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In any form or shape?

Introduction

This study places the history of stereochemistry into its rightful time span of the longue durée., To do so, it has been necessary to do three things.
First, I draw attention to Wollaston's and Ampère's contributions dealing with molecular geometry, and why they have been neglected. Second, I single out Ampère's paper for fleshing out Haüy's crystallographic ideas. Those ideas underline the geometric understanding of molecular structure. With their Pythagorean make-up, not only do they bridge a succession of visionary scientists across the centuries, from Kepler and Robert Hooke to Alfred Werner and others; they also attempt to link chemical structure to the incisive mathematical physics introduced by Galileo and Descartes. Finally, I shall also counter two misleading constructions: ascribing the birth of stereochemistry uniquely to Le Bel's and van't Hoff's announcement of the tetrahedral carbon atom; and the glib, hasty dismissal as "Whig" of the in-depth reworking of the historical narrative made necessary by more recent developments.

Wollaston's Bakerian Lecture

William Hyde Wollaston (1766-1828), a native of Dereham, Norfolk, 1 is best known for his production of platinum, 2,3,4,5 with a proprietary and highly lucrative process joint with Smithson Tennant at first, and from 1805 on in association with William Cary (1759-1825) 6. He had numerous interests, 7, 8 crystallography among them. He perfected the goniometer devised by René-Just Haüy (1743-1822) for measuring angles between crystal faces; he published in 1809, in the Philosophical Transactions, his design for a reflexion goniometer. Thus, he was very familiar with Haüy's work and ideas. Furthermore, he had become preoccupied with atomic theory, to oppose and also to sometimes alter John Dalton's ideas.
His interests combined in his 1812 Bakerian Lecture 9 at the Royal Society, published in 1813. 10 Wollaston built on a remark by Robert Hooke in Micrographia, regarding construction of geometrical bodies such as the tetrahedron from spherical particles. Wollaston is a little at a loss choosing between the tetrahedron and the octahedron as the primitive unit in crystallography. He is very much interested also in the rhomboidal shape of the fluor spar (also known as the Iceland spar) crystal. He shows how various arrangements of identical spheres can produce the tetrahedron, the octahedron, a rhomboid, an hexagonal prism, etc. 11
In passing, he expresses his reticence toward Dalton's atomic theory. I shall quote only the following statement, for its lucidity:

"though the existence of ultimate physical atoms absolutely
indivisible may require demonstration, their existence is by no means
necessary to any hypothesis here advanced, which requires merely
mathematical points endued with powers of attraction and repulsion
equally on all sides, so that their extent is virtually spherical, for from
the union of such particles the same solids will result as from the
combination of spheres impenetrably hard."

Ampère's Paper.

In 1814, the year following publication of Wollaston's ideas, appeared "A Letter From Mr Ampère to Count Berthollet, Upon Determination of the Proportions In Which Bodies Combine, From the Number and Relative Position of the Molecules From Which The Integrating Particles Are Composed." 12 Historians have neglected this paper because contemporary chemists gave it little shrift or pushed it aside. Although Ampère was not a chemist, he was a genius at chemistry: as a rule, authors of major discoveries are outsiders. 13 Ampère's audacious forays into chemistry were all quite a bit premature. For instance, he tried his hand at a systematic classification of chemical elements into families, an effort which historians nowadays tend to sweep under the Mendeleiev rug. 14,15
In Ampère's 1814 paper, after a short introduction (pp. 43-44), Ampère posits the existence of polyatomic molecules in three-dimensional space. If each atom 16 is at the corner of a polyhedron, this polyhedron will serve as the representative shape for the molecule (pp. 44-45). The relative numbers of atoms in a molecule are easily deduced from the volumes of the corresponding elements as gases, following the gas laws established by Gay-Lussac (pp. 45-47). There are five polyhedral building blocks for molecules, namely the tetrahedron, the octahedron, the parallelipiped, the hexahedral prism and the rhomboidal dodecahedron (p. 50). Chemical combination reduces to the congruent assembly of mutually compatible polyhedra (pp.55-71). Accordingly, chemical composition can be deduced from such geometrical considerations, and Ampère provides some concrete examples (pp. 72-86).
These seminal ideas about molecular geometry became eclipsed by a rather minor feature of the paper: the so-called Avogadro-Ampère hypothesis stole the limelight because the two physicists, the Italian and the Frenchman had come independently and quasi-simultaneously to the same conclusions. 17,18,19
Ampère himself was aware of having made a major find. The introduction and the conclusion of the paper are unambiguous in this respect. Likewise, Ampère in his assessment of his own work placed his chemical contributions at the top: 20 there is every indication that he was right to do so.
Ampère was building on two firm foundations. Gay-Lussac had found that the relative proportions of combining gases show simple numerical ratios. René-Just Haüy had discovered, from the shattering of a crystal of calcite, that the shape of the unit cell (as we term it nowadays) is indefinitely repeated in the three dimensions. Thus the observable outer geometrical shape of a macroscopic crystal provides information about the microscopic particles making up this crystal. 21 Haüy's finding, let me note in passing, was nothing but a mise en abyme, a rhetorical figure highly familiar to seventeenth and eighteenth Century literati.
Ampère's paper connects explicitly with René-Just Haüy's ideas. 22, 23 Haüy's molécule intégrante, which he introduced as early as 1784 in his Essai d'une théorie sur la structure des cristaux, 29 was conceived as a miniscule polyhedron, since the shape of the macroscopic crystal only enlarged upon the microscopic modules within it. Cleavage of the crystal, whether an actual performance or a gedanken experiment, would reveal the underlying "primitive form," which it shared with a whole family of related minerals. Ampère took over not only the concept of a molécule intégrante (which he termed "particule"), he also borrowed five out of the six "primitive forms" of Haüy's, with the exception of the dodecahedron with triangular isosceles faces. The minor departure of Ampère from Haüy's theory was his identification of molécules intégrantes with "primitive forms."
Haüy was still intellectually agile in 1814. He would formulate the following year his symmetry law, thus bringing to a close his founding of crystallography. Thus, one may have some confidence that both Wollaston's and Ampère's contributions were brought to his attention.
In any case, contemporaries saw them as complementary. A literary critic, gave in my opinion the most accurate evaluation of Ampère's 1814 paper; Sainte-Beuve (1804-1869) wrote in 1843: 24

"Mr Gay-Lussac's discovery of the simple proportions observed
between the volumes of a compound gas and those of the component
gases gave him [Ampère] the means for conceiving, about the atomic
and molecular structure of organic bodies, a theory which replaces
Wollaston's."

