Avogadro's Hypothesis and its Fate: A Case-Study in the Failure of Case-Studies

That Tilden was the first historian to attach blame to Avogadro's contemporaries is suggested by Fisher N. W. , “Avogadro and the chemists”, History of science, xx (1982, in press).

See, for example, Crosland M. P. , “Avogadro”, in Gillispie C. C. (ed.), Dictionary of scientific biography, i (1970), 346, where some blame is laid at the feet of the editors of the scientific journals.

Fisher , op. cit. (ref. 1).

Berzelius J. J. , Essai sur la théorie des proportions chimiques (Paris, 1819), 47–56.

See also the introduction by C. A. Russell to the reprint edition (New York, 1972), xxxiii. This generalization of Berzelius was simpler in the sense that it did not require the postulation of two theoretical entities (atoms and molecules) when one (atoms) would suffice. It was, however, restricted to the elementary gases because of combining volume data. It could not, for example, be applied to the formation of steam where two volumes of hydrogen were known to react with one of Oxygen to yield two volumes of the product.

The three levels on which Avogadro's hypothesis may be considered ‘unverifiable’ at the time of its enunciation would be: Firstly, that it required the postulation of a transcendent theoretical entity which, as with Dalton's atoms, was not directly observable; secondly, the assumption of equal numbers of molecules in equal volumes of gases was an assumption based, in Avogadro's original formulation, on two other assumptions—namely that the molecules of all gases were both contiguous and identical in size—which were not open to direct test; and thirdly, that the postulate of divisible elementary molecules of the form X₂. X₄, etc. could be construed as an ad hoc device to save the basic assumptions—a device which again was not open to direct confirmation. See Avogadro A. , “Essay on a manner of determining the relative masses of the elementary molecules of bodies, and the proportions in which they enter into these compounds”, translated from Journal de physique, lxxiii (1811), 58–76, and reproduced in Foundations of the molecular theory, Alembic Club reprint no. 4, re-issue edition (Edinburgh, 1969), 28–51, especially pp. 29–33.

There was a brief reference to the work of Clausius in the paper which is usually seen as the definitive revival of Avogadro's hypothesis; i.e. Cannizzaro S. , “Sketch of a course of chemical philosophy” (1858), the essentials of which were distributed at the Karlsruhe Congress (1860), and reprinted in translation by the Alembic Club (Edinburgh, 1969), 1–55. For further references to the deduction of Avogadro's hypothesis from the kinetic theory of gases, see Partington J. R. , A history of chemistry, iv (London, 1964), 193 and 492; Brush S. G. , The kind of motion we call heat (2 vols, Amsterdam, 1976), i, 174 and 196–7; Garber E. , “Molecular science in late-19th-century Britain”, Historical studies in the physical sciences, ix (1978), 265–97, esp. pp. 267–72. Whereas Clausius made reference to the divisibility of the oxygen molecule into two sub-units or atoms, the actual derivation of Avogadro's hypothesis from the kinetic theory appears to have been most explicit in the papers of Maxwell J. C. , “Illustrations of the dynamical theory of gases”, Philosophical magazine , xix(1860), 19–32; xx (1860), 21–37, reprinted in Niven W. D. (ed.), Scientific papers of James Clerk Maxwell (2 vols, Cambridge, 1890), i, 377–409, esp. pp. 388–90. For this last reference I am indebted to my colleague Peter Heimann.

In the electrochemical theory of Berzelius it was inconceivable that two identical particles could overcome their mutual repulsion to constitute a stable diatomic molecule. This point has been widely recognized and discussed: Crosland, op. cit. (ref. 2), 347; Mellor D. P. , The evolution of the atomic theory (Amsterdam, 1971), 81–82; Fisher , op. cit. (ref. 1). One of the reasons why this point has been fully appreciated is that it is made by Cannizzaro himself, op. cit. (ref. 6), 2–3. A similar prescription against stable diatomic species is to be found in the atomic theory of John Dalton where repulsion was between identical heat atmospheres. It was a prescription still authoritative for W. C. Henry in the 1830s when he reviewed Prout's Bridgewater treatise: Fisher , op. cit. (ref. 1).

Causey R. L. , “Avogadro's hypothesis and the Duhemian pitfall”, Journal of chemical education, xiviii (1971), 365–7.

Gay H. , “Radicals and types: A critical comparison of the methodologies of Popper and Lakatos…”, Studies in history and philosophy of science, vii (1976), 1–51.

Frické M. , “The rejection of Avogadro's hypotheses”, in Howson C. (ed.), Method and appraisal in the physical sciences (Cambridge, 1976), 277–307, esp. p. 278.

ibid., 300 (footnote 46).

Gay , op. cit. (ref. 9), 17.

Ravetz J. R. , Scientific knowledge and its social problems (Oxford, 1971), ch. 6, esp. footnote 18.

Causey , op. cit. (ref. 8), 366.

Ibid.

