CKYSTALLOGKAPHY 6rr * tD doubt that "Weiss preceded him in promulgating these new views, but also show that Mohs wrought them out in a more systematic form, and made them more generally known. In 1820 he published his Charakteristik des naturhistorischen Mineralsystem.es, followed in 1822 by his Grundriss der Mineralogie. Both these treatises were translated into English, the second by the well-known Haidinger, then residing in Edinburgh. The clearness and precision with which he marked out and defined the various terms and new ideas required, and followed out the laws regulating combinations, had a great effect in giving a wider currency to his writings. The thorough mode in which he traced out the series of forms in the systems and explained these also added to their popularity. Professor Jameson too gave it a higher authority and wider accept ance, describing it "as eminently distinguished by its originality and simplicity." Its success was further promoted by the remarkable discovery made about the
- r. same time by Sir David (then Dr) Brewster. In connection
with his observations on the polarization of light, this dis- tinguished optician had endeavoured to point out the con nection between Haiiy s nuclei or primitive forms of crystals and the number of their axes of double refraction, and even shown that Haiiy had in some cases chosen erroneous forms, as they did not agree with their optical characters. The appearance of Mohs s views threw unex pected light on the fact, as his system of crystallography harmonized in a most remarkable manner with the arrange ment proposed on optical grounds. In reality, as now well known, all minerals crystallizing in the regular system of Weiss and Mohs with equal and uniform axes show only single refraction ; those belonging to the two and one axial and three and one axial systems ( f Weiss, the pyramidal and rhombohedral of Mohs, have double refraction with only one optical axis ; whilst those in the three other systems show double refraction and two optical axes. As Whewell has well remarked, " Sir D. Brewster s optical experiments must have led to a classification of crystals into the above systems, or something nearly equivalent, even if the crystals had not been so arranged by attention to their forms." The establishment of this system, whether due to Weiss s. or Mohs, or in part to both, gave to crystallography as a pure science essentially its present form. Taken in connection with the law that the indices marking the relative dimensions of the parameters are always rational numbers, and seldom large, with the symmetry of forms, and the grouping of the faces in zones, we have the leading principles on which it depends. The subsequent progress of the science has been rather directed to working out and completing the structure, and showing the mutual relations of its essential principles, than to modifying the foundations on which it rests. These researches have taken two chief directions, the one explaining the geometrical properties of crystals, and the systems under which in consequence of these properties they necessarily fall to be classed, while the second has regard to the physical properties of crystals, that is, of the various bodies, especially the native minerals, assuming these forms. Before noticing these we must refer to another point in which Haiiy s views were also about the same time remarkably modified and extended. Haiiy, we have seen, maintained that a very close connec- 3m. tion always existed between the crystalline character and the chemical composition of minerals, so that from diversity in the angular measurement of two crystals we might infer a difference in their chemical composition, or the reverse. More accurate analyses soon showed that this law had not that universal application which Haiiy assumed, and even in 1815 Fuchs had pointed out that certain elements were what he named vicarious, so that in compounds a certain amount of one could replace so much of some other. The remarkable theories and researches of Berzelius soon rendered some change in this respect inevitable, and it was carried out by the discovery of isomorphism by his pupil Mitscherlich in 1822. The subject, however, belongs less to crystallography than to chemistry or mineralogy, and we can only mention the general principle. Mitscherlich showed that there are certain substances which crystallize in forms closely resembling each other, and with the corresponding angles only differing by one or two degrees, or even less. Thus the carbonates of iron and manganese, or lime and magnesia, agree nearly in form and dimensions. Such substances were named isomorphous, and were found to have the tendency to replace or be substituted for each other in compound bodies, with very slight modification of the forms or angles of the crystals. Though at first denied by Haiiy and his followers, this truth is now fully established, and has had vast influence in the determination and classification of minerals. As modifying the same conclusion of Haiiy, but in an opposite direction, we must also mention Mitscherlich s further discovery of dimorphism, according to which the same element (as sulphur), or the same compound (as carbonate of lime), when crystallizing under different conditions, especially as regards tempera ture, may assume two distinct forms of crystals belonging even to different systems. Instances are even known of trimorphism and polymorphism, in which the same sub stance may occur in three or more forms of crystalliza tion. The mode of formation of crystals, and the powers that Powers are active in their formation, were, as we have seen, operating favourite subjects of speculation with the earlier writers on j^ ^" crystallography, and are closely connected with the chemical composition of minerals to which we have just referred. This subject continues to attract many inquirers, and has given occasion to some remarkable speculations ; but it can hardly be affirmed that much progress has been made in this direction. Crystals may still be seen, as in the time of Leeuwenhoek, springing out of solutions under the microscope, and continuing to increase in size, but the powers that are active escape our notice, and we are still left almost in the same region of speculation as our predeces sors. Such discussions, in truth, concern ratfier the general constitution of matter than the special corner whose history we have been following, so that the words of Brewster still hold true : " In whatever way crystallographers shall succeed in accounting for the various secondary forms of crystals, they are then only on the threshold of their subject. The real constitution of crystals would be still unknown ; and though the examination of these bodies has been pretty diligently pursued, we can at this moment form no adequate idea of the complex and beautiful organization of these apparently simple bodies." Returning to the more special subject of pure or Crystallo- geometric crystallography, one great object of recent graphic inquiry has been to discover some method of designating the forms or faces of crystals by numbers or symbols, that would at once point out their general relations to each other, and facilitate the calculation of their angles so as to check or control observation. Haiiy had already attempted to do this in his great work, by means of his theory of decrements, but his materials were still too imperfect, and his symbols are often very complex. Still the weight of his name retains great influence in France, where a system founded on his, but modified by the more recent views, prevails. It is generally associated with the name of Armand Le"vy (born 1794, died 1841), who in 1837 published an important work on Mr Heuland s collection (Description dme collection des Minerauxform.ee par M. H.
Heuland) illustrated by numerous plates of crystals. He