Furthermore, this may well have been the first attested occurrence of the expression "atomic and molecular structure" with the meaning that would subsequently attach to it!
The expression forme représentative, which Ampère coins, is vitally interesting because apparently redundant. Its use confirms that Ampère in 1814 already was keenly aware of the epistemological considerations he would devote himself entirely to after 1828. 25 Had he concerned himself with the mere forme d'une particule, that is to say with a property intrinsic to the molecule, he would have slipped from stating a scientific hypothesis to speculative philosophy. By using the phrase forme représentative d'une particule, Ampère was emphasizing that the polyhedral shapes he was conjecturing were extrinsic and unessential - or not necessarily essential - properties of matter. They pertained to the description, 26 with no guarantee as to their relevance to the object described. This is what is implied by the surface tautology in forme représentative. In other words, the 1814 paper is written from what Ampère would later on term a "cryptoristic" rather than from a "cryptological" viewpoint: discovering something hidden, rather than trying to elucidate causes for the observed facts. 27
The importance of Ampère's paper stems from its extension of Haüy's intuition from mineralogy to chemical compounds in general. It embodies also a fundamental intuition, with potential programmatic value (never actualized in most of the nineteenth century most unfortunately): elemental composition is deducible from chemical structure, analytical chemistry is secondary to structural chemistry. Ampère asserts that one ought to first conjecture a likely structure for a chemical compound, and that the corresponding composition will automatically follow. He even provides a Table of correspondances! In his words

"one needs to seek the explanation of phenomena shown by compound
bodies in the manner in which (atoms) are positioned with respect to one
another upon formation of what I name a (molecule)". 28

Further on he writes:

"the corners (of a molecule) fit into the intervals left in-between the
corners of another, and vice-versa: I visualize chemical combination
in this way ..." 29

The Limited Influence of the Ampère Paper

We turn to reception of the Ampère paper. It fell into a near-vacuum. Few scientists within the mainstream of chemistry were interested. As is well known, the Avogadro-Ampère hypothesis was not taken seriously till Cannizzaro resurrected it triumphally at the Karlsruhe Congress in 1860.
To some,30 , 31 Avogadro's hypothesis comes under the heading of premature discoveries. 32 Professor Brooke has addressed this particular question with his usual learning and cogency and has answered it in the negative. 33 In so doing, he has provided a comprehensive list of (about two dozens!) possible explanations for the lag time between the publication by Avogadro and the protracted but enthusiastic acceptance of Avogadro's ideas at the Karlsruhe Congress. Most of those considerations are applicable to the reception of Wollaston's and of Ampère's papers as well.
Ampère's ideas were explicitly rejected on the two, damning counts of being speculative and of coming from a physicist. The first-class burial of Ampère's ideas by Dumas in 1836 remains an enduring blemish on my whole profession:

"Monsieur Ampère, with his mind both profound and naive, who was
both a subtle physicist and a chemist filled with audacious and
ingenious views, has left in the sciences seeds so novel and so fertile...
However, we have to conclude that Ampère's hypothesis, however
ingenious it is, is absolutely inadmissible. Too bad: that's fate and, let
me remark, this is the fate of affinity systems and of intellectual
systems on molecular arrangement presented by physicists. Even
when they have, as Monsieur Ampère did, exact notions about the
phenomena and the laws of chemistry, they always show their lack of
habitual practice of this science." 34

What happened between 1814, when Ampère sent his Open Letter to Berthollet 11 and 1836 when Dumas dismissed it so scornfully? A whole generation of chemists had the opportunity to consider Ampère's geometrical notions, as applied to molecular shape. But on the whole they dismissed them.
Besides reasons identical or similar to those listed by Brooke for the Avogadro case, I see four main explanations for their lack of interest. To rank these in order of increasing importance: 1. unfortunately, due to the state of scientific publishing at the time, due also to the strife in Europe, Avogadro, Wollaston and Ampère were not fully aware of each other's contribution; had they acted jointly, this might have changed the picture; 2. these contributions were not deemed applicable or useful, and they showed inconsistencies, both internal and external, the latter with respect to John Dalton's atomic theory; 3. they fitted a Newtonian program, as had been espoused by the School of Arcueil whose demise had been obvious, both scientifically and politically; 4. they smacked of mathematical physics, i.e. these hypotheses had a potential for blurring the distinction between chemistry and physics, for erasing a disciplinary demarcation which had come to be highly significant to many chemists at that time of incipient professionalization (I shall return to those last two points).
Although the history of chemistry is replete with similar rejections of seminal ideas. 35 some younger chemists took Ampère's ideas seriously. Marc-Antoine Gaudin (1804-1880) was one of them. Converted to the views of Ampère from his lectures, he made it his life work to describe molecular shapes and to deduce molecular architecture from crystal structure. 36 His contributions did not meet with rejection. Gaudin was outside the Establishment of French chemistry. He was considered a lightweight, he did not count, why bother, was the view from mainstream chemistry. 37 Alexandre-Édouard Baudrimont (1806-1880), a realist in the Ampère mold and an antipositivist, also in the intellectual descent of Ampère, pushed for structural chemistry as having priority upon reactivity, the former explaining the latter. 38 But he was also kept outside the mainstream of Establishment French chemistry: a physician and pharmacist in training, he became appointed to a chair of chemistry in Bordeaux in 1849 and his influence remained limited.

