is a transverse wave in an elastic aether. But there is no aether. One natural demand for the adequacy of an explanation of some phenomenon by a theory, in addition to the demand that the theory entail the phenomenon, is that there is evidence for the theory independent of the phenomenon explained. Dalton’s chemical atomism did not live up to that demand where the phenomena to be explained are the laws of proportion. If we focus on Dalton’s chemistry, then there was no evidence for his atomism over and above the evidence for the laws of proportion. If we include the physical aspects of his atomism this is no longer true, but hardly helps the case for Dalton given the fate of those aspects of his atomism that we have described above. The most charitable way to interpret Dalton’s atomism is to extract the chemistry and leave the dubious physics behind. But once this is done, we are faced with the circumstance that there was no evidence for Dalton’s atomism independent of evidence for the laws of proportion. As a consequence, a number of Dalton’s contemporaries, such as J. Heschel, H. Davy and J. Berzelius, were careful to separate the sound laws of proportion from what they regarded as the unduly hypothetical part of Dalton’s theory, namely, the atomism. (Brock, 1967, pp. 2-4)

The fact that Dalton’s atomic chemistry did not have testable content beyond what is implied by the laws of proportion is evident from the development of the theory in Dalton’s own hands. Following the publication of Volume 1, Part 1 of A New System of Chemical Philosophy in 1808, Dalton published Volume 1, Part 2 in 1810 and Volume 2, in 1827. A second edition of Volume 1, Part 1, published in 1842, two years before Dalton’s death, was an unchanged version of the 1808 work. The detailed chemistry in these works follows a common pattern. The sections on each chemical substance begin with a description of the key chemical properties and mode of preparation of the substance, details the results of the analysis of the proportions of elements in the substance where it is a compound and then concludes by suggesting an atomic constitution for each compound. What Dalton takes to be the atomic constitution of a compound is a result arrived at after the chemistry has been done. There is no evidence in Dalton’s work that the atomic theory played a role in fruitfully guiding chemical research. This contrasts with what others were able to do with an appropriate deployment of chemical formulae, as we shall see.

Berzelian Formulae

It was Berzelius who introduced into chemistry formulae of the kind now commonplace for representing the composition of compounds. By the time he did so, in 1813, he was able to take advantage of the addition of a further experimental law that had been added to the three laws governing combining weights. That was Gay Lussac’s law specifying that when gases combine at some definite temperature and pressure they do so in volumes that bear a simple ratio to each other and to the volume of the product if gaseous. Berzelius (1813, 1815) argued, that using formulae was preferable to using Daltonian diagrams because the former, in conjunction with a table of ‘atomic weights’ could capture all that was warranted by experiments on combining weights and volumes without commitment to the atomic hypothesis. This point is central to what follows and needs to be clarified in a way that will explain the use of italics around ‘atomic weights’ in the previous sentence.

An atomist will typically take the hydrogen atom as a standard so that the atomic weight of any other substance will be the weight of an atom of it compared to the weight of an atom of hydrogen. From this point of view, a formula of H2O for water indicates that a compound atom of water consists of two atoms of hydrogen combined with one of oxygen. This yields the measured proportions by weight for an atomic weight of 16 for oxygen. But there is no compulsion to take the weight of a hydrogen atom as the standard. More in keeping with what is actually done in the laboratory, any portion of hydrogen whatsoever can be taken as the standard and the ‘atomic weight’ of a second element can be defined relative to it. The formula H2O will then indicate two portions of hydrogen for every one of oxygen. Of course, if HO is taken as the formula for water then the atomic weight of oxygen will be 8 rather than 16. Some decision needs to be made to remove the under-determination of formulae and ‘atomic’ weights’ by weight and volume measurements in the laboratory, but that is the case whether one is an atomist or not.

