he peaks with more tension on us subject: «Noveriness save there's here a premie frystallization, ne neiination of the piles and of the anges s uvas rinstant." Ed even anticipates very nearty, the news of later rystallographers as the mole ʼn vii crystals are formei from dementary moieenies. Fram is time, marY persons laborei ani spermiated on this subject; as Cappeller vis Prodromus Crystallographic wearei at Lacera n 173: Burrit who pubishei Lettres Prilosophumnes mr a Fornation is Sala 4 is Cristant, it Ansteriam, in 1792; and Hencici, zihe Physms of the Elector of Saxony, whose Pyritologia zame irà in 1 hás last work we have an example of the description of the various žens of special classes of ninerus iron puntes, topper puntes, and arsene pyrites ;) and an example of the enthusiasm which this carently by and laborious study an exite: “Vather ngre ner stone," he exIES." can express the satisfaction which I received on setting eyes upon this sinter covered with gulena; and this it constantly happens, that one must have more pleasure in what seems worthless ribcish, than n the purest and most precious cres, f we know aught of minerais.” Sall, however. Henckel Esclaims the intention of arrangng nne rais according to their mathematical forms; and this which may be considered as the first decided step in the formation of crystallographie mineralogy, appears to have been first attempted by Lianeus. In this attempt, however, he was by no means happy; nor does he himself appear to have been satisfied. He begins his predice by aying. Lithology is not what I piume myself upon." (Lithologia nihi cristas non eriget.) Though his sagacity, as a natural historian, led him to see that crystalline form was one of the most definite, and therefore most important, characters of minerals, he failed in proditing by this thought, because, in appiving it, he did not employ the Eight of geome try, but was regulated by what appeared to him resemblances, arbitrarily selected, and often deinsive." Thus he derived the form of pyrites from that of vitriol; and brought together alum and damond on account of their common octohedral form. But he had the great merit of animating to this study one to whom, more perhaps than to other person, it owes its subsequent progress: I mean Rome de Lisle. "Instructed." this writer says, in his preface to his Essais ie Crystallographie, by the works of the celebrated Von Linnée, how any greatly the study of the angular form of crystals might become interesting, and fitted to extend the sphere of our mineralogical knowledge, I have followed them in all their metamorphoses with the most scrupulous attention." The views of Linnæus, as to the importance of this character, had indeed been adopted by several others; as John Hill, the King's gardener at Kew, who, in 1777, published his Spathogenesia; and Grignon, who, in 1775, says, "These crystallizations may give the means of finding a new theory of the generation of erystailine gems." The circumstance which threw so much difficulty in the way of those who tried to follow out his thought was, that in consequence of the apparent irregularity of crystals, arising from the extension or contraction of particular sides of the figure, each kind of substance may really appear under many different forms, connected with each other by certain geometrical relations. These may be conceived by considering a certain fundamental form to be cut into new forms in particular ways. Thus if we take a cube, and cut off all the eight corners, till the original faces disappear, we make it an octohedron; and if we stop short of this, we have a figure of fourteen faces, which has been called a cubo-octohedron. The first person who appears distinctly to have conceived this truncation of angles and edges, and to have introduced the word, is Démeste;" although Wallerius" had already said, in speaking of the various crystalline forms of calespar, I conceive it would be better not to attend to all differences, lest we be overwhelmed by the number." And Werner, in his celebrated work On the External Characters of Minerals," had formally spoken of truncation, acuation, and acumination, or replacement by a plane, an edge, a point respectively, (abstumpfung, zuschärfung, zuspitzung,) as ways in which the forms of crystals are modified and often disguised. He applied this process in particular to show the connexion of the various forms which are related to the cube. But still the extension of the process to the whole range of minerals and other crystalline bodies, was due to Romé de Lisle. 13 Lettres, 1779, i. 48. 15 Leipzig, 1774. 14 Systema Mineralogicum, 1772–5, i. 143. CHAPTER II. EPOCH OF ROME DE LISLE AND HALY.-ESTABLISHMENT OF THE FIXITY OF CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS OF DERIVATION. WE TE have already seen that, before 1780, several mineralogists had recognized the constancy of the angles of crystals, and had seen (as Démeste and Werner,) that the forms were subject to modifications of a definite kind. But neither of these two thoughts was so apprehended and so developed, as to supersede the occasion for a discoverer who should put forward these principles as what they really were, the materials of a new and complete science. The merit of this step belongs jointly to Romé de Lisle and to Haüy. The former of these two men had already, in 1772, published an Essai de Crystallographie, in which he had described a number of crystals. But in this work his views are still rude and vague; he does not establish any connected sequence of transitions in each kind of substance, and lays little or no stress on the angles. But in 1783, his ideas1 had reached a maturity which, by comparison, excites our admiration. In this he asserts, in the most distinct manner, the invariability of the angles of crystals of each kind, under all the changes of relative dimension which the faces may undergo; and he points out that this invariability applies only to the primitive forms, from each of which many secondary forms are derived by various changes. Thus we cannot deny him the merit of having taken steady hold on both the handles of this discovery, though something still remained for another to do. Romé pursues his general ideas into detail with great labor and skill. He gives drawings of more than five hundred regular forms (in his first work he had inserted only one hundred and ten; Linnæus only knew forty); and assigns them to their proper substances; for instance, thirty to calespar, and sixteen to felspar. He also invented and used a goniometer. We cannot doubt that he would have been 1 Cristallographie, ou Description de Formes propres à tous les Corps du Règne Minéral. 