It is true that Dumas's famous experiments on the vapour densities of mercury, phosphorus and sulphur can be reconstructed as tests of the generalization that equal volumes of gases at the same temperature and pressure contain the same number of particles. It is also true that Dumas's curious results diminished the confidence that Berzelius had placed in his own generalization that equal volumes of the elementary gases contain the same number of atoms: Berzelius, Théorie des proportions (Paris, 1835), 28. Because of the rather complex theory of matter that Dumas entertained, it is, however, far from clear that he was testing and rejecting a generalization about equal numbers of physical molecules. Dumas's theory of matter in fact had a three-tier structure: “La matière est formée d'atomes. Les chaleurs spécifiques nous enseignent les poids relatifs des atomes des diverses sortes. La chimie opère sur des groupes d'atomes de matière. Ce sont ces groupes qui en s'unissant dans différens rapports produisent les combinaisons en suivant les lois des proportions multiples…. Enfin la conversion en gaz ou en vapeur crée encore d'autres groupes moléculaires, dont dépendent les lois observées par M. Gay Lussac” (Le&çons sur la philosophie chimique (Paris, 1837), 282). If Dumas had tested and rejected Avogadro's hypothesis we should expect him to have rejected the proposition that equal volumes of gases contained equal numbers of these “groupes moléculaires”. In fact the proposition that he had actually rejected was rather different: “il faut le déclarer nettement: Les gaz, même quand ils sont simples, ne renferment pas, à volume égal, le même nombre d'atomes, du moins le même nombre d'atomes chimiques” (ibid., 268). The juxtaposition of these two passages suggests to me that it is not entirely correct to say, as some commentators have, that by “chemical atom” Dumas really meant “physical molecule”. Moreover, the context in which the rejection takes place, at least in the Le&çons, suggests that it was the ‘equal numbers of atoms’ principle of Berzelius to which Dumas was taking exception: “Quelques personnes ont voulu éviter ces distinctions et ont imaginé de restreindre la règle générale aux gaz simples” (ibid., 256). It must also be said that Dumas's original object had not been to test an equal numbers hypothesis, but simply to see whether vapour density methods would give the same ‘atomic weights’ as those obtained by other methods. Testing hypotheses of the Avogadro type was, for Dumas, never a real priority. His conclusion was not that the hypothesis had been put to the test and failed, but that “instead of investigating these hypotheses more thoroughly, it would be far better to seek some reliable foundations on which to base more substantial theories” (ibid., 270). On these last points see Fox R. , The caloric theory of gases (Oxford, 1971), 283–7.

Quoted from the Encyclopédie méthodique, iv (1822), 109 by Bonner J. K. , “Amedeo Avogadro: A reassessment of his research and its place in early nineteenth century science” (Johns Hopkins University Ph.D. dissertation, 1974), 305.

Cf. the demand for proof voiced by Berzelius, Théorie des proportions (1835), 28.

Mauskopf S. , “The atomic structural theories of Ampère and Gaudin: Molecular speculation and Avogadro's hypothesis”, Isis, lx (1969), 61–74.

Cole T. M. , “Early atomic speculations of Marc Antoine Gaudin: Avogadro's hypothesis and the periodic system”, Isis, lxvi (1975), 334–60, esp. p. 345.

ibid., 349–58.

Laurent to Gerhardt , 13 September 1845, in Grimaux E. and Gerhardt C. (fils), C. Gerhardt, sa vie, son oeuvre, sa correspondance (Paris, 1900), 505. The theoretical grounds were associated with the implications for organic formulae if Gerhardt's revision of equivalents was to be taken seriously. Gerhardt's revision was itself undertaken on largely theoretical grounds as he sought to base the formulae of organic and inorganic compounds on the same volume of vapour. The issues here are extremely complex but the critical point is that Laurent's announcement of what was in fact a corollary of Avogadro's hypothesis was not based on a test of that hypothesis but on his theoretical ‘even numbers’ rule which he applied to all organic formulae to see whether they contained a legitimate combination of equivalents: “Avec la règle des corps dont les équivalents sont constamment en nombre pair, j'arrive à une conclusion importante sur l'arrangement…des atomes. L'hydrogène, le chlore, l'azote, les métaux, ont des molécules doubles…”.

Causey , op. cit. (ref. 8), 366.

Cole , op. cit. (ref. 20), 341–5.

The case for regarding electrochemical dualism as germane even to the progress of organic chemistry, where it is usually thought to have come unstuck, is one that I have argued elsewhere: Brooke J. H. , “Chlorine substitution and the future of organic chemistry: Methodological issues in the Laurent-Berzelius correspondence”, Studies in history and philosophy of science, iv (1973), 47–94. See also Fisher , op. cit. (ref. 1).

One is tempted to say that the analysis fails at a more superficial level as a consequence of ambiguities in the author's use of the term ‘auxiliary hypothesis’. It is used to refer to hypotheses which make testing of Avogadro's hypothesis possible. It is also used to refer to Avogadro's own assumption, avowedly “that the molecules of many elemental gases are polyatomic” an assumption which in fact saved the equal numbers hypothesis rather than assisted its testing. And it is used to cover any hypothesis whatever that might be entertained by a chemist and which, at the same time, might turn out to be incompatible with inferences drawn from the hypothesis under test.

