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GENERAL GEOMETRICAL PROPERTIES OF CRTSTALS. 9 parameters may be found; and, among the remaining crystals Mith rectangular axes, some which have two of the parameters equal. Upon the differences in the positions of the axes with respect to each other, and in the relation between the para meters, above enumerated, is founded the arrangement of crystals in systems. In the cubic system the axes are rectangular and the parameters equal. 2. In the pyramidal system the axes are rectangular and two ot the parameters equal. In this system we shall always suppose a and b equal. 3. In the rhombohedral system the axes malce equal angles ■with each other, and the parameters are equal. 4. In the prismatic system the axes are rectangular. 5. In the oblique system one axis is perpendicular to each of ,. ie other two. We shall always suppose the axis ot perpen dicular to each of the axes oz and ox. ; 8- The anorthic system includes all crystals which cannot be erred 1° an y of the preceding systems. 29. The different systems of crystallization are further dis- inguished by the various kinds of symmetry observable in the istribution of the faces of the crystals belonging to them. or ’ o a mce occur having the symbol Itkl, it will generally be accompanied by the faces having for their symbols certain arrangements ot ± h, ± Jc, ± /, determined by laws peculiar to each system, and which will be fully explained when we come to describe each system separately. ,30. A ‘form’ in crystallography is the figure bounded by a given face and the faces which, by the laws of symmetry of the system of crystallization, are required to coexist with it. A ™ be denoted by the symbol of any one of its faces. The ‘holohedral forms’ of any system are those which pos sess the highest degree of symmetry of which the system ad- mits. ‘ Hemihcdral forms’ are those which may lie derived jrom a holohedral form by supposing half of the faces of the latter omitted according to a certain law. The figure bounded by the faces of any number of forms is called a ‘combination’ of those forms. 31. The elements of a crystal are the inclinations of the axes toz zox, xoy, and the ratios of two of the parameters a, b, c, o the third. In the cubic system, where the axes are rectan gular and parameters equal, all the elements are determined. 'r Pe ram ' ( !al system, where the axes are rectangular and wo ot the parameters are equal, the ratio of either of them to the rmrd is the only variable element. In the rhombohedral system, nere the axes make equal angles with each other and the para meters arc equal, the angle between any two of the axes is the 13 5
