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In our 62d volume, O.S. (p.55), when examining a distinct treatise of Romé de l'Isle on the exterior character of minerals,' we noticed the different classifications, and particularly adverted, as the work led us, to the form of crystals, as a constant unchangeable character. We resumed the subject in our review of Daubenton's Tableau de Minéralogie,, and have since noticed it in every work where it has occurred. Unfortunately, the form of the crystals has been little attended to by any English author ; and even Mr. Kirwan, in his last edition, though he has adopted the language and much of the precision of the school of Werner, has not noticed the form and the angles of crystals, and has even spoken of crystallography with contempt. It has been observed, and the remark has been often repeated in this journal, that the two contending classes of mineralogists—those who depend chiefly on external charac: ters as the means of distinguishing minerals, and those who think that the distinctions must be drawn from chemical analysisshould naturally yield to each other, and unite their powers. We particularly pointed out this union in our review of M. Daubenton's Table, where the advantages of the union were particularly conspicuous; and we now find our ideas coincide with those of M. Hauy, the chief supporter of the system of crystallisatio:, the most striking of the external forms. To chemistry, he observes, must belong the determination of species. It may be more proper to say that it completes this determination, in showing us the “principal molecules," of which the “integrant molecules,” the crystals, are assemblages. We can als ready perceive, and we shall in future find many examples of this truth, how important it is that the inquiries respecting these two kinds of molecules should be directed to one common object, that the chemist and mineralogist should mutually assist each other; and that the goniometer, which furnishes the data requisite to the calculation of crystalline forms, should be joined with the balance which weighs the product of the analysis.'
In this system, M. Hauy follows that of the chemical minesalogist; but the varieties are distinguished by the crystalline form, which in our author's hands is a science almost wholly new; and we believe he is right in asserting, that no varieties have been determined by the crystallographer which analysis has not confirmed.
an early work of Werner; and that the German mineralogist has extended his Janguage with the enlargement of the science, in consequence of new discoveries. Only the first volume of M. Brochant's work has yet appeared, and it contains the 'carths and stones,' though an appendix to these will be added. He speaks as if the other classes were to be comprised in another volume; but this is iinpracticable,
"The theory employed to develop these laws (viz. of crystallisation) rests on a fact which has been hitherto supposed rather than demonstrated. It consists in this, that the minute solids which are the elements of crystals, and which I call the integrant molecules, have, in every individual belonging to the same species, an invariable form; the planes of which are, in the direction of the natural joints, pointed out by the mechanical division of these crystals, whose respective angles and dimensions are ascertained by calculation joined with observation. Added to this, the integrant molecules relative to different species are more or less pointedly different, except in a very few cases, where the forms have regular characters, and constitute the connexion between different species. The determination therefore of integral molecules has a considerable influence on that of species; and this consideration has often conducted me, either in subdividing into many species a group which in the common methods created one alone, or in uniting the scattered limbs of a single species, of which many distinct ones had been made.'
dimensionsded to this, the less pointed regular ch
• The result of my labours, supposing them to be as complete as possible, can only be regarded as an introduction to the study of nature. The different substances of which this globe consists, placed in their respective positions by the concurrence of the causes, whose actions the Supreme Being has direcied to the end which seemed most suitable to his wisdom, offer a spectacle wholly new, even to the eye most experienced in viewing minerals brought from their native beds to our cabinets. Here we behold them arranged and disposed in a systematic order ; but nature, on every side despising the artificial limits traced by our systems, separates what we have united, and confounds what we have chosen to separate. On one side she disjoins, by striking contrasts, substances which touch and adhere to each other; on the other, she manages those progressive changes from one substance to another, those successions of shades, which say to an attentive and enlightened observer, Here we no longer belong either to this fossil or that.'
M. Hauy next explains his own plan of arrangement, and the circumstances which influence him in forming his genera from species and varieties. We own that we wished to have enlarged on ti.is subject; to have shown that Buffon had in this place committed a fundamental error in his celebrated canon -- that science formed species; and that Werner's mes thod was equally erroneous. The method of determining species, the most important part of classification, employed by botanists and zoologists, cannot here be practised ; and the philosopher must, in part, be directed by his own opinions,
perhaps by his fancy. M. Hauy's system is the least exceptionable of any. He adopts, as we have said, in his more extensive arrangements, the chemical analysis ; but, in species, the more constant and obvious characters, particularly the form of the crystals : yet, as this is the most distinguished part of the present work, it is necessary to enlarge farther on it, especially--we speak it with regret-as this part of mineralogy has been too much neglected by English mineralogists.