Causey , op. cit. (ref. 8), 365.

Pauling L. , “Amedeo Avogadro”, Science, cxxiv (1956), 708–13.

Frické , op. cit. (ref. 10).

Gay , op. cit. (ref. 9), 17 makes precisely this statement.

These points will be developed and clarified later in the text and in subsequent footnotes. The most thorough justification for them is to be found in Bonner, op. cit. (ref. 17), 308–9 and passim.

Even these apparently safe assertions are not without their difficulties. Because Avogadro subscribed to a hierarchical theory of matter essentially different from the atomic-molecular theory of later chemistry, Bonner is quite correct to insist that even by ‘molecular weight’ Avogadro would not have meant quite what we mean (ibid., 210 and 309). There is also a problem of meaning associated with the postulate of divisible molecules since the postulate could refer to two quite different divisions. It could refer to the division of the molecule of hydrogen, for example, into the smaller units which we describe as atoms. But it could also refer to the division of the expected product molecule when, for example, hydrogen and oxygen combine to form steam. One might have expected two volumes of hydrogen to react with one of oxygen to give one of steam. The fact that two volumes of the product are obtained demands that the product molecule be split into at least two identical but smaller molecules, the expected molecule of water actually splitting into two of half the mass. While it has been customary to focus attention on the first sense of ‘divisibility’, the context in which Avogadro introduced the idea suggests that his preoccupation was with the second. It was “the integral molecule which should result” that had to be split into two or more parts. See Avogadro , op. cit. (ref. 5), 31.

Avogadro , ibid ., 31–33; Frické , op. cit. (ref. 10), 290; Bonner , op. cit. (ref. 17), 221.

See for example Mellor , op. cit. (ref. 7), 73–83.

ibid., 77.

Bonner , op. cit. (ref. 17), 308–9.

Coley N. G. , “The physico-chemical studies of Amedeo Avogadro”, Annals of science, xx (1964), 195–210, esp. p. 198; Crosland , op. cit. (ref. 2), 345 and 347.

Thus in the particular case of carbon, Avogadro admitted that his method was conjectural, op. cit. (ref. 5), 41. He admitted that in the formation of carbonic acid he did not know into how many integral molecules the product might actually divide. And he admitted that his method relied on analogies between the combustion of carbon on the one hand, and of phosphorus and sulphur on the other (ibid., 41–42). See also Fisher , op. cit. (ref. 1).

Cannizzaro , op. cit. (ref. 6), 14.

Fisher has made the point that it is easy to exaggerate Avogadro's success: For the twenty-five or so compounds he got ‘right’, there were many more that were ‘wrong’, op. cit. (ref. 1). See also Frické , op. cit. (ref. 10), 289. ‘Correctness’ will simply not do as a criterion for Berzelius could obtain the formula H₂0 for water by an entirely different route from that taken by Avogadro. The problems that did arise for Berzelius, in the application of his equal volumes/equal atoms principle, were duly emphasized by Meldrum A. N. , Avogadro and Dalton (Aberdeen and Edinburgh, 1904), 71–82.

Gay , op. cit. (ref. 9), 17.

Cannizzaro , op. cit. (ref. 6), 11.

ibid., 22.

Cole , op. cit. (ref. 20), 347.

ibid., 355.

The possibility of checking atomic weights from the equation ‘atomic weight equals valency multiplied by equivalent’ was of course a non-starter until the doctrine of valency found definitive expression. But this was not until well into the 1850s. Russell C. A. , The history of valency (Leicester, 1971), chs 1–3. Cf. Fisher , op. cit. (ref. 1).

Fox , op. cit. (ref. 16), 285–90.

Mauskopf , op. cit. (ref. 19), 66.

This point has now been widely appreciated; e.g., Russell C. A. , The structure of chemistry (Milton Keynes, 1976), being units 1–3 of the Open University course entitled “The nature of chemistry”, unit 2, p. 20; Frické , op. cit. (ref. 10), 294.

The idea that abnormal vapour densities were due to the dissociation of the substances concerned, although proposed by Cannizzaro, Kopp and Kekulé in the late 1950s, was not even accepted by Seville—at least in the case of ammonium chloride and phosphorus pentachloride: Partington, op. cit. (ref. 6), iv, 495–7.

Wurtz testified that examples such as ammonium chloride and ammonium carbonate had often been cited as arguments against Avogadro and Ampère: Wurtz C. A. , A history of chemistry (London, 1869), 175. It is also worth noting that A. W. Hofmann was still perplexed by the behaviour of phosphorus and arsenic vapours as late as 1865. See his Introduction to modern chemistry (London, 1865), 82, 86, 96, 97, and 192.

To reiterate a well-known example: The specific heat law of Dulong and Petit does not work for carbon. Similarly, methods based on isomorphism could not be given general application: Frické , op. cit. (ref. 10), 292.

Cole , op. cit. (ref. 20), 345.

Fisher , op. cit. (ref. 1).