Blaming Disciplinary Boundaries

A plurality of factors in any historical fact does not amount to relativism. Just as light can bathe an object from several directions and an observer looking along one of them can still see and assign a characteristic shape, it remains possible to ascribe credit to a given historical explanation.
This will be my purpose here, in proposing a major reason for the acquired indifference of the chemical community, between the 1820s and the Karslruhe Congress in 1860, to the ideas of Ampère and Wollaston about molecular structure.
It stems from the New Science of Galileo and Descartes. Galileo had promoted the role of mathematics in physics and had forcefully argued that geometrical figures are the characters, the alphabet, in the language best describing nature, the language of mathematics. Both Galileo and Descartes saw applied mathematics as the instrument for scientific discovery, geometry for Galileo 39 and geometry assisted by algebra for Descartes. Descartes was thus able to pose physical problems mathematically and to interpret as physics the results of his mathematical treatment. 40
In so doing, the New Science achieved a pivotal move, the recourse to structural models and explanations, at least as important as the contemporary invention or new emphasis put on experimentation. 41 When, at a later stage of the 1780s and 1790s, Haüy invented crystallography, in the words of D'Arcy Wentworth Thompson, 42 he

"shewed the application of mathematics to the description and
classification of crystals, his methods were immediately adopted and a
new science came into being."

Let us note, in passing, that Haüy, in so doing, was emancipating the new discipline of crystallography from its former abode, natural history. When applied mathematics cast its shadow over rystallography at the turn of the nineteenth century, traditional practitioners of natural history could see it as a threat of secession, setting that field as a new discipline.
This is a prejudice which both Wollaston and Ampère were running against. Their approach to molecular structure (a phrase in itself revealing and indicative of the structural, Pythagorean program they had adopted) came out of mathematical physics. Hence, they threatened to subtract from chemistry a sub-discipline - admittedly still inchoate - and to tack it onto crystallography, a brand-new field then perceived as closer to physics or even mathematics. To conceive of molecules as regular polyhedra was a daring conceptual leap, akin to Galileo's in its bridging of the macroscopic world (in which models are built) with the microscopic and in conformity with Haüy's intuition of the structural uniformity of crystalline matter. Chemists might have followed, they might have attempted such a conceptual leap, had they been shown some operational merit, some pragmatic value in doing so. 43
Ampère's contribution took the form of an open letter to Berthollet.11 While Gay-Lussac's 1808 finding of fixed proportions between combining gases is at the origin of both Wollaston's and Ampère's papers, it was not congenial to Berthollet. The latter, jointly with Laplace, had convened the Société d'Arcueil, with its program of a Newtonian chemistry. 44 Ampère's letter, an invitation to a discussion, was a bold attempt to look into the interplay of attractive and repulsive forces involved in the build-up of a molecule. The later demise of the program of a Newtonian chemistry and the waning of the influence of the Arcueil Circle of course happened in the political context of the Bourbon Restoration 45 - a context less favorable to discussion of the issues raised in Ampère's letter, back in 1814.
Ampère proposed to make chemical analysis subservient to structural conjectures. There was the rub: by proposing representative shapes for molecules, Ampère was perceived by contemporaries such as Berzelius and Dumas as an outsider attempting to change the collective representation they shared (and had a vested interest in) of chemistry as a science. One does not take kindly to an outsider barging in and proposing to change the rules of the game. "Why would anyone care about molecular structures and their hypothetical representations?" could have been the reaction of many a contemporary to Ampère's proposals. To his chemical colleagues concerned, molecules could exist in any form and shape. They did not care. It was not their concern. To them, analysis and, to a lesser extent, synthesis superseded structural determination and explanation 46 as goals for chemistry. Furthermore, the vague threat of dispossession by physicists staking a claim to chemists' disciplinary territory drew the instinctive corporatist rejection.

Return of the Repressed

As late as 1856, the young William Henry Perkin was so utterly convinced of elemental composition being a unique descriptor for an organic molecule that he conceived and planned a synthesis of quinine (C20H24N2O2) based upon the attempted duplication of allyltoluidine (C10H13N). As is well known, this led him to the serendipitous discovery of mauve.
There are two lessons here from the episode. Destructive analysis of organic molecules for their elemental composition had, by 1856, been in full swing for a whole generation. Justus von Liebig had made it one of the mainstays of his training of young chemists in his laboratory in Giessen, where he stayed from 1824 till 1852, a laboratory viewed as a model all over Europe. Chemists made it their task to characterize compounds with their composition, complemented with determinations of the melting point, boiling point and a few other physical constants. Perkin's naive from hindsight attempted synthesis of quinine shows that, even on the threshold of the blossoming of structural chemistry, knowledge of elemental composition took precedence over all other considerations.
If determining elemental composition was deemed most important, conversely the immense proliferation of organic molecules had not yet permeated in depth the collective thinking of chemists. Perkin's inspired blunder was illustrative instead of a mentalité collective with a blind spot for the full consequences of isomerism, even though the phenomenon had been discovered 30 years earlier by Liebig and Wöhler and had been given its name by Berzelius in 1830-31. While lip service was being paid to isomerism, as a fascinating curiosity, the mentalité made chemists delude themselves with the notion of a one-to-one correspondence between a given chemical species and an elemental composition serving as its signature. Such a mentalité was rooted in the research program, dominating chemical science during most of the first half of the nineteenth century, viz. the attempt to devise classificatory schemes for chemical compounds analogous to biological systematics. Since a biological species is uniquely denoted with two words, one for the genus, the other for the species, elemental composition was being viewed as analogous. The mentalité was nurtured in routine analytical work as performed in Liebig's laboratory and in many others, which became durably influenced by his school, by the attendant professionalization of chemistry (a model that was to endure in the chemical industry, where it continues to this day to be very much alive; e.g. in the logo of the Amercan Chemical Society displaying Liebig's Kaliapparat).
Changing a mentalité is very difficult. As one might have expected, gadflys, i.e. scientists on the fringe of the established academic institutions, brought about and catalyzed the switch in mentalité which started to take place at about the time of Perkin's resounding triumphant failure. Auguste Laurent was one of them. He reminded his fellow chemists that their science goes beyond operations and material transformations; it is first and foremost 47 a combinatorial art producing a large multiplicity of forms in like manner as words are put together from component letters:

