374 MINERALOGY Axes of right angles to one another called the axes of optical optical elasticity such that the effect of the crystal on the Jtf?^" luminous vibrations of the elastic ether is a maximum in one of these directions, a minimum in a second, and a maximum-minimum in the third. The length of these axes is chosen in terms of this action. In certain cases the direction of the axes of optical elasticity is different for light of different colours. The position of these axes in relation to the crystallographic axes, and the ratios of their lengths, enable us to class all crystals as follows: 1. Crystals of the cubic system. Here the three axes of elasticity are all equal. The retraction is simple. 2. Crystals of the tetragonal and of the rhombohedral systems. Two of the axes of optical elasticity are equal in these systems ; the third is greater or less according as the crystals are negative or positive. The two equal axes lie in a plane perpendicular to the principal crystallographic axes ; the third axis coincides with the principal axis. 3. Crystals of the right prismatic system. The direction of the three axes of optical elasticity coincides with the crystallographic axes, taken parallel to the diagonals of the base of the rhombo- hedron, and to the vertical edge of the prism (the primitive parallel epiped of Levy). 4. Crystals of the oblique prismatic system. Only one of the axes of optical elasticity coincides necessarily with the crystallo- graphical horizontal axis, or the diagonally horizontal axis of the rhombic base, the direction of the two others not having any- evident relation, a priori, with the inclined or diagonally inclined axis of the base, and with the vertical axis (or vertical edge of the primitive parallelepiped). 5. Crystals of the anorthic system. The three axes of optical elasticity have no relation that can be assigned a priori to the crystallographic axes, whatever position may be assigned to these in relation to the primitive solid. In crystals belonging to the last three systems the three axes of elasticity are unequal. The axes of elasticity are in general such that a ray passing through the crystal in the direction of any one of them is divided into two, which follow that direction with different velocities depending on the lengths of the other two axes. To any other direction there will in general also correspond two different velocities ; but their ratio will now depend in a more complex manner on all three axes. In two directions (and only in two, if the axes are all unequal) the ratio becomes unity, or the ray is not divided. These directions are the optic axes. The displacement of the axes of elasticity for light of different colours, already mentioned, takes place for two axes in crystals of the oblique prismatic system and for all three axes in the anorthic (i.e., doubly oblique) system. In the other systems it does not occur. Colour In order to follow the distinctive features of the different systems pheno- farther, it is necessary to consider the colour phenomena which mena. they display, when examined in a beam of polarized light. Vari ous instruments have been devised for this purpose, as, e.g., the polarizing apparatus of Norrenberg, fitted with a condensing lens below and above the crystal slice, or with a low- power (3-inch) eye-piece. The polariscope of Hoff man of Paris is more efficient, but the appa ratus of Descloizeaux (fig. 240), who has made this mode of investiga tion a special study, lias the widest scope of use fulness. In this appa ratus a blackened mirror is employed for polariz ing the light, taking the place of a tourmaline plate, a Nicol s prism, or a bundle of thin glass. Fj(J _ 2 40.-Apparatus of Descloizeaux. 1 he mirror is interior to the other two in completeness of polarizing power, and in not admitting of rotation ; while it shares this defect with the last. It is, however, superior to all in extent of field, while it does not, like the first, affect white light. A Nicol s prism is used for examining or analysing the light which passes. The description of the many beautiful phenomena that may be observed with pciarizing apparatus when applied to sections of crystak belongs to the subject of OPTICS (PHYSICAL), to which heading also we must refer for the phenomena of circular polarization. Double Refraction and Polarization of Composite Crystals. In Optic all the crystallized bodies whose action upon light we have been proper- considering, the phenomena are identical in all parallel directions, ties of the smallest fragment having the same property as the largest, composite from whatever part of the crystal it is taken. In the mineral crystals. world, however (and among the products of artificial crystalliza tion), there occur crystals which are composed of several individual crystals whose axes are not parallel. These crystals sometimes occur in such regular symmetrical forms that mineralogists have long regarded them as simple forms ; and it is probable that they would have still been so viewed if they had not been exposed to the scrutiny of polarized light. A composite structure has been ob served in the case of Brazilian topaz, sulphate of potash, and apophyllite. Bipyramidal sulphate of potash, which Count Bournon supposed to be a simple crystal, was found to be a tesselated crystal, composed of three pairs of crystals of the prismatic sulphate of potash com bined so that each pair had their principal axes parallel. When exposed to polarized light, each pair gave the system of binaxal rings, and when held at a distance from the eye had the tesselated appearance shown in opposite pair of the triangles having the same tint. The most remarkable of this class of minerals is the tesselated apophyllite. The examination of this body by polarized light is due to Brewster. For his results the reader is referred to his paper in the Edinburgh Transactions, vol. ix. p. 323. Figs. 242, 243 are representations of the figure produced in polarized light by an internal slice of the barrel or cylindrical I) 243. Fig. 242. apophyllite from Kudlisaet, in Disco Island. The figures are from different specimens. The shaded part of them has only one axis of double refraction, while the four sectors have two axes. The mechanical structure of the cleav age planes resembles the optical figure even after the planes are ground. The minerals stilbite, heulan- dite, chabasite, and many others, are similarly complex in struc ture. Crystals with Planes of Double Refraction. Analcime, a mineral ranked among the cubical crys tals, was found by Brewster to be singular in its action upon light, and to exhibit the extraordinary property .of many planes of double refraction, or planes to which the double-refracting structure was related in the same manner as it is to one or two axes in other minerals. It crystallizes most com monly in the form of the icositetrahedron. If we suppose a com plete crystal of it to be exposed to polarized light, it will give the remarkable figure shown in fig. 244, where the dark shaded lines represent planes in which there is neither double refraction nor polarization, the double refraction and the tints commencing at these planes, and reaching their maximum in the centre of the space enclosed by three of the dark lines. When light is trans mitted through any pair of the four planes which are adjacent to any of the three axes of the solid, it is doubly refracted, the least refracted image being the extraordinary one, and consequently the double refraction nega tive in relation to the axes to which the doubly-refracted ray is perpendicular, If we suppose the crystal to have the form of a
Fig. 244.