The explanation undoubtedly is, that the long interregnum of conflicting investigations, doubt, and controversy, which followed the work of Haüy and Mitscherlich, and preceded the beginning of really accurate and painstaking investigation of an organised and systematic character, had caused chemists to regard with more or less of indifference the work of the crystallographers. Added to this we must remember that the subject of crystallography has hitherto been taught, when taught at all, merely as an appanage of mineralogy, although the pure chemical substances which crystallise well infinitely outnumber the naturally occurring minerals, and the results afforded by them frequently possess a much greater value by reason of the purity of the substances and their more definite chemical constitution. Also the mathematical and geometrical side has usually been unduly emphasised, and carried on in lectures without any practical goniometrical work at all. Moreover, the current text-books have often proved forbiddingly full of calculations and formulæ, and of the obsolete and unenticing symbols of Naumann. At last we have come to see that the subject is one of fascinating interest when its study is commenced in a practical manner from the beginning, armed from the very first lesson with the goniometer. The crystal itself is then our main and highly interesting study; its exterior form unravels itself in a most delightfully simple manner when we follow the arrangement of its faces in zones on the goniometer itself; and its symmetry becomes immediately patent to our eyes in all ordinary simple cases, when we construct for ourselves its plan in a stereographic projection, drawn at first in freehand while still at the goniometer. The calculations also become perfectly simple when we have learnt that only the simplest of the very easy formulæ of spherical trigonometry are required, and which a knowledge of only elementary plane trigonometry enables us to apply. Aided by a few very helpful rules, such as those of Napier for calculating right-angled spherical triangles, and the rule of the anharmonic ratio of four poles in a zone—which, when the positions of three crystal faces of the zone are known, at once enables us to calculate the situation of any fourth face of the zone—we have at once a stock-in-trade which carries us over all difficulties in the way of calculation, and relegates this side of the work to an altogether subordinate position, although accuracy in carrying it out is, of course, absolutely essential and even vital.