The term crystal, found in most modern European languages, is derived from the Greek word κ∕√σταλλoς, meaning ice or frozen water, and subsequently transferred to pure transparent stones cut into seals, and, as was thought, only produced in the extreme cold of the lofty passes of the Alps. Pliny, who notices this rock-crystal in his Natural History (book xxxvii.), points out clearly enough the hexagonal form of the crystals, remarking that it is not easy to give any reason why they grow in this foιm, more especially as the points have not the same appearance (yo magis quod neque mucronibus eadem species est), and the polish of the sides is such that no art can equal it. T1 e forms of other minerals are also noticed by him, but the term crystal still had regard to the ice-like transparency and purity of the stone, a reference entirely lost in the modern scientific use of the word.

It is not wonderful that these bodies, often so remarkable for the beauty of their forms, colours, and other physical properties, attracted considerable attention even in the so-called dark ages. But these notices rather amuse us by their quaint absurdity, as we should now regard it, than throw light on the progress of the science. Thus Albertus Magnus in the middle of the 13th century tells how the cold in the lofty mountains makes the ice so dry that it congeals into crystal (ex illo sicco coagulat glaciem, in crystallum). Agricola, three centuries later, knew little more, though affirming that crystallus was not ice but rather succus frigore densatus. Still he indicates some simple forms of crystals, and notes the fissile structure of some stones, as the lapis specularis (probably gypsum or mica), a property which as cleavage soon exercised much influence. Nicolaus Steno, the Dane, born in 1638 at Copenhagen, but for a time resident at Florence, amidst his well-known studies in anatomy, found leisure also to speculate on questions concerning the structure of the earth aud the nature of gems and precious stones. As his treatise De solido intra solidum, naturaliter contento, published in 1669, anticipated in geology some modern speculations and theories subsequently confirmed, so it also contains the germs of important facts in crystallography. It was still the wondrous rock-crystal with the polished sides of the middle prism and the terminal points of the pyramids, joined by the central axis of the crystal, that formed the starting-point of his speculations, and led him to introduce some new notions and terms into the science. How these crystals originated was doubtful, but they evidently grew, not from within like plants, but from without, by the addition of new layers of minute particles carried to the crystal by a fluid, and laid down specially at the ends, as shown by the fine striae that are never wanting on the middle planes. His rejection of extreme cold as the causa efficiens, for something similar to magnetic power, is again a suggestive idea, and not less his conclusion that crystals therefore were not formed only at the first beginning of things, but continue to grow even at the present day. Still more important as a step in the progress of the science would be his assertion that the number and length of the sides in the plane of the axis may vary widely without change in the angles (in piano axis, laterum et numerum et longitudinem varie mutari non mutatis angulis), could we regard it as having a wider application than to the case in hand. It was perhaps more a deduction from the mathematical form of the body than a generalization from observed facts. But some of his other descriptions show great powers of observation, and in his notice of the cleavage of calcspar, and its division into other rhomboidal bodies, we have again a fact that in other hands was to bear important fruits.

Erasmus Bartholinus, another Dane (born 1625, died 1698), made known, in his Experimenta Crystalli Islandiçi disdiadastid (1670), another property of the same mineral, very remarkable in itself and its results to science. This was the double refraction of the beautifully transparent variety sent from the Rödefiord in Iceland to Copenhagen. In the same tract, it may be mentioned in passing, occurs the first reference to the blowpipe as a mean of applying heat to minerals. But the optical fact, turning the attention of mathematicians to crystals, had more direct influence on our science. The celebrated Huyghens described the same miranda refractio, and pointed out its laws; he also measured the angles of the rhomboids with a close approximation to truth, and remarked the occurrence of a less distinct double refraction in quartz— in crystallo duplex esset refractio. He likewise observed the peculiar cleavage of calcspar, which he tried to explain by building up the crystals of spheroids. Leeuwenhoek also, in his Arcana Naturae (1695), mentions cleavage in gypsum and Muscovy glass, and tried to estimate the thickness of the laminae, which Newton in his Optics in 1706 showed could be calculated from his doctrine of the colour of thin plates. In the same work Newton gives an account of the double refraction of Iceland spar and the laws it follows, and, observing the changes tυ which the rays were subject, asks if these rays of light may not have different sides, with different properties—the first anticipation of the polarization of light, so important in this science. Returning to Leeuwenhoek, we find him showing salts of various forms, growing up in solutions under his microscopes. About this time too Guglielmini in his treatise on these bodies, De Salibus Dissertatio Epistolaris (1707), tried to prove that they could all be divided into molecules of a few regular forms, and affirms as a consequence that the inclination of the planes and angles is always constant. Ata somewhat earlier period the celebrated Robert Boyle had published a treatise on precious stones, in which he describes many properties of crystals and their peculiar forms which he compares to those of salts. He also pointed out the crystallization of bismuth from fusion by heat—a fact often overlooked by later observers.