"If every chemist follows his own particular course and changes his
formulae as often as he obtains a new reaction, [then] we should
arrive at results quite as satisfactory by putting the atomic letters of a
formula into an urn and then taking them out, haphazard, to form
the dualistic group." 48

Couper was another non-Establishment and utimately disenfranchised chemist 49 who, I think this is no accident, also reminded chemists of the combinatorial-artistic dimension of the science:

"To research the structure of words we must go back, seek out the
decomposable elements, viz. the letters, and study carefully their powers
and bearing. Having ascertained these, the composition and structure of
every possible word is revealed." 50

Thus the mentalité started to switch in the mid-1850s from the positivistic emphasis on accumulation of empirical data to a syntactic and semantic analysis of formulas as chemical words. It is no accident that this switch ushered in the new formulas, with information about connectivity of constituent atoms, as a multiple discovery associated to the names of the afore-mentioned Couper (1858), Kekulé (starting in 1857), Loschmidt (1861), Crum Brown (1861), Wurtz (1864), Hofmann (1865)...
Simultaneously with the switch from the bench to the blackboard, chemical science returned to the hypothetico-deductive methodology on which Ampère had attempted to set it. The intellectual evolution of Kekulé is exemplary. In 1858, he still equated "rational formulae" and Umsetzungformeln: the chemical formula, in this concept, was only a shorthand for empirical knowledge and it did not go beyond the summary of the reactions undergone by a particular compound. 51, 52 By 1866, with the devising of the benzene cyclic formula, Kekulé had completed a Gestalt switch. The formula, whether triangular or hexagonal, had become an a priori intellectual construction. It served as a hypothesis pitted against empirical data, in the form of the isomer count. The formula which accounted best for the number of known isomers would then endure, as adequate for description of the molecule with the maximum likelihood or probability: which signaled the return to Ampère's probabilistic notion of truth for chemical statements.

The History of Stereochemistry Demands the longue durée.

Let me start this part of the argument by noting the date for the coining of the terms "stereochemistry" and "stereoisomers", 1888 53 . Such denomination signals maturity rather than inception of a field. In general, sub-disciplines endow themselves with a name, a terminology, a journal, a program of studies for training young scientists only after the initial thrust (concepts, instruments, procedures,...) has ossified into such institutionalization.
If stereochemistry, as a mental attitude among a significant segment of the chemical community, was ripe in the late 1880s, when then did it originate? Conventional histories disagree on this point. 54 There are two main schools. Some authors pick 1874 and the quasi-simultaneous announcement 55 of tetrahedral carbon by Le Bel 56 and van't Hoff 57 as the start. Other authors, in a view which I find more congenial, place it with Pasteur's investigation of the tartric acids in 1847. Quite a difference: nearly 30 years separate these two highly significant events.
However, whether one adopts the Le Bel-van't Hoff or the Pasteur episode for the first seeding of stereochemical ideas, each position is made untenable by the existence of a sizeable prehistory. In the first case, one may argue validly that van't Hoff picked up the idea of a tetrahedral three-dimensional representation in Kekulé's Bonn laboratory during his residence there in 1872-1873. Kekulé himself came under the influence of Butlerov's conjecture (1862) of a tetrahedral organization of affinity forces for carbon at the corners of a tetrahedron. 58 Another root of van't Hoff's hypothesis was, as he himself granted, the 1869 study by Johannes Wislicenus of the lactic acids, which concluded that their isomerism stemmed from the differing spatial arrangements of the atoms 59 : as Wislicenus wrote in 1873,

"if molecules can be structurally identical and yet possess dissimilar
properties, this can be explained only on the ground that the difference is
due to a different arrangement of the atoms in space". 60, 61

The indebtedness of Achille Le Bel to pastorian ideas is equally clear. As for Pasteur's seminal contribution, the identification and the separation of left-handed and right-handed isomers for the tartric acids also did not spring instantaneously into existence: one cannot avoid mentioning Auguste Laurent having set Pasteur on his way, by recommending that he study crystals of tartrates for his doctoral work. 62 , 63
These are already sufficient arguments for dismissing the conventional views of stereochemistry being born in either 1847 or 1874. 64 The only tenable account of the history of stereochemistry, in my opinion, is to place it in Braudelian longue durée:

"a history whose passage is almost imperceptible, that of man in
relationship to the environment, a history in which all change is
slow, a history of constant repetition, ever-recurring cycles." 65