Berzelius (1815, 125 – 6) explained that he differed from Dalton insofar as he considered ‘the atomic theory as imperfect, and as clogged with difficulties’. He promoted his introduction of formulae as an alternative to Dalton’s diagrams precisely because they could be interpreted as representing combining weights and volumes without a commitment to atoms. Berzelius (1813, 359) described the view embodied in his formulae as ‘founded on something very analogous to the corpuscular hypothesis of Dalton’ but considered himself to have the advantage over the latter ‘of not founding my numbers on an hypothesis, but upon a fact well known and proved’. Two years later (1815, 127) he re-iterated this point.

I placed beside the corpuscular theory, a theory of volumes; because that theory is in some measure connected with facts that may be verified. To those who think that the theory of volumes may be fatal to the corpuscular theory, I would observe, that both are absolutely the same thing; but that the theory of volumes has this immediate advantage over the other that it may be more easily verified. … The only difference between the two theories consists in the words atom and volume, that is to say, in the state of aggregation of the elements.

Berzelius’s claims are problematic as they stand for it cannot at the same time be the case that his theory amounts to the same thing as Dalton’s whilst being less hypothetical. What Berzelius clearly intends is that his theory is the same thing as Dalton’s as far as the experimental evidence available at the time is concerned. But that draws into question the extent to which chemical atomism can be said to be supported by that evidence.

Berzelian formulae in conjunction with a table of ‘atomic weights’ can be used to represent chemical constitution without a commitment to atomism. Berzelius himself did not use this as a reason for denying atomism. Rather, he attempted to develop Dalton’s atomism further so that it would go beyond the prediction of combining weights and volumes to explain a mechanism for chemical combination. Inspired by the phenomenon of electrolysis he presumed that atoms were held together in compounds by electrostatic forces. It is doubtful whether Berzelius’s theory did have testable content in excess of the evidence for the laws of chemistry and of electrolysis that he was attempting to explain. In any case, he clearly separated this hypothetical part of his theory from the account of combining weights, claiming not to attach too much significance to the former, at least in 1815.

I do not consider the conjectures which I hazarded on the electro-chemical polarity of the atoms as of much importance. I scarcely consider them in any other light than as an ideal speculation deriving some little probability from what we know of the chemical effects of electricity. (1815, 123).

Berzelius’s hypothesis ran into serious trouble in organic chemistry when it was discovered, for example, that electropositive hydrogen can be readily replaced by electronegative chlorine in a range of organic compounds. The nature and fate of Berzelius’s atomism is beyond the scope of this paper. The main point is that Berzelian formulae can be used to express weight and volume relations involved in chemical composition without a commitment to atomism. Klein (2003, p. 20) has pointed out that those chemists who were inclined to take this path talked of combining equivalents (Wollaston), proportions (Davy), combining weights (Young), portions (Thomson) and parcels (Whewell) rather than atoms. To her list can be added doses (Donovan), combining quantities (Brande) and stoichiometrical numbers (Gmelin) as noted by Goodman (1969, p., 45).

Adaptation of Berzelian Formulae in Organic Chemistry.

Berzelian formulae were not much used in chemistry before the late 1820s, not even by Berzelius himself (Klein, 2003, p. 250, n. 2). This is understandable in light of the fact that, in inorganic chemistry where they were first introduced, they express little more than combining weights and volumes that can be just as well expressed in other ways. As Klein has argued in detail, this was to change when formulae were adapted for use in the much more complicated area of what is now referred to as organic chemistry. A large number of elements figure in the composition of inorganic compounds, with each compound consisting of fixed proportions of just a small number of those elements. By contrast, organic compounds are made up of complicated combinations of a small number of elements, mainly carbon, hydrogen and oxygen and to a lesser extent nitrogen. As a consequence, knowledge of the proportions of elements in a compound is by itself an inadequate indication of its properties. A further complication is that a reaction involving the production of some organic substance of interest is unavoidably accompanied by parallel reactions involving the production of by-products. In this section, drawing heavily on the work of Klein (2003) and Rocke (1984), I outline some of the ways in which order was brought to organic chemistry through the use of ‘rational’ chemical formulae, in which the ordering of terms is indicative of chemical properties, as opposed to ‘empirical’ formulae’ which are indicative of relative weights only. This adaptation of formulae succeeded to such a degree that, by around 1860, a fairly unique set of formulae adequately characterising the properties and composition of organic compounds had emerged. In the following sections I take up the issue of the relevance of the story for atomism.

