Scotland), had been named Strontia. The French chemists had ascertained that the two earths had, in some cases, been mixed or confounded; and Vauquelin, on examining the Sicilian crystals, found that their base was strontia, and not, as in the Derbyshire ones, baryta. The riddle was now read; all the crystals with the larger angle belong to the one, all those with the smaller, to the other, of these two sulphates; and crystallometry was clearly recognized as an authorized test of the difference of substances which nearly resemble each other. Enough has been said, probably, to enable the reader to judge how much each of the two persons, now under review, contributed to crystallography. It would be unwise to compare such contributions to science with the great discoveries of astronomy and chemistry; and we have seen how nearly the predecessors of Romé and Hauy had reached the point of knowledge on which these two crystallographers took their stand. But yet it is impossible not to allow, that in these discoveries, which thus gave form and substance to the science of crystallography, we have a manifestation of no common sagacity and skill. Here, as in other discoveries, were required ideas and facts;-clearness of geometrical conception which could deal with the most complex relations of form; a minute and extensive acquaintance with actual crystals; and the talent and habit of referring these facts to the general ideas. Haüy, in particular, was happily endowed for his task. Without being a great mathematician, he was sufficiently a geometer to solve all the problems which his undertaking demanded; and though the mathematical reasoning might have been made more compendious by one who was more at home in mathematical generalization, probably this could hardly have been done without making the subject less accessible and less attractive to persons moderately disciplined in mathematics. In all his reasonings upon particular cases, Hauy is acute and clear; while his general views appear to be suggested rather by a lively fancy than by a sage inductive spirit: and though he thus misses the character of a great philosopher, the 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 looked upon as a great discoverer, if his fame had not been dimmed by the more brilliant success of his contemporary Найу. Réné-Just Hauy 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 juxta-position 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 vigour 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 4 De Formis Crystallorum. Nov. Act. Reg. Soc. Sc. Ups. 1773. 5 Traité de Minér. 1822, i. 15. 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 fortythree, 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 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 Haüy 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 labours, 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 (calcspar) 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 6 Traité de Minéralogie, 1801, 5 vols, vivacity of style, and felicity and happiness of illustration, which grace his book, and which agree well with the character of an Abbé of the old French monarchy, had a great and useful influence on the progress of the subject. Unfortunately Romé de Lisle and Haüy were not only rivals, but in some measure enemies. The former might naturally feel some vexation at finding himself, in his later years (he died in 1790), thrown into shade by his more brilliant successor. In reference to Haüy's use of cleavage, he speaks of innovators in crystallography, who may properly be called crystalloclasts.' Yet he adopted, in great measure, the same views of the formation of crystals by lamina, which Haüy illustrated by the destructive process at which he thus sneers. His sensitiveness was kept alive by the conduct of the Academy of Sciences, which took no notice of him and his labours ;10 probably because it was led by Buffon, who disliked Linnæus, and might dislike Romé as his followe:; and who, as we have seen, despised crystallography. Haüy revenged himself by rarely mentioning Romé in his works, though it was manifest that his obligations to him were immense; and by recording his errours while he corrected them. More fortunate than his rival, Haüy was, from the first, received with favour and applause. His lectures at Paris were eagerly listened to by persons from all quarters of the world. His views were, in this manner, speedily diffused; and the subject was soon pursued, in various ways, by mathematicians and mineralogists in every country of Europe. 8 Pref., p. xxvii. 9 T. ii. p. 21. 10 Marx, Gesch. d. Kryst. 130. I CHAPTER III. RECEPTION AND CORRECTIONS OF THE HAUÏAN HAVE not hitherto noticed the imperfections of the crystallographic views and methods of Haüy, because my business in the last section was to mark the permanent additions he made to the science. His system did, however, require completion and rectification in various points; and in speaking of the crystallographers of the subsequent time, who may all be considered as the cultivators of the Hauïan doctrines, we must also consider what they did in correcting them. The three main points in which this improvement was needed were;-a better determination of the crystalline forms of the special substances;-a more general and less arbitrary method of considering crystalline forms according to their symmetry; and a detection of more general conditions by which the crystalline angle is regulated. The first of these processes may be considered as the natural sequel of the Hauïan epoch: the other two must be treated as separate steps of discovery. When it appeared that the angle of natural or of cleavage faces could be used to determine the differences of minerals, it became important to measure this angle with accuracy. Haüy's measurements were found very inaccurate by many succeeding crystallographers; Mohs says that they are so generally inaccurate, that no confidence can be placed in them. This was said, of course, according to the more rigorous notions of accuracy to which the establishment of Hauy's system led. Among the persons who principally laboured in ascertaining, with precision, the crystalline angles of minerals, were several Englishmen, especially Wollaston, Phillips, and Brooke. Wollaston, by the invention of |