In order to sketch out what a history of stereochemistry ought to be, upon its inscription in such long-range historical change, 66 it is enough to note that it is intimately linked with the rise of crystallography, at all stages, 67 and that it goes back therefore to the Renaissance.
Pythagorean beliefs in numerology became inscribed in the sky when the neo-Platonic mystique induced Kepler to inscribe the orbits of the planets in the regular solids of Plato. This idea of 1595 gave him in 1618 his third or harmonic law for description of the solar system. Any historical narrative of molecular shapes ought to take into account Kepler's ascribing the hexagonal form of the snowflake to the packing of elementary, invisible droplets of water. 68 In the Seventeenth Century, Kepler's suggestion was expanded upon by Descartes, Bartolinus, Boyle, Hooke and Huygens. For instance, Robert Hooke showed the regularity of angles independently of the sizes of a crystal face. Kepler had seen Platonic solids in various samples of ores. Steno abandoned Platonic solids for exact measurements of models for the crystals of hematite from the island of Elba. A century of observations then led to Haüy's formulation of the reticular hypothesis in 1802 69 . And, to return to the snowflake, Haüy recognized that its hexagonal symmetry was consistent only with bent water molecules, to express his profound insight in today's words. 70
The second stage in the gradual, step-by-step mise en abyme of the material world came about at the end of the eighteenth century with Haüy's representation of crystal shapes, also with a small number of regular polyhedra as building units. The Platonic idea inherited from the Renaissance then came to encompass the whole of mineralogy.
Step 3 was Ampère's 1814 open letter to Berthollet: henceforth molecules could also be described by regular geometries, with their component atoms located at the corners of polyhedra, in arrangements obeying very simple mathematical relationships. Ampère pioneered the notions of molecular structure and architecture as goals for chemistry to establish and understand, and as tools for chemists to apply to the unravelling of the laws of chemical combination.
Step 4, definitely influenced by a sound knowledge of crystallography and by his being steeped in René-Just Haüy's writings, perhaps also echoing Ampère's 1814 paper, was Auguste Laurent's. He provided a conjectural account in his doctoral dissertation (1837) of the reactivity of organic molecules, additions and substitutions, using a schematic diagram in the shape of a parallelipiped for a hydrocarbon "nucleus" of 12 hydrogens and 8 carbon atoms. 71 In so doing, Laurent was experimenting with the notion of a three-dimensional regular solid or polyhedron in order to recapitulate (and abstract) the whole series of metamorphoses a molecule was capable of undergoing. This was one of the seeds for the molecular formula as Kekulé would conceive it 20 years later (1858 and step 5).
Step 6 in the mise en abyme that unfolded with slow and inevitable deliberation across the ages was Le Bel's and van't Hoff's discovery that the tetrahedron (the simplest of the Platonic solids) proved to be an adequate descriptor of carbon asymmetry and of tetravalent bonding (1874).
Step 7 is, as mentioned, Alfred Werner's parallel establishment in the 1890s of a similar role for the octahedron, another Platonic solid, as an organizing template for a whole class of coordination complexes, of "higher-order compounds" as he termed them, and for their isomerism. Thus it is that Ampère's 1814 paper bridges Haüy and Werner. Alfred Werner's contribution brought order into the proliferation of coordination compounds by organizing them into the three families with coordination numbers of four, six and eight. He also used representative polyhedral shapes, focussing especially on the octahedron for coordination number six. 72 Ampère's and Werner's contributions are both geometrical in spirit. Alfred Werner wrote for instance of the

"theoretically possible symmetrical groupings of a corresponding
number (four, six and eight) of points about a center, if the neighboring
points are equidistant."

to describe his concept of the coordination sphere. 73
Then, in the early 1900s, Gilbert N. Lewis became puzzled by the coexistence of two types of bonding interactions, normal covalent in organic molecules and dative coordinative as present in the Werner complexes. This led him, as early as March 28 1902 to draw on the back of an envelope the electronic configuration as yet another Platonic solid: the cube. In his scheme, the electrons made up a shell, occupyingd gradually and symmetrically the eight corners of a cube. 74,75 Recognition in Lewis's words

"that the pair of electrons forms the stable group, (and that) in general
the pair rather than the group of eight should (...) be regarded as the
fundamental unit"

gave him both the notion of the two-electron bond and the tetrahedral carbon atom. Thus, Lewis was led to the conclusion, anticipating the discovery of electronic spin and of Pauli Principle, of the electron pair being held together in like manner as coupled little magnets. This would be step 8 in the gradual Platonicization of matter. It would also be a major step in the reopening of a creative dialog between chemistry and physics during the first three decades of the twentieth century, which would end with Linus Pauling importing into chemistry the key ideas of the new quantum mechanics, and with the physicists (Hans Bethe, Fritz London, Julius R. Oppenheimer, Edward R. Teller, and very few others) beating a hasty retreat from the complexities of chemistry, after some magnificent forays of lasting benefit. Afterwards the two sciences would resume their separate ways, with chemistry developing

"predictive models in a Fourier expansion, by acquiring low order
information over a wider and wider domain. A physicist typically strives
to develop predictive or interpretative capacity in a Taylor expansion
about some prototypical case, such as the hydrogen atom, by acquiring
higher and higher order information about the prototype and its close
relatives." 76

Furthermore, the numerology underlying atomic and nuclear structure which physicists such as Elsasser and Goeppert-Mayer established during subsequent decades, came as a further understanding of nature, from the macrocosm to the microcosm, on the basis of posited Pythagorean harmonies.
To restrict myself to the topic at hand, molecular formulae, and also to bring the story yet closer to present times, I would mention as further stages in this mise en abyme unfolding since at least the time of Albrecht Dürer and Johannes Kepler, 77 the devising by a number of chemists in 1957 of the valence shell electron pair repulsion or VSEPR model (Gillespie-Nyholm);78 the reunification of inorganic and organic structures encompassing atomic clusters, coordination complexes and organic molecules, performed once again (and in very much the spirit of Ampère's 1814 paper) in the 1960s, to which the name of Earl R. Muetterties is attached predominantly; the discovery by Aaron Klug of icosahedral viruses; the syntheses during the latter half of the twentieth century of hydrocarbons in the shape of Platonic solids, ushered in by Philip E. Eaton's synthesis of cubane and leading to Paquette's synthesis of dodecahedrane; 79 and the accidental discovery of the C60 molecule with its soccer ball shape derived from the icosahedron. 80 , 81 , 82