The complexity of organic reactions due to the many by-products invariably accompanying the preparation of some product was confronted by using chemical equations to track the formation of each product. The formation of ether from alcohol by the action of sulphuric acid can be represented, using atomic weights now known to be the correct ones, by the equation 2C2H6O = C4H10O + H2O. The numbers of occurrences of C, H and O on each side of the equation must balance, so that the weight of each element remains unchanged. Equations representing the formation of the various by-products can be represented by other balanced equations. In this way the messy process involving several parallel reactions and the formation of a mixture of products is comprehended by representing it as a superposition of identified reactions independent of each other and each represented by a balanced equation. Klein (2003, 118-129) has shown how, in the late 1820s, Jean Dumas and Polydore Boullay first used this technique to understand the formation of ether and its by-products from alcohol, thereby bringing order to a reaction that had caused confusion for decades. Thereafter, the use of chemical equations became commonplace and indispensable.

Another device that proved productive involved moving beyond Berzelius’s initial innovation by introducing some order into the symbols representing the elements in an organic compound so that they represented properties other than mere combining weights and volumes. So-called radicals were understood as groupings of elements that remained intact through a chemical reaction and played a role similar to that of elements in inorganic chemistry. So, for instance, series of compounds could be understood as resulting from various additions to the methyl radical, CH3, so that we have methyl alcohol, CH3OH, methyl chloride, CH3Cl and so on using modern atomic weights. A fruitful idea was that of homologous series, an example of which is that involving the successive addition of CH2 to the methyl radical to form ethyl, propyl, butyl and higher order compounds. Using this device, the properties, and even the existence and method of preparation, of higher order substances could be predicted on the basis of knowledge of the lower order ones. Berzelius introduced the terminology that distinguished ‘empirical formulae’, which simply indicated the proportion by weight of elements in compounds from ‘rational formulae’ which included some ordering of symbols to reflect chemical properties other than combining weights. So CH2O is the empirical formula for acetic acid whereas C2H3O2H is a rational formula for that acid.

A further use of formulae that was to have wide ramifications involved the concept of substitution.4 The substitution of one element in a compound for another in the laboratory was represented by the interchange of the symbols for the elements in the corresponding formula. This device was soon extended to the substitution of groups of elements (radicals) for other groups or elements in a formula. The recognition that, for instance, one chlorine can be substituted for one hydrogen whereas one oxygen needs to be substituted for two hydrogens was eventually to lead to the notion of valency.

The demand that the symbols in chemical formulae for compounds be arranged in ways that reflect the properties of those compounds had resulted, by around 1860, in a set of formulae that were virtually unique, the main conclusion reached by Rocke (1984). Here I give a few examples to indicate some of the key types of argument that led to this result. The simplest empirical formula for acetic acid is CH2O as pointed out above. This formula cannot be used to reflect the experimental fact that the hydrogen in acetic acid can be replaced by chlorine in the laboratory in four different ways yielding four distinct chemical compounds. Three of those compounds are acids similar to acetic acid and in which the relative amounts of chlorine vary as 1:2:3. The fourth compound has the properties of a salt rather than an acid. These experimental facts can be captured in a formula by doubling the numbers and rearranging the symbols in the empirical formula so that we have C2H4O2, rearranged to read C2H3O2H. The experimental facts can now be readily understood in terms of the substitution of chlorine for one or more of the hydrogens, with the three chloro-acetic acids represented as C2H2ClO2H, C2HCl2O2H and C2Cl3O2H and the salt, acetyl chloride, as C2H3O2Cl. Another productive move involved the recognition that the action of acids needed to be understood in terms of hydrogen replacement. Polybasic acids became recognised as producing two or more series of salts depending on whether one, two or more hydrogens were replaced. Another insight involved the requirement that rational formulae adequately represent certain asymmetric compounds such as methyl ethyl ether, CH3C2H5O, as distinct from methyl ether, (CH3)2O and ethyl ether, (C2H5)2O. These kinds of demands on the connection between rational formulae and the properties of the compounds they represented eventually led, by chemical means, to the solution of the problem of the under-determination of formulae and atomic weights. By that time, chemical elements were understood to possess a novel property, valency.