The attention of men of science was now thoroughly directed to the forms and origin of these bodies, and many curious observations might be collected from the writings of De la Hire, Woodward, Cappeller, Henckel, and others. But we pass on to Linnaeus, whose Systema Naturae formed, in this as in other departments of natural science, the commencement of a new period in its history. In his first edition in 1736 he gave a classification which, as he says himself, though far from perfect and often blamed, had enabled others mounted on his shoulders to see wider. Some of these successors he enumerates in the twelfth edition of his System (1768)—among them Wallerius, Swab, and Cronstedt. He admits in the preface that he had laid aside the study of stones in which he once delighted, and therefore could not boast of his knowledge of lithology. Lithologia mihi cristas non eriget, lapides en im quos quondam in deliciis habui, tradita demum aliis disciplina, seposui, are his characteristic words Still there is much that was important in his work. Thus he distinguishes figured stones from those that are amorphous, and notes the difference of the tessellata or cubical from the prisma or long columnar and the pyramis or pointed forms. Then he figures rudely, it may be, and describes some forty common forms of crystals, and gives examples of minerals in which they occur. His table of “Affinitates crystallorum!' is even more suggestive, and could scarcely fail, if followed out, to lead to further advances. The use he made of these forms as important characters in describing and classifying minerals was well calculated to promote their study. Even the fact that he cut out models in wood of the forms he saw, shows in what a truly practical manner he regarded the subject. His notions regarding the formation of crystals were, however, very imperfect. Salt, he affirms, is the only known natural cause of crystallization, and consequently the forms of the crystals of other substances were determined by the salts in union with them. This is the more remarkable, as he refers to an anonymous author in his own country, to whom he applies the words of Isaac, vox Swabii, manus Cronstedti, as refuting this theory from the fact that crystals of metals were produced by fusion.

The advanced character of these views of Linnaeus appears more strongly when we contrast them with those of his great rival Buffon. According to him crystals are only a result of organization, so that the prisms of rock crystal, the rhombs of calcspar, the cubes of sea salt, the needles of nitre, and others are produced by the motions of organic molecules, and specially of those derived from the remains of animals and plants found in calcareous masses, and in the layer of vegetable earth covering the surface of the globe. Hence he takes no note of crystallization among the characters of minerals. Very different was the influence of Linnaeus on Romé Delisle (born 1736, died 1790), whose Essai de Cristallographie appeared first in 1772, and in an enlarged form in 1783. Working· in the spirit of his master, he formed a large collection of mineral crystals which he examined with great care, comparing the forms of the faces and measuring the angles. In doing this he soon found that the same mineral assumed various forms,— calcspar, for instance, sometimes that of a six-sided prism, at others of a rhomboid, and fluor-spar in some cases forming cubes, in others octahedrons. In trying to explain this fact, he assumed that in each species there w as a certain original form, generally the most simple he could find, from which all the others might he derived when cut in a particular manner. Thus by cutting off the angles of the cube, it may be converted into an octahedron. Werner in his treatise On the External Character of Minerals had used the terms truncation, bevelling, acumination (Abstumpfung, Zuschärfung, Zuspitzung) for similar changes on the fundamental forms, but Delisle probably had no knowledge of this fact, and in other respects could borrow little from Werner, who in crystallography scarce went beyond Linnaeus. The progress Delisle made in the ten years between his first and second work (Cristallographie ou Description des formes propre à tous les corps du règne minéral, 1783) is truly remarkable. He now affirms in clear and distinct terms “that amidst all the innumerable variations of which the primitive form of a salt or crystal is susceptible, there is one thing that never varies and remains constantly the same in each species,—that is, the angle of incidence, or the respective inclination of the faces to each other.” Hence these angles are truly characteristic of each species, but only of the primitive forms, from which others, which he names secondary, are derived by various modifications. Of these principal primitive forms he assumes six; but these are less skilfully chosen and, as now seen, not always truly distinct. But many defects were compensated for by the great labour he expended on figuring and his superior accuracy in measuring crystals. This he was able to secure by the use of the goniometer recently invented by Carangeau, the new instrument, as it were, transforming the science. Then his observation of twin crystals, or macles, as he named them,—which he showed were characterized by their re-entering angles as made up of two crystals, or two halves of one crystal, in a reversed position,—was also a noteworthy step. How much he accomplished may be judged from the fact that he gives figures of more than 500 regular forms, in place of the forty described by Linnaeus. He had probably carried his system as far as it could go, and not merely familiarized the forms of crystals to mineralogists, but also suggested the possible connections that might exist among them.

Delisle seems to have assigned little value to cleavage, and in his preface speaks contemptuously of the crystal-loclastes {brise-cristaux) as innovators in the science. But even earlier, in 1773, Bergman, the well-known Swedish chemist, had shown its importance, and used this peculiar structure to explain the relations of the different forms of crystals observed in the same mineral. Starting from the rhombohedron of calcspar, he placed it with the chief axis upright, and then building up other similar rhombs on it, formed a six-sided prism with rhombic ends. By stopping at a certain stage, it became a dodecahedron, or body with twelve rhombic faces, which he assumed, not quite accurately, to be the same as that proper to garnet. Again, placing this garnet-form in proper position and adding other rhombs, he showed how it easily changed into another characteristic of the hyacinth (in aliam facile migrat), Whilst by other changes different crystals were produced. But he did not proceed far in the direction thus indicated, and deeper views, with more accurate facts and measurements, were required before this could be done.