Acknowledgements

Christopher Ritter, University of California, Berkeley, brought to my attention the 1812 Bakerian Lecture at the Royal Society, and he also made me befit from his reading of a first draft of this manuscript, for which I thank him heartily. I am grateful to Georges Bram, Roger Hahn, Mary-Jo Nye, Alan J. Rocke and Anthony S. Travis for most enlightening discussions.
1 G. Bayfield, "Dereham's forgotten scientist: William Hyde Wollaston", Dereham Antiquarian Society 1990.
2 M. C. Usselman, Platinum Metals Review 22 (1978) 100-106.
3 M. C. Usselman, Annals of Science 37 (1980) 253-268.
4 L. L. Coatsworth, B. I. Kronberg, M. C. Usselman, History of Technology 6 (1981) 91-111.
5 B. I. Kronberg, L. L. Coatsworth, M. C. Usselman, Ambix 28 (1981) 20-35.
6 J. A. Chaldecott, Platinum Metals Review 23 (1979) 112-123.
7 B. A. Smith, Physics Education 15 (1980) 310-314.
8 M. C. Usselman, Annals of Science 35 (1978) 551-579.
9 G. L. Turner, Notes and Records of the Royal Society of London 29 (1974) 53-79.
10 W. H. Wollaston, Philosophical Transactions of the Royal Society of London 103 (1813) 51-63.
11 Models still visible at Imperial College, London, made from wood and from plate glass, were devised by Wollaston in conjunction with his Bakerian Lecture. He must have demonstrated to the assistance how elementary polyhedral solids can be assembled into various crystalline structures.
12 Ampère, A.-M. Ann. de Chim. et de Phys. 1814, XC, 43. For an interesting translation into German, see "Brief des Herrn Ampere an den Herrn Grafen Berthollet,. . .", W. Ostwald, Ed.; Akademische Verlagsgesellschaft: Leipzig, 1921.
13 Laszlo, P. La découverte scientifique; Presses universitaires de France: Paris, 1999.
14 Scheidecker-Chevallier, M. doctoral thesis, Université des sciences et technologies de Lille, 1992.
15 Scheidecker-Chevallier, M.; Locqueneux, R. Archives internationales pour l'histoire des sciences 1992, 42, 227-268.
16 In the 1814 memoir, Ampère calls an atom a "molécule" and a molecule a "particule". In a latter paper, he converted to our modern terminology: Ampère, A. M. Annales de chimie et de physique 1835, 63, 432-444.
17 A. J. Rocke, Chemical atomism in the nineteenth century: From Dalton to Cannizzaro, Ohio State University, Columbus, Ohio 1984.
18 M. Morselli, Amedeo Avogardo: A scientific biography, D. Reidel, Dordrecht 1984.
19 M. G. Kim, History of Science XXX (1992) 69-96.
20 Taton, R. Revue d'Histoire des Sciences 1978, 31, 233-248; Sadoun-Goupil, M. Revue d'Histoire des Sciences 1977, 30, 125-141.
21 Haüy, R.-J. Essai d'une théorie sur la structure des cristaux appliqué à plusieurs genres de substances cristallines; Goguée & Née de la Rochelle: Paris, 1784.
22 Mauskopf, S. H. Isis 1969, 60, 61-74.
23 R. Halleux, P. Laszlo, Représentations anciennes du savoir chimique et alchimique Université de Liège, Liège, Belgium 1980.
24 Sainte-Beuve, in A.-M. Ampère: Essai sur la philosophie des sciences, Vol. 2, Bachelier, Paris 1843, p. liij.
25 Taton, R. Revue d'Histoire des Sciences 1978, 31, 233-248.
26 R. Hoffmann, P. Laszlo, Angew. Chem. Int. Ed. Engl. 30 (1991) 1-16.
27 Ampère Essai sur la philosophie des sciences, ou exposition analytique d'une classification naturelle de toutes les connaissances humaines.; Bachelier: Paris, 1834 & 1843.
28 Ampère, A.-M. Ann. de Chim. et de Phys. 1814, XC, 43-86, p. 44.
29 ibid., p. 55.
30 M. Frické, in C. Howson (Ed.): Method and appraisal in the physical sciences, Cambridge University Press, Cambridge 1976, p. 277-307.
31 such as, more recently, A. Greenberg, A Chemical History Tour.
Picturing Chemistry from Alchemy to Modern Molecular Science, Wiley, New York 2000, p. 176.
32 G. S. Stent, Scientific American 227 (1972) 84-93.
33 J. H. Brooke: Thinking About Matter. Studies in the History of Chemical Philosophy, Variorum, Aldershot, Hampshire, UK 1995, pp. 235-273.
34 Dumas, J.-B. Leçons sur la philosophie chimique, professées au Collège de France en 1836. . .; facsimile reprint, Brussels, 1972 ed.; Paris, 1837, p. 352.
35 Stereochemistry can be singled out for such episodes which indeed account, to a large extent, for its much delayed and protracted vindication, only in the 1950s with the advent of conformational analysis. There is the scornful put-down by Kolbe of van't Hoff's tetrahedral carbon:"...the atoms appeared to him to have grouped themselves throughout universal space. ... It is one of the signs of the times that modern chemists hold themselves bound to consider themselves in a position to give an explanation for everything, and, when their knowledge fails them, to make use of supernatural explanations." Kolbe's vitriolic and venomous pamphlet came complete with castigation of van't Hoff for not being a mainstream chemist, relegated that he was in a veterinary school. H. Kolbe, J. prakt. Chem. 15 (1877) 473. Behind this outburst against the tetrahedral carbon, there was a positivistic bias: "To Kolbe, talk of directed valencies was pure fantasy, marking a return to the a priori speculations typical of German Naturphilosophie before Berzelius and Liebig had placed organic chemistry on to the firm empirical grounds of analysis." W. H. Brock, The Norton History of Chemistry, W.W. Norton, New York 1993, pp. 262-263 .
36 Gaudin, A. Annales de chimie et de physique 1833, 52, 113-133; Gaudin, M.-A. L'architecture du monde des atomes; Gauthier-Villars: Paris, 1873.
37 Mauskopf, S. H. Isis 1969, 60, 61-74.
38 Baudrimont, A. E. Traité de chimie générale et expérimentale; J.B. Baillière: Paris, 1844-1846.
39 D. Mertz, Studies in the History and Philosophy of Science 13 (1982) 11-131.
40 J. Merleau-Ponty, Leçons sur la genèse des theories physiques. Galilée, Ampère, Einstein, Vrin, Paris 1974.
41 D. W. Mertz, The Modern Schoolman LXXVI (1999) 211-219.
42 D. W. Thompson, On Growth and Form, Cambridge University Press, Cambridge 1942, p. 1028.