I draw attention to the fact that in this section I have been able to describe the emergence of definitive formulae in organic chemistry quite naturally without referring to atoms.

The Case for Atomism Circa 1860

By the 1860s organic chemistry had developed to the extent that rational formulae indicative of the properties and composition of chemical compounds had been identified, relative atomic and molecular weights determined and a new property of chemical elements, their valency, fashioned. Apart from the theoretical implications of these advances, their practical importance was manifest in the emergence of the synthetic chemical industry. To what extent can these undoubted successes be attributed to Dalton’s theory and to what extent can they be taken as support for atomism?

To do justice to the subtleties of issues surrounding atomism I introduce a distinction between three positions which I refer to as physical atomism, chemical atomism and agnostic anti-atomism.

Physical atomism involves atoms that are embedded in some physical theory such as those of the mechanical philosophers or Newton and possess physical properties such as mass, shape, size and the propensity to attract or repel other atoms. The kinds of properties possessed by physical atoms are determined in advance of chemical research by the physical theory that governs them.

Chemical atoms are the least parts of chemical elements. As well as mass, a property shared by chemical and physical atoms, chemical atoms are presumed to possess chemical properties characteristic of the elements they are atoms of. The kind of property it is necessary to attribute to chemical atoms is to be determined by chemical research. An example is valency, interpreted as a property of atoms by chemical atomists, which emerged in the course of chemical research as we have seen.

Agnostic anti-atomism involves a refusal to commit to atomism. It is not a denial of atomism, which is a claim of similar strength to its affirmation. An agnostic anti-atomist would claim that the practise and success of the chemistry with which we are concerned does not require a commitment to atoms and is compatible with the idea that chemicals retain their properties however much they are divided. Consequently, the dramatic successes of the enterprise cannot straightforwardly be taken as evidence for atomism.

It is clear that both a physical and a chemical atomist is free to use chemical formulae, interpreting the symbols in those formulae as representing physical and chemical atoms respectively. But an agnostic anti-atomist is free to use them too. The discussion in the previous section of the path that led to unique rational formulae for compounds makes perfect sense if formulae are taken simply as describing chemical properties as well as combining weights and volumes. As already indicated, I deliberately omitted any reference to atoms in that section. The appearance of OH at the end of the formulae for a compound indicates that it has the properties of an alcohol, whilst CO2H is indicative of an organic acid and so on. Further, the substitution of one element for another in a compound in the laboratory is mapped by the replacement of one symbol for another in a chemical formula. The formula of a compound represents some structure of that compound, but it does not have to be an atomic structure. The compound could possess the structure all the way down, as it were.

An analogy will help illustrate the coherence and intelligibility of agnostic-anti-atomism and its assumption that the indefinite divisibility of chemical substances is compatible with their characterisation using formulae. The electric field, E, has the symmetry of an arrow whilst the magnetic field, H, has the symmetry of a spinning disc. These facts led Maxwell and his followers to assume that E represents a strain in the aether whilst H represents a vortex in that aether. But there is no aether. The fields of classical electromagnetism are continuous and possess what structure they have all the way down. Agnostic anti-atomism was viable up until 1860 and beyond because no chemical evidence told against the possibility that chemical compounds possess their structure all the way down. Given the state of affairs in 1860 there was no guarantee that physical and chemical atoms would not be banished from science in the way that the aether came to be.