These were found in the works of Réné Just Haüy (born 1743, died 1822), who seems to have been led almost by accident to his theory. Curiously it is still the same mineral that with him, as with so many of his predecessors, forms the starting-point. When looking over the cabinet of Citizen Defrance a hexahedral prism of calcspar was accidentally broken from a group to which it belonged, and given him in a present. This crystal showed at the base, where it had been detached, a broken corner with the peculiar brilliant lustre, “poli de la Nature,” of the cleavage faces. Haüy’s attention was arrested by the fact, and he tried to obtain similar faces on other corners, but he only succeeded on the three alternate edges at each end of the prism. Continuing the process further, he found that he could remove slice after slice, till no vestige of the original prism was left, but in place of it a rhomboid perfectly similar to the Iceland spar and lying in the middle of the prism. The fact struck him with surprise, mingled with the hope that it was not isolated, and this, he says, served to “develop my ideas regarding the structure of crystals, and has been, as it were, the key of the theory” (et a été comme la clef de la théorie). Following it out on differently formed crystals of this mineral he found they could all be reduced to a similar internal nucleus. But when the mineral was distinct the nucleus had a different form. Thus in fluor-spar the nucleus was an octahedron; in heavy spar a right prism with rhombic bases; in galena, or sulphate of lead, a cube; and so of other substances. In each also these forms were constant, relative to the entire species, so that its angles were subject to no appreciable variation. Even where crystals cannot be thus mechanically divided, Haüy stated that theory aided by certain indications might serve to discover the primitive form.

On these and other similar facts, Haüy erected his celebrated theory of the structure of crystals. In each mineral there exists what he calls its integrant molecules,—solid bodies incapable of further division and of invariable form, with faces parallel to the natural joints indicated by the mechanical division of the crystals, and with angles and dimensions given by calculation and observation combined. These molecules are marked in different species by distinct and determinate forms, except in a few regular bodies, such as the cube, which do not admit of variations. From these primitive or integrant molecules all the various crystals found in each species are built up according to certain definite laws, and thus the secondary crystals, as he names them, are produced. Of primitive forms only six were known from observation. These were the parallelepiped, the octahedron, the tetrahedron, the regular hexahedral prism, the dodecahedron with equal and similar rhombic faces, and the dodecahedron with triangular faces, consisting of two regular six-sided pyramids joined base to base. In order to produce those secondary crystals which covered over the primitive form, so as to disguise it in so many different ways, he supposed the enveloping matter to be made up of a series of laminae, each decreasing in extent either equally in all directions, or only at certain parts. This decrease takes place by the regular subtraction of one or several ranges of integrant molecules in each successive layer; and theory, determining by calculation the number of these ranges, can represent all the known results of crystallization, and even anticipate discoveries, and indicate hypothetical forms which may one day reward the research of naturalists. He thus claims for his theory that greatest proof of its truth and value which a scientific theory can present,—the power to anticipate observation and to foretell future discoveries. As an example of this process Haüy showed how by applying successive layers of integrant molecules, each less by one row all round, to the faces of the primitive cube, a rhombic dodecahedron was necessarily formed. In other cases he assumed that the decrease was not parallel to the edges, but took the angles as its point of departure, and thus was parallel to a diagonal. In the case above supposed the decrease took place by two ranges in breadth for one in height or thickness, but other less simple ratios might be supposed, as of two in breadth to, three in height, and to these the name mixed decrements were given. There were other possible modes of decrease also distinguished, to which it is needless now to refer. But by these and other modes of procedure Haüy showed how the various secondary crystals could arise from his assumed primitive forms or molecules.

The great advance secured by this theory of Haüy’s was the firm establishment of the idea that the forms of crystals were not irregular or capricious, but definite and based on fixed and ascertainable laws. Hence he showed that, whilst certain secondary forms may be deduced from a given nucleus, there are other forms that cannot occur. Further he pointed out what he named “the law of symmetry,” in consequence of which, when any change of a crystal form took place by its combination with other forms, all similar parts—angles, edges, faces—were modified in the same way at the same time. AU these changes too, he said, could be indicated by rational coefficients or commensurable numbers.

A not less important principle, which Haüy endeavoured to establish, was the intimate relation of the crystalline form to the chemical composition of minerals, so that even prior to analysis the real diversity of species formerly conjoined might be inferred from differences in the angles. As an example of this may be mentioned his discovery of the difference of the angles in crystals classed together as “heavy spar,” a difference only explained when Vauquelin showed that those with the larger angle from Sicily contained the new earth strontia, discovered by Klaproth, instead of the baryta found in those from Derbyshire. The modifications which this view has had to undergo from wider observations will be noticed afterwards, but even its enunciation by Haüy formed a great stimulus to research both as to the forms and the composition of minerals. Taken in connection with the perspicuous and elegant style of his work, its clear arrangement and full illustration by figures, its influence on the progress of the science may be readily understood....