43 Ursula Klein has very nicely described how experimental practice in chemistry during the seventeeth century did not steep itself in a philosophical tradition and evolved its own, separate conceptual framework: U. Klein, Science in Context 9 (1996) 251-287.
44 M. P. Crosland, The Society of Arcueil. A View of the French Science at the Time of Napoléon I, Heineman, London 1971.
45 R. Fox, Historical studies in the physical sciences iv (1975) 89-136.
46 E. McMullin, American Philosophical Quarterly 15 (1978) 139-147.
47 Laszlo, P. La parole des choses; Hermann: Paris, 1993.
48 Laurent, A. Méthode de chimie (avec un avis au Lecteur de J. B. Biot); Paris, 1854.
49 He became incensed at being scooped by Kekulé when he had first submitted his memoir on the tetravalency of carbon and on the presence of carbon-carbon links in organic molecules. After he confronted about this priority loss Adolphe Wurtz, the head of his laboratory, probably vehemently on account of his volatile temper, he quit, either in a huff or having been dismissed. The episode became for Wurtz and his group the proverbial skeleton-in-a-closet. The only mention of Couper in this context is by Friedel in the biography of Wurtz that serves as the Introduction to posthumous editions of La Théorie Atomique .
50 Couper, A. S. Compt. Rend. 1858, 46, 1157; quoted by W. H. Brock, History, p. 254.
51 Kekulé, F. A. Annalen 1858, 106, 153.
52 An epistemic switch took place between 1854 and 1858: the formula turned from a retrodictive device to a predictive tool. A key ingredient was the gradual integration of isomer count as a mapping instrument. The Kekulé benzene formula was swiftly adopted by the chemical industry which very greatly helped its acceptance by the academic community, and this was another key ingredient.
53 Meyer, V.; Auwers, K. Berichte der deutschen chemischen Gesellschaft 1888, 21, 3510-3529.
54 Even though most share the methodological oversight of restricting stereochemistry to organic molecules only.
55 The lack of a priority quarrel between Le Bel and van't Hoff is all the more remarkable in view of the violent controversies that flared up at the time. For instance, Professor Colin A. Russell beautifully documents Frankland's bitterness at the tetravalency of carbon being credited to Kekulé alone with no acknowledgement of his own contribution: Russell, C. A. Edward Frankland. Chemistry, Controversy and Conspiracy in Victorian England.; Cambridge University Press: Cambridge, 1996. As proof of the mutual esteem and sympathy between Le Bel and van't Hoff, in 1887 the latter dedicated to the former his Dix années dans l'histoire d'une théorie, the second edition of La Chimie dans l'espace to "M. J.A. Le Bel, en témoignage de ma respectueuse affection".
56 Le Bel, A. Bull. soc. chim. 1874, 22, 337.
57 Hoff, J. H. v. Archiv. néerl. sci. exact. nat. 1874, 9, 445.
58 Rocke, A. J. BJHS 1981, 14, 27-57.
59 see for instance Brock, W. H. The Norton History of Chemistry; W.W. Norton: New York, 1993, p. 260.
60 Wislicenus, J. Annalen 1873, 166, 47.
61 Peter J. Ramberg, who devotes himself to a most useful history of stereochemistry, Ramberg, P. J. Ph. D. Thesis, Indiana, 1993, rightfully singles out Wislicenus as the determined and persistent apostle of van't Hoff's hypothesis in the 1880s and 1890s. He presents also Arthur Michael as the main opponent of stereochemistry, which is an oversimplification. Michael, no stranger to theoretical thinking himself, objected to what he rightly saw as sloppy and self-contradictory work. Michael was responsible for establishing firmly the key stereochemical finding, to use modern terminology, of antiperiplanar addition onto double bonds, Ramberg, P. J. Historical Studies in the Physical and Biological Sciences 1995, 26, 89-138.
62 see for instance Brock, W. H. The Norton History of Chemistry; W.W. Norton: New York, 1993. p. 258.
63 Auguste Laurent, who as mentioned convinced Pasteur to study the tartrates, was nurtured himself on crystallography at Ecole des Mines:
C. J. Schneer, in H. Woolf (Ed.): The Analytic Spirit, Cornell University Press, Ithaca NY 1981, p. 279-292; and in his own doctoral dissertation (1837)
"offered a crystallographic interpretation of substitution reactions, representing the 'fundamental radical' of a compound by a prism." S. C. Kapoor, Isis 60 (1969) 477-525.
64 To return to the alleged ripeness of stereochemistry among a significant segment of the chemical community in the 1880s, if indeed this had been the case, how should one account for the indifferent neglect, or the neglectful indifference, with which the publication by Hermann Sachse of the chair and boat forms of hexamethylene (cyclohexane) (H. Sachse, Berichte der Deutschen Chemischen Gesellschaft 23 (1890) 1363) was met? Arguably at the origin of conformational analysis, (C. A. Russell, in O. B. Ramsay (Ed.): Van't Hoff-Le Bel Centennial, American Chemical Society, Washington DC 1974, p. 159-178) even though Sachse's ideas (H. Sachse, Zeitschrift für physikalische Chemie 10 (1892) 203-241) were much later revived ( E. Mohr, Journal für Praktische Chemie 98 (1918) 315-353; E. Mohr, Berichte der deutschen chemischen Gesellschaft 55 (1922) 230-231) such geometric notions remained in the backwaters of chemistry till their resurrection in the late 1940s only by Derek Barton, Odd Hassel and a few others. I would pin the indifference to Sachse's depiction of the cyclohexane chair and boat in 1890 on a number of factors, among which the two predominant ones were the contemporary focus on energetics and thermochemistry (as exemplified, inter alia, by van't Hoff's work in those areas) and the emphasis, within industrial chemistry, on planar conjugated dye molecules.
65 Braudel, F. The Mediterranean and the Mediterranean World in the Age of Philip II; 2 vols., University of California Press: Berkeley, 1995.