There is an instructive example in the way Berzelius rewrote the formula for benzoyl chloride once he had decided that the benzoyl radical of Liebig and Wöhler had been misconceived. In 1832 Berzelius had accepted the formulation [C¹⁴ H¹⁰ O²] Cl² by analogy with an inorganic salt M.Cl². However, after rejecting the postulation of oxygen in a putatively electropositive radical, he adopted the more complex formulation 2[C¹⁴ H¹⁰]. O³ + [C¹⁴ H¹⁰]Cl⁶, yet one which still displayed an analogy with an inorganic salt, chromyl chloride, 2 Cr. O³ + Cr. Cl⁶. The critical point is that, for Berzelius at least, the freedom to multiply empirical formulae (in this case by 3) was a desideratum for the application of his regulative principle which required the construction of analogies between the constitution of organic and inorganic compounds.

Berzelius wrote: “les partisans de la théorie de substitution avaient admis que le produit de transformation avait le même nombre d'atomes élémentaires que l'éther d'où il provenait; c'est pourquoi il leur était impossible d'arriver à une composition rationnelle”: Traité de chimie (Paris, 1845–50), vi, 742. As an example(cf. ref. 55), Malaguti's chlorine derivative of ethyl formate C³H⁴O²Cl² was transcribed by Berzelius into 12C² H² O³ + C² H² Cl⁶] + [2C⁴ H⁶ O³ + C⁴ H⁶ Cl⁶].

Meldrum wrote that “In general, it is impossible to say that the Daltonian atom of an element is either the modern atom or molecule of that element”: op. cit. (ref. 40), 59–60 and passim.

Bonner , op. cit. (ref. 17), 126–7.

Fox , op. cit. (ref. 16), 206.

Avogadro refers to “molécules”, “molécules intégrantes”, “molécules constituantes”, and “molécules élémentaires”. An attempt to impose consistency on his usage by invoking modern categories will be found in the Alembic Club reprint of his 1811 paper, op. cit. (ref. 5), 28n. Once again, the most thorough critique of this anachronistic interpretation has been presented by Bonner, op. cit. (ref. 17), 200–10.

Alembic Club reprint, op. cit. (ref. 5), 28n.

There are several passages in the 1811 essay which at first sight do suggest that Avogadro sought to determine the number of atoms in a molecule. Closer inspection however shows that they are at least ambiguous. To give a complete exegesis of his argument is beyond the scope of this paper, but it might be useful to comment on a few of his remarks which might be thought to support the conventional reading. (i) Setting out from his hypothesis he notes that “we have the means of determining very easily the relative masses of the molecules of substances obtainable in the gaseous state, and the relative number of those molecules in compounds; for the ratios of the masses of the molecules are then the same as those of the densities of the different gases at equal temperature and pressure, and the relative number of molecules in a compound is given at once by the ratio of the volumes of the gases that form it”. Clearly this passage can be read as a claim to be able to determine the number of atoms in a molecule, but it should be read as a claim concerning the compound resulting from gaseous combination. As Avogadro himself explained: “since we know that the ratio of volumes of hydrogen and oxygen in the formation of water is 2 to 1, it follows that water results from the union of each molecule of oxygen with two molecules of hydrogen.” There is nothing here to justify the view that Avogadro was trying to determine the number of ‘atoms’ in the molecules of the elementary gases themselves. Avogadro , ibid., 30. (ii) There is no doubt that Avogadro supposed that “the constituent molecules of any simple gas whatever…are not formed of a solitary elementary molecule, but are made up of a certain number of these molecules united by attraction to form a single one; and further, that when molecules of another substance unite with the former to form a compound molecule, the integral molecule which should result splits up into two or more parts (or integral molecules) composed of half, quarter, &c., the number of elementary molecules going to form the constituent molecule of the first substance, combined with half, quarter, &c., the number of constituent molecules of the second substance that ought to enter into combination with one constituent molecule of the first substance…; so that the number of integral molecules of the compound becomes double, quadruple, &c., what it would have been if there had been no splitting up, and exactly what is necessary to satisfy the volume of the resulting gas” (ibid., 31–32). The reference here to a half molecule of oxygen or of hydrogen invites the traditional identification of these molecules with Dalton's atoms. But the identification is not made by Avogadro himself. As Bonner has observed (ref. 17, 214), he does not say how many elementary molecules make up a half molecule of oxygen or hydrogen. On the conventional view it would have to be one, but it is essential to note that Avogadro simply does not pursue this point. See also Fisher , op. cit. (ref. 1). (iii) Frequent references to “the division of molecules on combination” again invite the conventional reading, but closer inspection shows that, as in the passage quoted in (ii), Avogadro's preoccupation is with the splitting up of the expected product molecule. It is “the number of integral molecules of the compound” which becomes “double, quadruple, &c., what it would have been”. (iv) Support for the conventional reading might also be drawn from Avogadro's reference to the power of his own hypothesis to confirm or rectify the results of Dalton (ibid., 33–34) who is said to have “endeavoured to fix ratios between the masses of the molecules of simple substances”. There is, however, the immediate problem of incommensurability since, in this context, Avogadro appears to identify his “molecules” with Dalton's atoms without making the necessary distinction between the integrant molecules and their sub-units. It is also clear from the context that his object is to correct Dalton's formulae for gaseous compounds such as nitrous gas and steam (ibid., 34–35). “Above all”, Avogadro claims, “our hypothesis…puts us in a position to assign the magnitude of compound molecules according to the volumes of the gaseous compounds…”. Thus, by his hypothesis of the division of the expected product molecule he can “correct” the number of molecules in the product. In the case of ammonia formation his volumetric data lead to the conclusion that nitrogen and hydrogen are not united molecule to molecule but in the ratio 1 to 3. (v) The fact that Avogadro states a figure of 13 for the molecular weight of nitrogen (ibid., 35) might encourage the rejoinder that he really was determining atomic weights in the Daltonian sense. The proximity to the ‘correct’ value of 14 is, however, illusory since Avogadro is presupposing the number 1, not 2, for the molecule of hydrogen. In other words, his ratio of 13 to 1, can be construed as the ratio of molecular weights (in the modern sense of molecule) without having to concede the point that he was fixing the relative weights of molecular sub-units in the elementary gases.