Minerals have nothing constant in their external aspect; and, to recognise species concealed under an uncommon form, much ingenuity is often required. M. Hauy's dexterity demands our praise. An accidental observation led him to subdivide the hexaëdral prism of carbonated lime in the direction of his laminæ ; and he discovered a riiomboidal nucleus similar to the bodies called Iceland spar. Other calcareous crystals, examined in the same manner, afforded a 'similar result. From these observations, combined with many others on minerals of very different kinds, he concluded that crystals belonging to the same species contained a nucleus, which was a solid that might be styled the primitive form. On subdividing the different nuclei determined from observation, he ascertained the form of what he calls the ' integrant molecules,' which, in every known mineral, are only three in number, and of peculiar simplicity; viz. the regular tetraëdon, the triangular-prism, and the parallelopiped. In studying the progressive structure of what may be called the secondary forms, he conceived that they might result from a superposition of laminæ, which, departing from the primitive structure, might decrease by a regular subtraction of one or more ranks of integrant molecules. This departure may sometimes take place from the sides of the nucleus, and sometimes from its angles. To these subtractions he gives the appellation of laws of decrease ;' and from this point begins a series of rigorous geometrical calculation, which we cannot abridge. This calculation conducts him to a precise determination of the angles, planes, and solids, of the secondary forms; and the constant agreement between the angles, - produced by calculation and by observation, is the best demon
stration of the truth of the laws. A general formula thus becomes, in the hands of the author, an instrument, by means of which, without any difficulty, with the assistance of some undoubted facts, he determines not only the forms hitherto known, but all those which can occur, and of which many certainly exist in nature ; thus anticipating future discoveries. His inquiries into the nature of crystals have conducted him to this general principle,-- that all those which belong to the same species are composed of similar integrant molecules, the form and dimensions of which are determined by observation, assisted by.calculation. From the consideration of these molecules, he has reduced to the same species bodies arranged in molecules widely different, and separated those formerly associated without sufficient foundation. In all these instances, as we have already remarked--to adopt his own words-chemical analysis has supported the arrangement of the crystallographer.
Romé de l'Isle, whose work is spoken of by our author with great respect,--and which in truth contains a vast treasure of mineralogical information,-established his species from the forms combined with concomitant hardness and specific gravity; but he stopped at the surface, instead of penetrating the interior mechanism of the structure. He suspected that there were primitive forms, but he did not always ascertain them with accuracy : they are chosen indiscriminately; and many are very distant from the true ones, ascertained by mechanical division. He was embarrassed also in the application of his principle to the secondary forms, which retain no resemblance of the adopted primitive; and, in consequence of this difficulty, he sometimes admits two different primitive forms in each species. On the contrary, by the assistance of our author's theory, we may be certain of disco- ering whether any given form can exist among the varieties of a particular species, or whether it should be excluded from it. What is of more consequence, this naturalist, instead of stopping at the primitive forms themselves, afforded by mechanical division, which are the only data proper to facilitate the applications of his theory, has taken, for the foundation of his species, the elements of the crystallisation; that is, the integrant molecules resulting from the subdivision of the primitive forms, and which often differ from them. It was calculation only-a mean which De l'Isle has not employed-that could establish the specific differences between the molecules of the same genus : such are those between the equilateral triangular prism, and the prism with square bases, in determining the particular relation which exists in each species between the dimensions of the prism that nature employs in the production of crystals which belong to this species.
About the time when M. Hauy published his first essays on the structure of minerals, the Academy of Sciences received a memoir from M. Bergman, in which he proposed the reduction of all the figures of calcareous spar to the primitive rhomboid. He had remarked the position of the nucleus in the dodecaedron with scalene triangular faces, of the variety styled the ' hog's-toothed spar. He considered it as produced by the superposition of planes, which decreased around the primitive rhomboid, in separating from the lateral angles. He even verified this explanation by fracture, which is wholly conformable to nature ; but he stopped short at this first view, and did not think of determining, by the help of calculation,
either the laws of decrease, or the form of the integrant molecules. With respect to the secondary figures, he indulged some hypothetical conjectures, scarcely supported by observation-a remarkable example of the failure of the most acute genius, when not assisted by more rigorous methods of inquiry. By founding crystallography on calculation, M. Hauy has created a science which no fashion can destroy: it rests on a foundation as certain as the Newtonian system of the world ; and has contributed to fill many vacuities in the series, which were apparently wanting in former systems. The reader will find that the author's theory is simple in its method, certain in its principles --resting on facts afforded by undoubted observation and unequivocal evidence. It reposes on this—the existence of a primitive form, the faces of which coincide with the natural joints of crystals; and the whole is supported so far by the nature of every known mineral. It is indeed so well founded and supported, that it has often anticipated analysis, and has been supported in turn by chemical investigation. In this work the system is explained in two ways; viz. by reasoning, assisted by figures, which illustrate the progress of the decrease ; 2dly, by analysis, which supposes only a common acquaintance with geometry. Some new geometrical properties are interspersed, which would, independent of mineralogy, interest the geometer.
The species in this work are determined by characters, the most constant and the most unexceptionable, as they are con. nected with the constitution of the integrant molecule. They are of three kinds, viz. physical, geometrical, and chemical. Among the former are, the specific gravity ascertained by Mr. Nicholson's hydrometer, at 14° of Reaumur; hardness, ascertained by the property of scratching a given body; refraction of light, showing objects single or double; electricity, acquired by heat or rubbing ; and phosphorescence, either in consequence of rubbing, or the projection of its powder on hot coals. The geometrical characters are those afforded by a mechanical divisjon, joined to a measure of the angles, which together form the natural joints. The chemical characters are those ascertained by the most simple and easy experiments, with the blow. pipe, acids, or alkalis. **After describing each species in all these views, it is subdivided into varieties, of which some relate to the forms, either regular or undeterminable ; others to the accidents of light,' that is, to the colours and transparency. Each regular form is first represented by a sign composed of letters and ciphers, which show the laws of decrease,' on which the form depends; and next by a figure in projection, which is in some measure a portrait. Each species is also characterised by pointing out the principal angles, in which its relation to the other