A number of chemists involved in the developments of concern in this paper can be classified as chemical atomists. August Kekulé (1867, 303-4), for example, made the distinction between physical and chemical atomism, and his commitment only to the latter, quite explicit. The historian Christopher Meinel (2004, 257) confidently invokes ‘the usual distinction between chemical and physical atoms’ which ‘provided a common denominator for those who did not want to engage in metaphysical debates about the existence of atoms, but sought to pursue chemistry pragmatically’. Chemical atomists were certainly judicious in distancing themselves from physical atomism. The gap between the abstract claims of physical atomic theories and chemical experimentation could not be bridged prior to the 1860s at least, and physical atomic theories gave no useful guidance to organic chemistry. If the rise of the latter owed a debt to Dalton at all, it was to the chemical atomism that others creatively extracted from his work, rather than to the physical atomism that he espoused.

The fact that the use of chemical formulae is compatible with agnostic anti-atomism raises the possibility that the rise of organic chemistry did not constitute a strong case for atomism at all. The productive enterprise of arranging symbols in chemical formulae to capture chemical properties other than combining weights or volumes, and the representation of the replacement of one element or group of elements in a compound in the laboratory by the replacement of one symbol or group of symbols by others in a formulae made perfect sense without a commitment to atomism as we have seen. Pierre Duhem (1902) spelt out a detailed defence of this position at the turn of the century. Many of the relevant research papers invoke formulae with no mention of atoms, whilst use of the term ‘atom’ is dispensable in those that did invoke the term. Further, many of the chemists that did refer to atoms interpreted them as useful fictions when pressed on the matter.5 As David Knight (1992, 120) puts it, ‘chemists were almost all atomists, but recognised atomism as an optional extra’ when pressed. The scepticism of many chemists concerning the existence of atoms is borne out by the ‘atomic debates’ that took place in Britain in the 1860s and 1870s, documented by Brock (1967). There is little doubt that, as the century progressed and as links were forged between chemistry and physical processes such as the behaviour of gases, electrolysis, optical rotation, the osmotic pressure of electrolytes and non-electrolytes, spectroscopy and so on, the case for interpreting the symbols in formulae as representing atoms became increasingly powerful. But those developments took place after the advances in chemistry considered in this paper.

Comparison with Rocke and Klein.

I have drawn on the historical work of Alan Rocke and Ursula Klein in this article, The epistemological points I wish to make overlap with theirs, but do not coincide because those authors do not distinguish clearly between what I have called chemical atomism and agnostic anti-atomism.

Rocke (1984, pp. 10 – 15) distinguishes between physical and chemical atomism. For him, it is the latter, rather than the former, that productively informed the rise of organic chemistry in the nineteenth century. In Rocke’s view, chemical atomism ‘was universally (if implicitly and often unknowingly) accepted throughout the course of the nineteenth century’ whereas physical atomism ‘was controversial and far from universally accepted’ (p. 10). He characterises chemical atomism as affirming the existence for each element of ‘a unique “atomic weight”, a chemically indivisible unit that enters into combination with similar units of other elements in small integral multiples’ (p. 12). He insists that this chemical atomism ‘has greater content than stoichiometry’ (p.13). Most of this is consistent with chemical atomism and agnostic anti-atomism as I have defined them. The exception is Rocke’s inclusion, in his chemical atomism, of the notion of chemical atoms assumed to be ‘chemically indivisible units’. My claim is that the story of the rise of organic chemistry, as Rocke himself has told it, did not require a commitment to chemical atoms and could be accommodated by an agnostic anti-atomist.

Organic chemistry in the third to the sixth decades of the nineteenth century owed its dramatic success to assumptions that went beyond what could be sensibly construed as generalisations from observations made in the laboratory, and certainly went beyond what is contained in the laws of proportion. The idea that the properties of organic compounds are related to an invisible structure that goes beyond weight relations and which can be mapped by rational formulae, the representation of the replacement of one element by another in a compound by the substitution of one symbol by another in a rational formula, the construal of acids in terms of replaceable hydrogen and so on were all theoretical assumptions. In light of this, I can agree with Rocke (1984, pp. 12 – 13, 84 – 87, 177 -80) that those chemists, notably William Wollaston and Leopold Gmelin, who expressed themselves in terms of a definite set of equivalents rather than atomic weights, did not thereby avoid a commitment to theory. Such a commitment was necessarily involved in use of formulae to express more than combining weights and volumes. However, my position differs from Rocke’s because my distinction between chemical atomism and agnostic ant-atomism allows me to deny that this theoretical commitment amounted to a commitment to chemical atomism.

