Confirmation of the Distinction of Systems by the Optical Properties of Minerals.—Brewster.—I must not omit to notice the striking confirmation which the distinction of systems of crystallization received from optical discoveries, especially those of Sir D. Brewster. Of the [332] history of this very rich and beautiful department of science, we have already given some account, in speaking of [Optics]. The first facts which were noticed, those relating to double refraction, belonged exclusively to crystals of the rhombohedral system. The splendid phenomena of the rings and lemniscates produced by dipolarizing crystals, were afterwards discovered; and these were, in 1817, classified by Sir David Brewster, according to the crystalline forms to which they belong. This classification, on comparison with the distinction of Systems of Crystallization, resolved itself into a necessary relation of mathematical symmetry: all crystals of the pyramidal and rhombohedral systems, which from their geometrical character have a single axis of symmetry, are also optically uniaxal, and produce by dipolarization circular rings; while the prismatic system, which has no such single axis, but three unequal axes of symmetry, is optically biaxal, gives lemniscates by dipolarized light, and according to Fresnel’s theory, has three rectangular axes of unequal elasticity.
[2nd Ed.] [I have placed Sir David Brewster’s arrangement of crystalline forms in this chapter, as an event belonging to the confirmation of the distinctions of forms introduced by Weiss and Mohs; because that arrangement was established, not on crystallographical, but on optical grounds. But Sir David Brewster’s optical discovery was a much greater step in science than the systems of the two German crystallographers; and even in respect to the crystallographical principle, Sir D. Brewster had an independent share in the discovery. He divided crystalline forms into three classes, enumerating the Hauïan “primitive forms” which belonged to each; and as he found some exceptions to this classification, (such as idocrase, &c.,) he ventured to pronounce that in those substances the received primitive forms were probably erroneous; a judgment which was soon confirmed by a closer crystallographical scrutiny. He also showed his perception of the mineralogical importance of his discovery by publishing it, not only in the Phil. Trans. (1818), but also in the Transactions of the Wernerian Society of Natural History. In a second paper inserted in this later series, read in 1820, he further notices Mohs’s System of Crystallography, which had then recently appeared, and points out its agreement with his own.
Another reason why I do not make his great optical discovery a cardinal point in the history of crystallography is, that as a crystallographical system it is incomplete. Although we are thus led to distinguish the tessular and the prismatic systems (using Mohs’s terms) [333] from the rhombohedral and the square prismatic, we are not led to distinguish the latter two from each other; inasmuch as they have no optical difference of character. But this distinction is quite essential in crystallography; for these two systems have faces formed by laws as different as those of the other two systems.
Moreover, Weiss and Mohs not only divided crystalline forms into certain classes, but showed that by doing this, the derivation of all the existing forms from the fundamental ones assumed a new aspect of simplicity and generality; and this was the essential part of what they did.
On the other hand, I do not think it is too much to say as I have elsewhere said[35] that “Sir D. Brewster’s optical experiments must have led to a classification of crystals into the above systems, or something nearly equivalent, even if crystals had not been so arranged by attention to their forms.”]
[35] Philosophy of the Inductive Sciences, B. viii. C. iii. Art. 3.
Many other most curious trains of research have confirmed the general truth, that the degree and kind of geometrical symmetry corresponds exactly with the symmetry of the optical properties. As an instance of this, eminently striking for its singularity, we may notice the discovery of Sir John Herschel, that the plagihedral crystallization of quartz, by which it exhibits faces twisted to the right or the left, is accompanied by right-handed or left-handed circular polarization respectively. No one acquainted with the subject can now doubt, that the correspondence of geometrical and optical symmetry is of the most complete and fundamental kind.
[2nd Ed.] [Our knowledge with respect to the positions of the optical axes of the oblique prismatic crystals is still imperfect. It appears to be ascertained that, in singly oblique crystals, one of the axes of optical elasticity coincides with the rectangular crystallographic axis. In doubly oblique crystals, one of the axes of optical elasticity is, in many cases, coincident with the axis of a principal zone. I believe no more determinate laws have been discovered.]
Thus the highest generalization at which mathematical crystallographers have yet arrived, may be considered as fully established; and the science of Crystallography, in the condition in which these place it, is fit to be employed as one of the members of Mineralogy, and thus to fill its appropriate place and office.
~Additional material in the [3rd edition].~ [334]