Mundy B. W. , “Avogadro on the degree of submolecularity of molecules”, Chymia, xii (1967), 151–5. See also Bonner , op. cit. (ref. 17), 209, footnote 44.

After Dulong's discovery that the specific heats of equal volumes of all elementary gases (and hence of their individual molecules) were identical—a discovery that ran contrary to the data of Delaroche and Bérard on which Avogadro had relied — the specific heats could no longer be interpreted as indicators of a characteristic attractive power of the molecule for caloric. Not until his paper of March 1830 did Avogadro abandon his suspect view of affinities. At this stage he modified his position and argued that specific heats reflected the physical condition of the particles of matter and not their chemical nature. Previously, the characteristic affinity for caloric had been ascribed to the whole molecules only, but now the degree of submolecularity assumed greater importance as Avogadro argued that it was the number of partial molecules rather than the number of integrant molecules that determined specific heats. On these points see Fox , op. cit. (ref. 16), 221–2. Even so, this presumably still left open the possibility that the partial molecules were themselves capable of further division.

For a reconstruction of the original manuscript see Morselli M. , “The manuscript of Avogadro's ‘Essai’ (1811)”, Ambix, xxvii (1980), 147–72.

See ref. 62, paras ii and iii.

Reviewing the various compound gases “most generally known”, Avogadro only found examples of duplication of the volume “relatively to the volume of that one of the constituents which combines with one or more volumes of the other” (op. cit. (ref. 5), 32). He admitted, however, that in “other cases the division might be into four, eight, &c.” It will also be clear by now that the division he is talking about is the division of the compound molecule formed. On this he is quite explicit: “the possibility of this division of compound molecules might have been conjectured a priori; for otherwise the integral molecules of bodies composed of several substances with a relatively large number of molecules, would come to have a mass excessive in comparison with the molecules of simple substances” (ibid., 32–33). See also Fisher , op. cit. (ref. 1).

As Mundy has emphasized, op. cit. (ref.63), there are statements in the 1811 paper which suggest that the molecules of nitrogen and oxygen must be at least divisible into four parts. Mundy is surely right in saying that it is Avogadro's “law of duplication of volume” which is the origin of the prevalent misconception that his molecules of the elementary gases were diatomic. The former, however, did not entail the latter. On the precise degree of submolecularity, Ampère and Gaudin were both more forthcoming than Avogadro himself: Cole , op. cit. (ref. 20), 342 and 347.

Cannizzaro , op. cit. (ref. 6), 2.

It was possible to assume that one was supporting Avogadro's hypothesis if one accepted the proposition that the particles of all gases were equidistant at any given temperature and pressure—a proposition which, according to Dumas in 1826, was in fact accepted by all physicists (Annales de chimie, xxxiii (1826), 337–8). The critical point of course is what kind of particles they were supposed to be from a chemical point of view, but the very fact that Dumas could blithely assume this general agreement does suggest that some might have considered themselves advocates of Avogadro when they had not, in fact, considered the question of divisible molecules. That the molecules of the elementary gases were divisible was a proposition that Dumas felt was in need of justification. See Fox , op. cit. (ref. 16), 283–4.

For this reason at least (and others will be given later), the substantial essay of Frické, op. cit. (ref. 10), cannot be described ēfinitive. Despite many insights, his discussion is spoiled by a failure to appreciate the ontological divide separating the chemical atomists from the theory of matter to which Avogadro subscribed. His reconstruction is weakened by the attribution of a vocabulary of ‘molecules’ to Dalton (footnote 39), and by following the Alembic Club footnote in his ascription to Avogadro of an ontology incorporating ‘atoms’.

Bonner , op. cit. (ref. 17), 292–300.

Crosland M. P. , “The origins of Gay-Lussac's law of combining volumes of gases”, Annals of science, xvii (1961), 1–26; idem, “The first reception of Dalton's atomic theory in France”, in Cardwell D. (ed.), John Dalton and the progress of science (Manchester, 1968), 274–87.

Foxx , op. cit. (ref. 16), 196.