An anonymous referee of an earlier version of this paper objected to my claim that Ursula Klein’s portrayal of the emergence of organic chemistry is compatible with agnostic anti-atomism. That referee interpreted Klein as defending chemical atomism in this context and invited me to read her book more closely. I have done so, and find no need to alter my original claim. Klein agrees with Rocke in claiming that the use of formulae by organic chemists went beyond what is implied by laws of proportion insofar as they were used ‘to model the invisible constitution of organic substances’ (2003, p.11). The symbols in chemical formulae indicated ‘scale-independent bits or portions of elements, which overlapped but [were] not identical with the concept of “atom” in the philosophical and physical tradition’ (2003, p. 12) so that ‘Berzelian formulas had a theoretical meaning that differed from “atomic” composition” ’ (p. 14-15). The notion of a ‘scale-independent bit or portion’ is ambiguous. According to one interpretation, the bits or portions are discrete ontological entities which have a definite weight and any other property that they possess whatever scale one might choose to measure them by. According to a second interpretation, the bits or portions are any sample of a chemical element, however small. These bits or portions will all alike posses the chemical properties of the substances they are bits or portions of, whilst the ‘atomic weights’ involved in specifications of weight relations in chemical combinations and substitutions will be scale invariant because they are relative weights. It is the second of these interpretations that makes most sense of Klein’s work. Her distinction between ‘scale independent chemical portions’ and ‘particles in the micro-world’ (p. 252, n. 420) would seem to require this as does her insistence that the object of the work of the organic chemists in deploying formulae ‘was not the behaviour of sub-microscopic atoms but rather, in a traditional intellectual framework, the macroscopic level of substances or substance components and their recombinations’ (p. 265-6, n. 24). In short, Klein’s work on the introduction into and productive use of formulae in organic chemistry fits well with what I have termed agnostic anti-atomism.

Concluding Remarks

A variety of attitudes towards atomism can be found in the writings of nineteenth-century chemists. The differing attitudes did not prevent them collaborating in a highly productive and progressive enterprise, namely, organic chemistry informed by the use of chemical formulae. That enterprise did not require or depend on a commitment to atomism prior to 1860 and beyond, whether some of the participants thought so or not, and its success should not be regarded as a triumph for atomism. Experimental access to atoms was eventually accomplished and the symbols in chemical formulae could successfully be interpreted as referring to them. Progress in organic chemistry was one of the preconditions for that accomplishment rather than a result of it.

The foregoing remark can be illustrated by reference to the classic paper by Cannizzaro (1858) which formed the substance of his address to the Karlsruhe Conference of 1860. In that paper Cannizzaro showed how atomic weights of chemical elements can be deduced from measurements of equivalent weights and molecular weights. The molecular weights were themselves deduced from measured vapour densities on the assumption that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Once atomic weights are known, definitive formulae for compounds can be deduced from measurements of the proportion of elements in them.

