Hermann Kopp (Einleitung in die Krystallographie, Braunschweig. 1849) has given the description and measurement of the angles of a large number of laboratory crystals.
Rammelsberg (Krystallographische Chemie, Berlin, 1855) has collected an account of the systems, simple forms and angles of all the laboratory crystals of which he could obtain descriptions.
Schabus of Vienna (Bestimmung der Krystallgestalten in Chemischen Laboratorien erzeugten Producte, Wien, 1855; a successful Prize Essay) has given a description, accompanied by measurements, of 90 crystalline species from his own observations.
To these attempts made in other countries to simplify and improve crystallography, I may add a remarkable Essay very recently made here by Mr. Brooke, and suggested to him by his exact and familiar knowledge of Mineralogy. It is to this effect. All the crystalline forms of any given mineral species are derived from the primitive form of that species; and the degree of symmetry, and the parameters, of this form determine the angles of all derivative forms. But how is this primitive form selected and its parameters determined? The selection of the kind of the primitive form depends upon the degree of symmetry which appears in all the derivative forms; according to which they belong to the rhombohedral, prismatic, square pyramidal, or some other system: and this determination is commonly clear. But the parameters, or the angles, of the primitive form, are commonly determined by the cleavage of the mineral. Is this a sufficient and necessary ground of such determination? May not a simplification be effected, in some cases, by taking some other parameters? by taking a primitive form which belongs to the proper system, but which has some other angles than those given by cleavage? Mr. Brooke has tried whether, for instance, crystals of the rhombohedral system may not be referred with advantage to primitive rhombohedrons which have, in all [629] the species, nearly the same angles. The advantage to be obtained by such a change would be the simplification of the laws of derivation in the derivative forms: and therefore we have to ask, whether the indices of derivation are smaller numbers in this way or with the hitherto accepted fundamental angles. It appears to me, from the examples given, that the advantage of simplicity in the indices is on the side of the old system: but whether this be so or not, it was a great benefit to crystallography to have the two methods compared. Mr. Brooke’s Essay is a Memoir presented to the Royal Society in 1856.
2. Optical Properties of Minerals.
The Handbuch der Optik, von F. W. G. Radicke, Berlin, 1839, contains a chapter on the optical properties of crystals. The author’s chief authority is Sir D. Brewster, as might be expected.
M. Haidinger has devoted much attention to experiments on the pleochroism of minerals. He has invented an instrument which makes the dichroism of minerals more evident by exhibiting the two colors side by side.
The pleochroism of minerals, and especially the remarkable clouds that in the cases of Iolite, Andalusite, Augite, Epidote, and Axinite, border the positions of either optical axis, have been most successfully imitated by M. de Senarmont by means of artificial crystallizations. (Ann. de Chim. 3 Ser. xli. p. 319.)
M. Pasteur has found that Racemic Acid consists of two different acids, having the same density and composition. The salts of these acids, with bases of Ammonia and of Potassa, are hemihedral, the hemihedral faces which occur in the one being wanting in the other. The acids of these different crystals have circular polarization of opposite kinds. (Ann. de Chim. 3 Ser. xxviii. 56, 99.) This discovery was marked by the assignation of the Rumford Medal to M. Pasteur in 1856.
M. Marbach has discovered that crystals of chlorate of soda, which apparently belongs to the cubic or tessular system, exhibit hemihedral faces of a peculiar character; and that the crystals have circular polarization of opposite kinds in accordance with the differences of the plagihedral faces. (Poggendorf’s Annalen, xci. 482.)