On the fortunes of the Laplacian programme see Fox's subsequent essay, “The rise and fall of Laplacian physics”, Historical studies in the physical sciences, iv (1975), 89–136.

Bonner , op. cit. (ref. 17), 290–1. This is a perspective which makes good sense of the eighth and concluding section of Avogadro's 1811 paper where he is looking for distinctions which “may serve to reconcile M. Berthollet's ideas as to compounds with the theory of fixed proportions” (op. cit. (ref. 5), 51). Avogadro's basic distinction was, in fact, between reactions involving gases (where fixed proportions would obtain) and reactions involving solids and liquids (where more complicated ratios, and “even…combinations of all proportions” could arise). Consequently, one of his most fundamental claims was that “the recognition of the simple ratios observed on combination, and in particular in cases where neutral substances are the result, leads us now to a more exact manner of conceiving the state of neutrality” (ibid., 49–50). The effort of reconciliation which Bonner emphasized is transparent in Avogadro's own account (ibid., 50) and especially in his contention that some of a reagent's “mass” might be “held back” as a consequence of the necessity to “complete a certain simple relation between the number of combining molecules” (ibid., 49).

Coley , op. cit. (ref. 37); Fox , op. cit. (ref. 16).

The best known example concerns Avogadro's assumption that the attractive power for caloric was given by the square of the specific heat at constant volume—exactly the square despite empirical values as high as 2.812 and as low as 1.333 for the power to which the specific heat should be raised: Fox , ibid., 208–9. His ulterior assumptions were equally suspect; e.g. that the attractive power for caloric could be derived from just one observable quantity, and his construction of imaginary reactions to pursue the enterprise. It is not difficult to see why Dulong should have dismissed Avogadro's writings as a “long succession of purely speculative works” (cited by Fox, ibid., 215).

For a particularly useful summary of the relations between Avogadro's concepts see Bonner , op. cit. (ref. 17), 277–8.

Fox , op. cit. (refs. 16 and 75).

Ibid . (ref. 16), 216 and 219; Coley , op. cit. (ref. 37).

ibid. (ref. 16), 207 and 215.

ibid., 222.

Frické , op. cit. (ref. 10).

ibid., 300.

ibid., 295–8.

ibid., 278 and 288.

ibid., 288.

Ibid ., 278. Whether full justice is done to the differences between the programmes of Dalton and Gay-Lussac is still open to doubt since the essential difference, as Frické perceives it, is a purely philosophical one—namely that Dalton was a realist about atoms whereas Berthollet and Gay-Lussac were positivists (ibid., 284–5). This reduction to conventional philosophical categories would seem to gloss over the deeper problems of incommensurability concerning the respective programmes of Berthollet and Dalton. It is also to some degree misleading since Berthollet was often acknowledged as an inspiration by the French chemists of the nineteenth century who regarded the construction of theoretical models as a prerequisite of progress, Auguste Laurent being the outstanding example.

ibid., 296.

Ibid.

ibid., 295. The italics are Frické's.

ibid., 297.

Graebe C. , “Der Entwicklungsgang der Avogadroschen Theorie”, Journal, für praktische Chemie , cxcv(1913), 145–208, p. 172; Mauskopf , op. cit. (ref. 19), 74. Gerhardt's reforms were given great prominence in Cannizzaro's Sketch and Gaudin too was given due mention: “First Dumas and afterwards Gaudin showed that the molecule of mercury, differing from that of hydrogen, always entered as a whole into compounds”, op. cit. (ref. 6), 24.

Fisher , op. cit. (ref. 1). Hartley Harold Sir , Studies in the history of chemistry (Oxford, 1971), 186.

For a particularly provocative analysis of the dangers inherent in the Lakatos approach, see Feyerabend P. , “On the critique of scientific reason”, in Howson C. (ed.), op. cit. (ref. 10), 309–39, esp. p. 318.

Cole , op. cit. (ref. 20).

Cited in ibid., 359.

Lohne J. A. , “Experimentum crucis”, Notes and records of the Royal Society, xxiii (1968), 169–97. Lakatos has himself insisted that crucial experiments in the falsificationist sense do not exist, but reaches that conclusion using a meta-criterion (that a rationality theory is to be rejected if it is inconsistent with basic value judgments of the scientific community) which he admits requires replacement: Lakatos I. , “The role of crucial experiments in science”, Studies in history and philosophy of science, iv (1973–4), 309–25.

Mauskopf , op. cit. (ref. 19), 61. It is true that Mauskopf does not regard this source as having been particularly fruitful, but that is no ground for dismissing it altogether.

Feyerabend , op. cit. (ref. 96), 323.

ibid., 336.

I would not suggest for a moment that a profound debt was not sometimes acknowledged. The dependence of the periodic table on an unequivocal series of atomic weights was such that Mendeleev naturally regarded Cannizarro as his “immediate predecessor”. See Hartley , op. cit. (ref. 95), 193. That the legends surrounding Karlsruhe may have led to an inflated estimate of Cannizzaro's impact is suggested by Fisher, op. cit. (ref. 1).