There are several ways in which the significance of Cannizzaro’s work owes a debt to progress in organic chemistry in a way that has not been adequately acknowledged. Firstly, Cannizzaro shows how a unique set of atomic weights can be derived. But are they the correct atomic weights? This depends on the truth or otherwise of the equal volumes/equal numbers hypothesis and that, in 1858, was unclear. However, the atomic weights derived by Cannizzaro coincide with those already arrived at by organic chemists by chemical means. This is the main vindication of Cannizzaro’s method. It should also be noted that the formulae for compounds that follow from Cannizzaro’s derivation of atomic weights are empirical formulae, not the rational formulae so central to organic chemistry. Cannizzaro’s deployment of rational formulae in the latter sections of his paper is parasitic on the work of the organic chemists. This is the case, for instance, when he write acetic acid as C2H3HO2, ‘to indicate that one of the four atoms of hydrogen contained in the molecule is in a state different from the other three’ (1858, p. 72). A little later Cannizzaro prefers to write this as HX where X stands for C2H3O2 to single out the replaceable hydrogen characteristic of the acidic property of acetic acid, but, significantly from the point of view of the argument of this paper, he notes that ‘without touching the question of the disposition of the atoms within the molecule of acids, I only wish to indicate distinctly the part that is changed in the transformation of the acid into its corresponding salt’ (p. 74). Cannizzaro’s debt to the work of the organic chemists is clear, work that I have argued was compatible with agnostic anti-atomism. This exemplifies and reinforces my point that organic chemistry informed by formulae was a precondition for rather than a result of atomism in chemistry.

At the turn of the nineteenth century T. E. Thorpe gave expression to a common assessment of Dalton’s achievement in chemistry, claiming that ‘the characteristic feature of the chemistry of our time is, in a word, the development and elaboration of Dalton’s doctrine; for every great advance in chemical knowledge during the past ninety years finds its interpretation in his theory’. (Cited by Thackray, 1970, p.279) Such assessments require considerable modification in the light of the considerations of this paper. They fail to do justice to the creative modification of Dalton’s ideas by innovative organic chemists such as Jean-Baptiste Dumas who not only extracted the chemistry from Dalton’s theory leaving the physical atomism behind, but also deployed chemical formulae in a way that opened up a productive experimental program that could succeed in laying the foundations of the synthetic chemical industry without getting sidetracked by questions concerning the reality and nature of invisible atoms to which they had no experimental access.

Thorpe was writing at a time when experimental paths to knowledge of atoms independent of organic chemistry had been opened up and when it had become uncontroversial and automatic to interpret the symbols in chemical formulae as referring to atoms. Edward Frankland was a chemist whose pioneering work on the chemistry of organo-metallic compounds preceded the subsequent vindication of chemical atomism. In 1851 he gave his inaugural lecture as the first professor of chemistry at Owens College, later to become the University of Manchester. One might have expected him to ingratiate himself with the dignitaries of Manchester that were present by making much of John Dalton, the figure they would have been keen to claim as one of their own and the ‘father of modern chemistry’. In fact, Frankland (1852) made just one passing reference to Dalton, mentioning him in the same breath as William Henry. The lack of significance of Dalton’s chemistry that is implied here, made public by Frankland in 1851 in Manchester, is difficult to comprehend if Thorpe’s assessment of Dalton’s place in chemistry is correct. But it is totally explicable in light of the view I have pressed in this paper.


Berzelius, J. (1813), ‘Experiments on the Nature of Azote, of Hydrogen, and of Ammonia and upon the Degrees of Oxidation of which Azote is Susceptible’ Annals of Philosophy, 2, 276 – 84 and 357 – 68.

Berzelius, J. (1815), ‘An Address to Those Chemists who Wish to Examine the Laws of Chemical Proportions, and the Theory of Chemistry in General’, Annals of Philosophy, 5, 122 – 31.

Brock, W. H. (1967), The Atomic Debates: Brodie and the Rejection of the Atomic Theory, Leicester: Leicester University Press.

Cannizzaro, S. (1858), ‘A Sketch of a Course of Chemical Philosophy’, reprinted in M. J. Nye (ed.), The Question of the Atom: From the Karlsruhe Congress to the First Solvay Conference, 1860 – 1911, Los Angeles: Tomash Publishers, 1986, pp. 30 - 87.

Chalmers, A. (1993), ‘The Lack of Excellency of Boyle’s Mechanical Philosophy’, Studies in History and Philosophy of Science, 24, 541 –64.

Cole, T. (1978), ‘Dalton, Mixed Gases and the Origins of the Atomic Theory’, Ambix, 25, 119 – 30.

