The pervasiveness of the model's influence between 1760 and 1810 is well exemplified in mineralogy, chemistry, and medicine. Spurred by the practical needs of mining and metallurgy and the curiosity of naturalists, mineralogy was an active field in the latter 18th century. Linnæus included a scheme for the mineral kingdom in the Systema naturae . His example was decisive both in his implicit commitment to the existence of mineral species, and in his use of crystalline form as classificatory criterion. The formal parallel between crystalline forms and the sexual parts of plants was strengthened by the analogy he perceived between the chemical formation of crystals
and the reproduction of living things, an analogy that assured constancy of species in the mineral as in the plant or animal kingdoms. Linnæus distinguished each mineral genus by a basic geometrical figure, and the species within each genus by truncation of the edges or angles of the generic figure. In keeping with his general practice, he assigned each species a genus-species binomial.
Linnæus' system entirely subordinated physical and chemical properties of minerals to the geometrical form of the crystal. In part this may be attributed to the weakness of contemporary chemical analysis and to the absence of quantitative techniques for the measurement of physical properties like hardness. Far more determinative, however, was the compatibility of crystalline form with the requirements of Linnæus' systematic model. Just as the sexual system abstracted from the plant just those visible qualities that could be expressed in numbers or spatial relationships, so did crystalline form abstract from the mineral visible external characters that could be numerically or geometrically defined.
Linnæus' mineral scheme did not enjoy the success of the sexual system. Mauskopf has identified three distinct approaches to mineral classification in the last quarter of the 18th century, based on chemical analysis, groups of external characteristics, and crystal form. All three recognized the need to know chemical composition. Given the state of chemistry at the time, however, chemical criteria were very difficult to apply. The other two approaches looked for characteristics other than the chemical that would still express degrees of essential identities and differences.
In 1774 Abraham Werner, a professor of mineralogy at the mining school of Freiberg, published a work entitled On the external characters of minerals . Aiming to produce a practical handbook for the miner and naturalist, Werner made use of readily accessible mineral characteristics like color, shape, hardness, and texture. He did not
group his species in higher categories, but did restate the Linnæan concept of primary forms of crystals, and pointed out that certain forms were related and could be derived from one another by truncation.
More theoretical, and more directly in the Linnæan tradition, was the work of the French crystallographers Romé de l'Isle and Haüy. Both came to mineral classification by way of crystallography. In his Essai de cristallographie of 1772 and his revised and expanded Cristallographie of 1784, Romé de l'Isle attempted a comprehensive classification of crystals based on the theory that there were a limited number of primitive crystalline forms. In his theory, the diversity of forms observed in nature arose from variations on the primitive ones induced by different conditions of solution or by varying proportions of the constituent chemical principles. The Cristallographie incorporated steps toward a quantitative science of crystals, including use of the contact goniometer and statement of the fundamental law of constant interfacial angles.
Linnæus had not drawn a hard-and-fast line between the kingdoms of living things and minerals. He had therefore not felt a need to justify mineral taxonomy. As the line between organic and inorganic was more and more sharply drawn, however, the need for justification and explicit methodological discussion became inescapable. Prompted by an essay of Louis Daubenton that denied the existence of mineral species, Romé de l'Isle made explicit his commitment to their reality, distinctness, and fixity. In Des caractères extérieurs des mineraux (1784), he argued that invariable laws of chemical affinity assured the same fixity for mineral species that reproduction did for organic ones. In practice, however, he relied on more accessible external features—crystal form, hardness, density—that he presumed to be the direct expression of uniform chemical composition.
Haüy is said to have come to crystallography from botany, seeking a mineral analogue to botanical regularities of form. If so, the botanical inspiration did not immediately extend to questions of mineral taxonomy, for in the Essai d'une théorie sur la structure des cristaux of 1784 Haüy denied the relevance of crystal form to mineral classification. The Essai introduced the concept of the molécule constituente (later termed the molécule intégrante ), a theoretical entity understood as the smallest molecule of a crystal that displayed a characteristic chemical composition and geometrical form. In his emphasis on the geometry of the molécule intégrante and its relationship to the geometry of macroscopic crystals, and in his insistence on the agreement of theoretical and measured results, Haüy took a decisive step in the mathematization of crystallography and attracted the patronage of Laplace. He also provided an original basis for mineral taxonomy.
In a paper of 1793, Haüy defined the mineral species in chemical terms, remarking that just as in botany it is reproduction that assures uniformity in the species, so in mineralogy it is the nature and proportions of the combined chemical principles that guarantee specific identity. In this sense, Haüy argued, chemistry is well suited to accomplish one of the two main purposes of method, that is, classification. For the other purpose—the ready recognition and naming of bodies—chemistry is ill adapted, however, if only because chemical analysis often requires long and laborious procedures that use up all or part of the specimen. Seldom can species be grouped into genera by a single character that is easy to recognize. Thus classification in mineralogy does not compare favorably with that in botany, "where the characters, always drawn from the figure of the organs, that is to say, from a modification that is plainly visible (qui parle aux yeux ) follow a simple, uniform course, and have the merit of offering a picture in which a small number of colors suffice to give a rich and varied expression." In botany, unlike mineralogy, the same means serve the ends of both classification and recognition. A useful
mineralogical method therefore involves much more groping than is the case in botany.
In Haüy's major work of the early 19th century, the molécule intégrante figures in the chemical composition and geometrical form that defined mineral species. The molécule intégrante was, however, a theoretical entity. In practice the results of crystallography and chemistry sometimes diverged. Bodies grouped together by crystallography might be separated by chemistry, and vice versa. Some of this dissonance might be accounted for, Haüy argued, by the imperfection of current chemical analysis or by impurities in the mineral samples. So far as species determination was concerned, however, crystal structure offered the more certain guide: "Only for geometry are all minerals pure." Crystal form, more accessible and less ambiguous than chemical composition, dominated Haüy's determination of species, while his genera, orders, and classes were decided by chemical composition (fig. 3.3).
The practical difficulties resulting from the use of both chemical and crystallographic criteria in mineral classification are reflected in Haüy's struggles with nomenclature. His ideal was a binomial based on the new chemistry by Lavoisier and his circle. The state of the art did not make the ideal possible. In practice, therefore, the unavoidable mix of chemical and crystallographical criteria blurred the clarity of Haüy's nomenclature, which remained only partially rationalized.