CRYSTALLOGRAPHY 673 master, he formed a large collection of mineral crystals vliich he examined with great care, comparing the forms of the faces and measuring the angles. In doing this lie 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 form ing cubes, in others octahedrons. In trying to explain this fact, he assumed that in each species there was a certain original form, generally the most simple he could find, from which all the others might be derived when cut in a parti cular 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 , Zuschdrfung, 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 AYerner, 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 h tous les corps du regne mineral, 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 measure ments, were required before this could be done. These were found in the works of Re ne Just Haiiy (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. Haiiy 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 per fectly 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 ete comme la clef de la theorie). 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, Haiiy stated that theory aided by certain indica tions might serve to discover the primitive form. On these and other similar facts, Haiiy erected his cele- Haiiy s brated theory of the structure of crystals. In each mineral theory of there exists what he calls its integrant molecules, solid structure of bodies incapable of further division and of invariable form, cr y stal s - 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 parallelopiped, the octahedron, the tetrahedron, the regular hexahedral prism, the dodecahedron with equal and similar rhombic faces, and the dodecahedron with triangular faces, consist- ing 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 bo 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 crys tallization, and even anticipate discoveries, and indicate hypothetical forms which may one day reward tLe 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 Haiiy 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
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