66 The obvious definition of stereochemistry is "chemistry in three-dimensional space," considering both inorganic and organic systems alike.
67 Which incidentally makes much better sense of the resurgence of stereochemistry in the mid-twentieth century (see for instance Kurt Mislow, An Introduction to Stereochemistry, W. A. Benjamin, New York, 1966).
68 Kepler, J. De Nive Hexangula (On the Six-Cornered Snowflake); (reprint: Clarendon Press: Oxford), 1611.
69 Schneer, C. J. In The Analytic Spirit; H. Woolf, Ed.; Cornell University Press: Ithaca NY, 1981; pp 279-292.
70 Haüy, Traité élémentaire de physique, Courcier, Paris 1806, 2 vols., vol.2, p. 249, section 358, starting with the sentence: "On pourrait plutôt présumer que les molécules de la glace sont des tétraèdres réguliers etc." Haüy had published in 1802 the first edition of this textbook, upon Napoléon's urging.
71 Nye, M. J. Before Big Science. The Pursuit of Modern Chemistry and Physics 1800-1940.; Twayne-Prentice Hall: New York and London, 1996; pp. 122-123.
72 Werner, A. In Nobel Lectures. Chemistry 1901-1921.Elsevier: Amsterdam, 1966, pp 256-269.
73 ibid, p. 259.
74 Lewis, G. N. J. Am. Chem. Soc. 1916, 38, 762-785.
75 Brock in his History of Chemistry, pp 468-469 downplays the role of crystallographic considerations in Lewis's coming-up with his cubic model for the atom. He stresses Lewis's indebtedness to Alfred Werner's revolutionary teachings in Neuere Anschauungen. I agree with the latter but not with the former statement. See also in this respect Kohler, R. Hist. Stud. Phys. Sci. 1971, 3, 343-376.
76 Herschbach, D. Physics Today 1997, 11-13.
77 Yet another benefit accruing from reframing the history of stereochemistry in la longue durée derives from its improved insertion within intellectual history, with the attendant analogies and contrasts. Two examples come to mind. Can we begin to chart as parallel histories those of molecular structure and representation, on one hand, and those of geographic mapping (D. Wood, The Power of Maps, The Guilford Press, New York 1992. ) on the other? Do they partake of the same episteme of the spatial metaphor? Can we and should we chart as parallel histories those of molecules conceived as combinatorial assemblies of atoms and radicals, on one hand, and those of speech acts conceived as combinatorial assemblies of modules (such as phonemes or morphemes), on the other, as partaking of the same linguistic metaphor episteme ( P. Laszlo, La parole des choses, Hermann, Paris 1993)? On this latter point: la longue durée is also enlightening on the topic of the recourse to "paper tools" in chemistry. For instance, typographical symbols for the elements - as devised say by Hassenfratz or by John Dalton - show obvious connections with alphabets for utopian languages, as first published in Thomas More's Utopia (T. More, Utopia, Thierry Martin, Leuven 1516.). To my knowledge, the history of such links has yet to be researched and told.
78 Gillespie, R. J.; Hargittai, I. The Vsepr Model of Molecular Geometry; Prentice Hall: Englewood Cliffs NJ, 1990.
79 Paquette, L. A.; Teransky, R. J.; Balogh, D. W.; Kentgen, G. J. Am. Chem. Soc. 1983, 105, 5446.
80 Baggott, J. Perfect Symmetry. The Accidental Discovery of Buckminsterfullerene.; Oxford University Press: Oxford, 1994.
81 Such a quick-and-dirty sketch of the history of stereochemistry, as a longue durée endeavor, will undoubtedly face rejection by professional historians as typical of Whig history which scientists are wont to tell (see on this score P. Forman, ISIS 82 (1991) 71-86; S. G. Brush, OSIRIS 10 (1995) 215-231. ). I feel amply vindicated by the attitude of a Marc Bloch: he repeatedly stressed that study of the past ought to be rooted to a large extent in an understanding of the present (M. Bloch, Apologie pour l'histoire, Armand Colin, Paris 1974, p. 32. ) and in recent contributions to historiography, such as R. Hahn, Journal of the History of Philosophy 3 (1965) 235-242, B. Lepetit, Annales 51 (1996) 525-538 and others aptly summarized by François Dosse: " p. 74: "Such a creationist approach to history implies revising the distance which most historiographic traditions put between the dead past and the historian in charge of its objectivation. To the contrary, history has to be recreated. The historian is the mediator, the go-between in such a re-creation. It occurs in the work of the hermeneut, who reads reality as a text whose meaning shifts with time according to its various phases of actualization. The object of history thus becomes a construction continually opened up by its very writing. History originates therefore in events: it consists of its own inscription in the present which gives it ever-renewed novelty by placing it in an original configuration."F. Dosse, Le Débat (2000) 67-90, p. 74.
82 The history of stereochemistry is thus marked with the occasional resurgence of the polyhedral paradigm inherited from Plato and the Pythagoreans. According to Fernand Braudel's definition, the longue durée is the dimension needed for manifestation of periodicities, such as economic cycles, which are up to historians to explain. Resurgences, as exemplified here, can also take the form of rediscoveries (J. Samuel Y. Edgerton, The Renaissance Rediscovery of Linear Perspective, Harper and Row, New York 1975. A succession of resurgences make up the history of stereochemistry. They stem from the structuralism of Galileo's and Descartes's New Science, but countered - and forced underground for long periods of time - by the reticence of chemists to penetration of their science by mathematical concepts and symbolism. An alternate explanation of the resurgence of polyhedral models at various times would invoke the notion of themata (G. Holton, The Scientific Imagination. Case studies., Cambridge University Press, Cambridge 1978.)