The history of the progress of discovery in the Natural Sciences, records innumerable instances, where the different ways of considering the same subject have created apparent contradictions, which have subsequently been reconciled by more accurate examination. The first observation of facts is very often far from being accurate; and, in most cases, this inaccuracy cannot be corrected, till the science itself has attained a higher degree of perfection. The optical and crystallographic inquiries into the nature of mineral substances, refer equally to the regular forms which these bodies present. The object of Crystallography is to ascertain this regular form from direct observations; and that of the department of Optics, which relates to this subject, is to determine the action of regularly crystallised bodies upon light. According to certain general laws, it has been found possible to argue from the optical phenomena to the external forms of minerals, and inversely from these forms to the actions dependent upon them, which affect light in its passage through crystallised substances.