4

an opinion very natural in one who had been immersed in the study of the general analogies of the forms of plants. But though this is excusable in Casalpinus, the rejection of this definiteness of form a hundred years later, when its existence had been proved, and its laws developed by numerous observers, cannot be ascribed to anything but strong prejudice; yet this was the course taken by no less a person than Buffon. "The form of crystallization," says he, "is not a constant character, but is more equivocal and more variable than any other of the characters by which minerals are to be distinguished.” And accordingly, he makes no use of this most important feature in his history of minerals. This strange perverseness may perhaps be ascribed to the dislike which Buffon is said to have entertained for Linnæus, who had made crystalline form a leading character of minerals.

causes.

5

It is not necessary to mark all the minute steps by which mineralogists were gradually led to see clearly the nature and laws of the fixity of crystalline forms. These forms were at first noticed in that substance which is peculiarly called rock-crystal or quartz; and afterwards in various stones and gems, in salts obtained from various solutions, and in snow. But those who observed the remarkable regular figures which these substances assume, were at first impelled onwards in their speculations by the natural tendency of the human mind to generalize and guess, rather than to examine and measure. They attempted to snatch at once the general laws of geometrical regularity of these. occurrences, or to connect them with some doctrine concerning formative Thus Kepler, in his Harmonics of the World, asserts a “formatrix facultas, which has its seat in the entrails of the earth, and, after the manner of a pregnant woman, expresses the five regular geometrical solids in the forms of gems." But Philosophers, in the course of time, came to build more upon observation, and less upon abstract reasonings. Nicolas Steno, a Dane, published, in 1669, a dissertation De Solido intra Solidum Naturaliter contento, in which he says, that though the sides of the hexagonal crystal may vary, the angles are not changed. And Dominic Gulielmini, in a Dissertation on Salts, published in 1707, says, in a true inductive spirit, "Nature does not. employ all figures, but only certain ones of those which are possible; and of these, the determination is not to be fetched from the brain, or proved à priori, but obtained by experiments and observations." And

7

4 Hist. des Min. p. 343. 5 Linz. 1619, p. 161.

6

he speaks with entire decision on this subject: "Nevertheless since there is here a principle of crystallization, the inclination of the planes and of the angles is always constant." He even anticipates, very nearly, the views of later crystallographers as to the mode in which crystals are formed from elementary molecules. From this time, many persons labored and speculated on this subject; as Cappeller, whose Prodromus Crystallographic appeared at Lucern in 1723; Bourguet, who published Lettres Philosophiques sur la Formation de Sels et de Cristaux, at Amsterdam, in 1792; and Henckel, the "Physicus" of the Elector of Saxony, whose Pyritologia came forth in 1725. In this last work we have an example of the description of the various forms of special classes of minerals, (iron pyrites, copper pyrites, and arsenic. pyrites ;) and an example of the enthusiasm which this apparently dry and laborious study can excite: "Neither tongue nor stone," he exclaims,"

can express the satisfaction which I received on setting eyes upon this sinter covered with galena; and thus it constantly happens, that one must have more pleasure in what seems worthless rubbish, than in the purest and most precious ores, if we know aught of minerals."

Still, however, Henckel1o disclaims the intention of arranging minerals according to their mathematical forms; and this, which may be considered as the first decided step in the formation of crystallographic mineralogy, appears to have been first attempted by Linnæus. In this attempt, however, he was by no means happy; nor does he himself appear to have been satisfied. He begins his preface by saying, "Lithology is not what I plume myself upon." (Lithologia mihi 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 profiting by this thought, because, in applying it, he did not employ the light of geometry, but was regulated by what appeared to him resemblances, arbitrarily selected, and often delusive." Thus he derived the form of pyrites from that of vitriol;12 and brought together alum and diamond 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 any other person, it owes its subsequent progress; I mean Romé de Lisle. "Instructed," this writer says, in his preface to his Essais de Crystallographie, "by the works of the celebrated Von Linnée, how

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 crystalline 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;13 although Wallerius" had already said, in speaking of the various crystalline forms of calcspar, '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,15 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.

66

13 Lettres, 1779, i. 48. 15 Leipzig, 1774.

14 Systema Mineralogicum, 1772–5, i. 143.

CHAPTER II.

EPOCH OF ROME DE LISLE AND HAUY.-ESTABLISHMENT OF THE FIXITY OF CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS OF DERIVATION.

WE

E 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 calcspar, and sixteen to felspar. He also invented and used a goniometer. We cannot doubt that he would have been

1

2

3

Cristallographie, ou Description de Formes propres à tous les Corps du Règne Minéral. 3 vols. and 1 vol. of plates.

3 p. 73.

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.

5

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 calcspar, 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.

5 Traité de Minér. 1822, i. 15.

VOL. II.-21.