3 vols. and 1 vol. of plates. 3 p. 73. 2 p. 68. looked upon as a great discoverer, if his fame had not been dimmed by the more brilliant success of his contemporary Haüy. Réné-Just Haüy is rightly looked upon as the founder of the modern school of crystallography; for all those who have, since him, pursued the study with success, have taken his views for their basis. Besides publishing a system of crystallography and of mineralogy, far more complete than any which had yet appeared, the peculiar steps in the advance which belong to him are, the discovery of the importance of cleavage, and the consequent expression of the laws of derivation of secondary from primary forms, by means of the decrements of the successive layers of integrant molecules. The latter of these discoveries had already been, in some measure, anticipated by Bergman, who had, in 1773, conceived a hexagonal prism to be built up by the juxtaposition of solid rhombs on the planes of a rhombic nucleus.* It is not clear whether Haüy was acquainted with Bergman's Memoir, at the time when the cleavage of a hexagonal prism of calespar, accidentally obtained, led him to the same conception of its structure. But however this might be, he had the indisputable credit of following out this conception with all the vigor of originality, and with the most laborious and persevering earnestness; indeed he made it the business of his life. The hypothesis of a solid, built up of small solids, had this peculiar advantage in reference to crystallography; it rendered a reason of this curious fact that a certain series of forms occur in crystals of the same kind, while other forms, apparently intermediate between those which actually occur, are rigorously excluded. The doctrine of decrements explained this; for by placing a number of regularly-decreasing rows of equal solids, as, for instance, of bricks, upon one another, we might form a regular equal-sided triangle, as the gable of a house; and if the breadth of the gable were one hundred bricks, the height of the triangle might be one hundred, or fifty, or twenty-five; but it would be found that if the height were an intermediate number, as fifty-seven, or forty-three, the edge of the wall would become irregular; and such irregularity is assumed to be inadmissible in the regular structure of crystals. Thus this mode of conceiving crystals allows of certain definite secondary forms, and no others. The mathematical deduction of the dimensions and proportions De Formis Crystallorum. Nov. Act. Reg. Soc. Sc. Ups. 1773. VOL. IL-21. of these secondary forms:-the invention of a notation to express them;—the examination of the whole mineral kingdom in accordance with these views;-the production of a work in which they are explained with singular clearness and vivacity;-are services by which Hauy richly earned the admiration which has been bestowed upon him. The wonderful copiousness and variety of the forms and laws to which he was led, thoroughly exercised and nourished the spirit of deduction and calculation which his discoveries excited in him. The reader may form some conception of the extent of his labors, by being told that the mere geometrical propositions which he found it necessary to premise to his special descriptions, occupy a volume and a half of his work;-that his diagrams are nearly a thousand in number; that in one single substance (calespar) he has described forty-seven varieties of form;-and that he has described one kind of crystal (called by him fer sulfuré parallélique) which has one hundred and thirty-four faces. In the course of a long life, he examined, with considerable care, all the forms he could procure of all kinds of mineral; and the interpretation which he gave of the laws of those forms was, in many cases, fixed, by means of a name applied to the mineral in which the form occurred; thus, he introduced such names as équiare, métastatique, unibinaire, perihexahèdre, bisalterne, and others. It is not now desirable to apply separate names to the different forms of the same mineral species, but these terms answered the purpose, at the time, of making the subjects of study more definite. A symbolical notation is the more convenient mode of designating such forms, and such a notation Hauy invented; but the symbols devised by him had many inconveniences, and have since been superseded by the systems of other crystallographers. Another of Haüy's leading merits was, as we have already intimated, to have shown, more clearly than his predecessors had done, that the crystalline angles of substances are a criterion of the substances; and that this is peculiarly true of the angles of cleavage; that is, the angles of those edges which are obtained by cleaving a crystal in two different directions;—a mode of division which the structure of many kinds of crystals allowed him to execute in the most complete manner. As an instance of the employment of this criterion, I may mention his separation of the sulphates of baryta and strontia, which had Traité de Minéralogie, 1801, 5 vols. |