Essai d'une Théorie sur la Structure des Crystaux, appliquée a plusieurs Genres de Substances crystallisées.

Paris: Gogué & Née de la Rochelle, 1784.

First edition of Haüy’s first printed book, the foundation of the mathematical theory of crystal structure. This is an exceptionally fine copy in original wrappers, very rare in this condition. Haüy proposed six types of primary crystal forms (parallelpiped, rhombic dodecahedron, hexagonal dipyramid, right hexagonal prism, octahedron and tetrahedron), and argued that the primitive form or ‘nucleus’ of a crystal species results from the cleavage of all secondary forms.


First edition of Haüy’s first printed book, an exceptionally fine copy, very rare in this condition. “The foundation of the mathematical theory of crystal structure. Haüy proposed six types of primary crystal forms (parallelpiped, rhombic dodecahedron, hexagonal dipyramid, right hexagonal prism, octahedron and tetrahedron), and argued that the primitive form or ‘nucleus’ of a crystal species results from the cleavage of all secondary forms, although for him this ‘nucleus’ was a mathematical concept rather than a physical reality. He put forward the idea of the crystal molecule, and recognized the discontinuity principle; i.e., that not all angles and inclinations of crystal faces are possible, and therefore the varieties of a crystal species are limited. He derived secondary forms theoretically by stacking layers of molecules on the faces of the nucleus, enunciating the laws of decretement (reduction of each successive layer) and symmetry that regulate their growth. His law of decretement led his successors directly to the law of rational indices (sometimes called ‘Haüy’s law’) (Norman). “Romé de l’Isle had deduced the various forms of the same crystal species by truncating the edges or the solid angles of the rather arbitrarily selected primitive form. Haüy established a more rigorous mathematical relationship between primary and secondary forms of the same species, and his choice of the primary form was founded on more physical grounds” (DSB). “L’Essai d'une Théorie sur la Structure des Crystaux est la premier grand ouvrage d’Haüy. C’est un modèle de logique dans le raisonnement et de clarté dans l’expression” (En Français dans le Texte).

Haüy’s first works were two memoirs submitted to the Académie Royale des Sciences in 1781. In these papers Haüy developed a lamellar theory of crystal structure, following Torbern Bergmann, although Haüy’s approach was much more rigorous and elaborate. “With his 1784 Essai d'une Théorie sur la Structure des Crystaux, appliquée a plusieurs Genres de Substances crystallisées, Haüy breaks away radically from his own and Bergmann’s lamellar theory and introduces his molecular theory: in the case of calcite, for example, ‘the nucleus, or primitive form, has as constituting molecules small rhombohedra, rather than lamellae’. The constituting molecules (‘molécules constituantes’) are those which were floating in the fluid where the crystal was dissolved, which were mutually attracted and became agglomerated during crystallization. The shape of these constituting molecules can be found with the help of the mechanical division of the crystal, or the striations on the surface. The cleavage takes place between two molecules and can be done at any place in the crystal; if the mechanical division is pushed to its ultimate limit, therefore, it leads necessarily to identical and uniform molecules. Their arrangement, which constitutes the ‘structure’ of the crystal, spreads regularly throughout the crystal. This is a crucial point, since the notion of three-dimensional periodicity of crystals is here clearly introduced for the first time.

“The secondary forms, which are the external forms actually observed, are obtained by the deposition of layers of constituting molecules. A single layer or group of two or more layers is shifter with respect to the layers beneath it by one, two, three or, rarely, four rows. In theory, the number of possibilities is very large, but in practice the law describing how the secondary form is derived from the primitive form is always simple, it is the law of decrements, or law of simple rational truncations (‘Haüy’s law). The French mineralogist and crystallographer G. Friedel pointed out that the term ‘simple’ in the wording of the law is essential. Without it, the law would be a simple mathematical statement, impossible to verify, and not a physical law.

“Haüy observes that the resultant faces of the secondary forms will be stepped, and look like a staircase, but that these steps are so small that they are invisible to the naked eye. Due to the irregularities of the growth, they may in fact sometimes be larger and give rise to the situations one observes at the surface of the crystal. There are no longer half-rhombs along the edges of the layers. The decrements can take place along an edge, around a summit or both (mixed decrements).

“The habit of a particular crystal is the result of the association of various secondary forms which can be interpreted by means of appropriate laws of decrement. After having described the different forms of calcite, the primitive forms of various minerals are determined: the rhombic prism for barite, the octahedron for fluorspar (fluorite), a prism with a rectangular base for gypsum, the rhomb-dodecahedron for garnet, which Haüy recalls is the shape of the honeycomb cell, a rhombic prism for topaz. There is a particular difficulty in the case of fluorspar. A common habit is the cube, and Haüy notes that the smallest crystals, at the start of growth, are little cubes. But the primitive form, obtained by cleavage, is an octahedron. During growth, the layers which agglomerate are parallel to the surface of the cube, but they are not smooth, and are covered with tiny spikes corresponding to the summits of octahedra or tetrahedra” (Authier, Early Days of X-ray Crystallography (2013), pp. 322-3).

“As a boy, René-Just (1743-1822) loved music, and his frequent attendance at the services of the local church drew the attention of the prior of an abbey of the Premonstrants. Thanks to his recommendation, Haüy obtained a scholarship at the College de Navarre in Paris around 1755. After completing his studies, he was appointed, in 1764, as regent (master) in the College and in 1770 in the Cardinal Lemoine College where he taught until his retirement in 1784. In 1770, he was ordained priest. He was elected at the Académie Royale des Sciences in 1783 as adjoint in the class of botany and, in 1788, as associé in the class of Natural History and Mineralogy. In 1791 he became a member of the commission in charge of elaborating the metric system. During the French Rcvolution, all priests were required to take an oath, which Haüy refused to do, with the result that he was briefly imprisoned in August 1792, freed thanks to the help of his friend, the French naturalist Geoffroy Saint-Hilaire (1772-1844). He was appointed Professor of Physics at the École Normale Supérieure in 1795, when the École was created. His lectures served as the basis of his treatise on physics for high schools (1803), commissioned by Bonaparte; the book was an immediate success and was re-edited several times. In 1795 he was appointed Professor of Mineralogy at the École des Mines and curator of its mineralogy collection, and, in 1802, at the Museum of Natural History. His fame extended beyond the frontiers and attracted many students from every part of Europe. In 1809, he became the first Professor of Mineralogy at Paris University, where he created the still existing Laboratory of Mineralogy. After the Restoration he lost his pension and finished his life in poor conditions” (ibid., p. 319).

Dibner, Heralds of Science, 92; En Français dans le Texte 176; Horblit 47; Norman 1021-1022; Sparrow, Milestones of Science, 94; Ward & Carozzi, Geology Emerging (1984), no. 1020; Wilson, History of Mineral Collecting (1994), pp. 53-56.

8vo (192 x 128 mm), pp. [viii], [1], 2-236, with eight folding engraved plates by Sellier after Fossier.

Item #4871

Price: $8,500.00