Dalton, J. (1805), ‘On the Absorption of Gases by Water and other Liquids’, Memoirs and Proceedings of the Manchester Literary and Philosophical Society, 1, 271 – 86.

Dalton, J. (1808), A New System of Chemical Philosophy, Vol. 1, Pt. 1, London: R. Bickerstaff, reprinted by Citadel Press, New York, 1964.

Dalton, J., (1810), A New System of Chemical Philosophy, Vol. 1, Pt. 2, London: R. Bicherstaff.

Dalton, J. (1827), A New System of Chemical Philosophy, Vol. 2, Pt., 1, London: George Wilson.

Dalton, J. (1842), A New System of Chemical Philosophy, Vol. 1, Pt. 1, 2nd Edition, London: John Weale.

Duhem, P. (1902), Le Mixt et la Combinaison Chimique: Essai sur L’evolution d’une Idée, Paris: C. Naud, translated by P. Needham, Pierre Duhem: Mixture and Chemical Combination and Related Essays, Dordrecht: Kluwer, 2002, pp. 2-118.

Fox, R. (1968), ‘Dalton’s Caloric Theory’ in D. S. L. Cardwell (ed.), John Dalton and the Progress of Science, Manchester: Manchester University Press, pp. 187 – 201.

Frankland, E. (1852), ‘On the Educational and Commercial Utility of Chemistry’ in Introductory Lectures on the Opening of Owens College, London: Longman, Brown, Green and Longmans, pp. 112 – 133.

Goodman, D. C. (1969), ‘Wollaston and the Atomic Theory of Dalton’, Historical Studies in the Physical Sciences, 1, 37 – 59.

Kekulé, A. (1867), ‘On Some Points of Chemical Philosophy’, The Laboratory, 1, 303 – 6.

Klein, U. (2003), Experiments, Models, Paper Tools: Cultures of Organic Chemistry in the Nineteenth Century, Stanford: Stanford University Press.

Knight, D. (1992), Ideas in Chemistry: A History of the Science, London, Athlone Press.

Meinel, C. (2004), ‘Molecules and Croquet Balls’ in S. De Chadarevian and N. Hopwood (Eds), Models: The Third Dimension of Science, Stanford: Stanford University Press, 242 – 275.

Nash, L. K. (1956), ‘The Origin of Dalton’s Chemical Atomic Theory’, Isis, 47, 101 – 16.

Needham, P. (2004), ‘Has Daltonian Atomism Provided Chemistry with any Explanations?’, Philosophy of Science, 71, 1038 – 48.

Rocke, A. (1984), Chemical Atomism in the Nineteenth Century: From Dalton to Cannizzaro, Columbus: Ohio University Press.

Roscoe, H. E. and Harden, A. (1896), A New View of the Origins of Dalton’s Atomic Theory, London: MacMillan.

Thackray, A. (1970), Atoms and Powers: An Essay on Newtonian Matter Theory and the Development of Chemistry, Cambridge, Mass.: Harvard University Press.

Thackray, A. (1972), John Dalton: A Critical Assessment of his Life and Science, Cambridge, Mass.: Harvard University Press.


1 This aspect of Berthollet’s work is summarised in Thackray (1970), pp. 230-233.

2 For details see Roscoe and Harden (1896), Nash (1956), Thackray (1972), Cole (1978)and Rocke (1984, Chapter 2)

3 The assumption that atoms of a gas repel each other with forces proportional to 1/r has the consequence that the pressure of a large sample of a gas will have a greater pressure than a smaller sample when the density of the two samples are the same, contrary to what experiment straightforwardly shows to be the case.

4 See Klein (2002, pp. 188 – 206) for the historical details of the emergence of this notion in the work of Dumas in the 1830s.

5 For instance, Edward Frankland, whose work helped in the formation of the concept of valency, referred to talk of atoms as ‘a kind of ladder to assist the chemist’ (as cited by Brock, 1967, p. 21).