As Feyerabend points out, it is another characteristic of the attempts at rational reconstruction that they have to ignore the opinions of distinguished men of science who happened to take a different view of a particular matter from that which is recognized to have prevailed. Their ‘irrationality’ would be too great an embarrassment: op. cit. (ref. 96), and 315.

Frické , op. cit. (ref. 10), 306.

Ibid . Fisher has rightly pointed out that one is not safe in assuming that Avogadro's hypothesis was widely unknown, op. cit. (ref. 1), but I take it that he would not wish to extrapolate that insight into the generalized presupposition that Frické both affects and disaffects.

Gaudin M. A. , “Note sur quelques propriétés des atomes”, Bibliothèque universelle des sciences, belles-lettres et arts, ill (1833), 127–41, esp. pp. 132–6; Cole , op. cit. (ref. 20), 346. On the question whether Gay-Lussac had adopted Avogadro's hypothesis, see Rocke A. J. , “Gay-Lussac and Dumas: Adherents of the Avogadro-Ampère hypothesis?”, Isis, lxix(1978), 595–600.

Brodie B. C. , “On the condition of certain elements at the moment of chemical change”, Philosophical transactions of the Royal Society, cxl (1850), 759–804, p. 760.

Cole , op. cit. (ref. 20), 341.

Brooke J. H. , “Laurent, Gerhardt and the philosophy of chemistry”, Historical studies in the physical sciences, vi (1975), 405–29.

Gay , op. cit. (ret. 9), 17–18; Frické , op. cit. (ref. 10), 278.

Feyerabend , op. cit. (ref. 96), 336.

I find it interesting that when she suggests that the non-acceptance of Avogadro's hypothesis reveals deficiencies in Popper's criteria for theory acceptance, Miss Gay has seen the need for an additional “pragmatic criterion” which would include considerations such as “that the time be ripe”, or that “theories must relate to current problems”, or that “the significance of a discovery must be widely recognised”, op. cit. (ref. 9), 18. It is hard to see how such a situational logic could be formalized without circularity, and harder still to see how it could be profitably detached from its wider historical context.

Fox , op. cit. (ref. 75), 91.

ibid., 116.

ibid., 123–7.

Frické , op. cit. (ref. 10), 305–6.

Fox , op. cit. (ref. 75), 120–2.

That is not to say that readers of Avogadro's 1811 paper would have experienced no difficulty in rationalizing his distinctions between “elementary”, “constituent” and “integrant” molecules. The manuscript version (cf. ref. 65) shows alterations to the adjectives, and in part 2 of the published paper “constituent” replaced “integrant”. The evidence from this set of alterations is, however, ambiguous since it might suggest either that Avogadro was uncertain of his own distinctions or that he made a deliberate attempt to clarify them.

See the introduction which Berthollet wrote for the French translation of Thomas Thomson's textbook, Système de chimie (2 parts in 9 vols, Paris, 1809), i, 20–21; Bonner , op. cit. (ref. 17), 126–7.

Bonner , ibid., 181 and 207–8.

Ibid ., 208 (footnote 42); Coley , op. cit. (ref. 37), 205. The incommensurability is most clearly seen at this point since Dalton's atoms were of course chemically indivisible; cf. Bonner , ibid., 213–4.

Cited by Crosland , “The first reception…”, op. cit. (ref. 73), 283.

Brodie , op. cit. (ref. 108). In the last edition of his textbook, Berzelius was still maintaining that the greater the similarity between two elements, the less was their tendency to unite: op. cit. (ref. 56), i, 25.

On the recourse to analogical argument as a regulative principle in Berzelius's theorizing see Brooke , op. cit. (ref. 25).

Acetic acid, for example, was conventionally written in the form of C⁴ H⁶ O³ + H² O, by analogy with sulphuric, written SO³ + H²O. The purity of the analogy was lost on dividing the former by two.

The strength of the ‘anhydride plus water’ model for the oxacids derived from the fact that it allowed neutralization reactions to be rationalized as the straightforward addition of two oxides—the acid and the base. The addition was itself rationalized in electrochemical terms according to the tenets of Berzelius's theory. When Dumas reviewed the various theories of acidity in his Le&çons sur la philosophie chimique (Paris, 1837) he conceded the merits of alternative schemes, especially the view that all acids might be hydracids, but still preferred to retain the anhydride plus water formulation. He was swayed by the work of Thomas Graham on the phosphorus acids, and particularly by the fact that a tribasic acid, phosphoric, could be converted into metaphosphoric simply by dehydration. To write the phosphoric acids in the form P² O⁵ + 3H²O; P²O⁵ + 2H²O; P²O⁵ + H²O was distinctly more elegant than redrafting them in terms of hydracids when there would be no common group: H⁶ + P²O⁸; H⁴ + P²O⁷; H² + P²O⁶. On the background to acidity theory in the early nineteenth century, see Brooke J. H. , “Davy's chemical outlook: The acid test”, in Forgan S. (ed.), Science and the sons of genius: Studies on Humphry Davy (London, 1980), 121–75. On the important role of Liebig in reconsidering the oxacid/hydracid distinction see the article on Liebig by F. L. Holmes in DSB, op. cit. (ref. 2), viii (1973), 329–50, esp. pp. 338–44.

Brooke , op. cit. (ref. 25).

Kolbe H. , Journal of the Chemical Society, ii (1850), 157–84; Frankland E. , Philosophical transactions of the Royal Society, cxlii (1852), 417–44. For an introduction to the history of ‘radical’ theories in organic chemistry see Russell , op. cit. (ref. 46), ch. 2.

A full discussion of this circularity problem will be found in Brooke J. H. , “The role of analogical argument in the development of organic chemistry” (University of Cambridge, Ph.D. dissertation, 1969), ch. 6, esp. pp. 194–8.

Leicester H. M. , The historical background of chemistry (New York, 1965), 179.

Laurent A. , Chemical method, transl. by Odling W. (London, 1855), 74 and 77.

A further aspect of this reformation is illustrated by the progress made in the formulation of alcohol and ether. During the 1830s, there had been one factor common to the etherin theory of Dumas and the ethyl theory of Liebig: Alcohol was regarded as a hydrate of ether. But such a formulation had evidently presupposed that the alcohol possessed the larger molecular weight. For consistency on this score, the molecular weight of the alcohol had been based on twice the volume of vapour as that for ether. Basing their equivalents on equal volumes of vapour, Laurent and Gerhardt were compelled to renounce this simple and prevalent relation. The synchronization of formulae demanded that ether be the result of the condensation of two molecules of alcohol. Williamson was demonstrating the truth of this new supposition by the early 1850s, but prior to that the old relation must have seemed too perfect to dismiss. Laurent himself confessed that he had been reluctant to take the crucial step. The “apparent discordance between alcohol and ether was one of the principal circumstances that estranged many chemists from Gerhardt's views. They could not resolve upon adopting equivalents which destroyed connections so natural…. For my own part, I was for some time arrested by this difficulty” (ibid., 76).

Hartley , op. cit. (ref. 95), 189. It is instructive to note that the other pioneer of structural chemistry, Butlerov A. , defined his concept of chemical structure in such a way that it was possible to investigate the structure of compounds by means of chemical experiment alone. To erect a barrier between physical and chemical criteria was expedient in the sense that it allowed one to side-step the difficult epistemological question concerning the relationship between a chemical structural model and the ‘real’, ulterior physical arrangement of atoms. One suspects that it was sometimes expedient in another sense: That of preserving the purity of the chemist's domain against intrusion from another discipline. Butlerov's argument was contained in his “Eineges über die chemische Structur der Körper”, Zeitschrift für Chemie, iv (1861), 549–60, esp. pp. 552–3.

Laurent , op. cit. (ref. 132), 81–82.

ibid. (ref. 132), 81.

Gerhardt , Annales de chimie, viii (1843), 245.

Gerhardt's avowed objective in basing organic and inorganic formulae on the same volume of vapour had simply been to introduce unification, simplification, and the elimination of inconsistency. Revue scientifique et industrielle, xii (1843), 592–600, p. 594.

It is well known that in this respect Gerhardt over-reached himself; for simple addition reactions, such as the combination of potassium sulphide with oxygen, had to become special cases of double decomposition in which the products were thought by Gerhardt not to separate. There is no doubt, however, that Gerhardt's critique of dualistic addition and subtraction was immensely important.

Laurent , op. cit. (ref. 132), 77.

Williamson A. , Philosophical magazine, xxxvii(1850), 350–6.

The binary association of atoms, Laurent argued, “nous permettrait peut-être aussi de nous rendre compte, jusqu'à un certain point, de l'affinité que possèdent les corps à l'état naissant”, Annales de chimie, xviii (1846), 266–98, pp. 296–8. See also Brodie , op. cit. (ref 108), 759–62.

Brodie , ibid. This interpretation was then ratified by the production of iodine monochloride from the action of hydrochloric acid on an iodate: Iodine was evidently analogous to iodine monochloride, and must therefore contain two particles.

ibid., 770.

Similarly Favre and Silbermann reported that the heat of combustion of carbon was greater in nitrous oxide than in oxygen; and this they explained by appealing to diatomic oxygen. The heat absorbed in the decomposition of nitrous oxide must be less than in the dissociation of the oxygen molecule. Comptes rendus hebdomadaires de l'Académie des Sciences, xxiii (1846), 199–206.

Laurent , op. cit. (ref. 132), 345. In Laurent's diagram two hexagons merged as the zinc removed the chlorine from molecules of cacodyl chloride. The point is not so much that Kekulé might have been subconsciously indebted to Laurent for his benzene ring, but rather that Laurent's scheme introduced an extra degree of subtlety in the representation of a chemical reaction. In this particular case he could show how “something indicative” of a compound's constituents could remain in the product molecule without having to postulate entirely preformed structures.

Gerhardt , Traité de chimie organique (4 vols, Paris, 1853–6), i, 132f.; Daxhelet A. , Cours de chimie inorganique d'après la théorie typique de M. Gerhardt (Brussels and Liege, 1865).

Meldrum , op. cit. (ref. 40), 23.