MINERALOGY aggregating themselves in lines of minute crystals of the very shape of which they were projecting the skeleton form. More over, a polar aggregation at the terminal ends of these octahedral axes is here shown by the amount of concreting and crystallizing Fig. 20. material being larger at the terminations of these axes than else where. In the hollow-faced cube again (fig. 21), an aggregation of molecules in the direction of the lines D and C has tilled the edges and solid angles, while none have been deposited along 0. Fig. 21. Fig. 22. This occurs in crystals of salt. In the hollow-faced octahedron, again (fig. 22), there has been no deposition of matter along the line C. Cuprite often shows this form; and it as frequently occurs in hollow-faced dodecahedra, wherein the vacuity is in the direc tion of D. In the specimen of pyrite from Elba (fig. 23), a deposition along I) and C would ultimately have erected the scaffolding of a hollow cube, in twelve lines of minute combinations of the cube and octahedron. Such directional arrangements may, moreover, not only be intermittent but often alternate. The pyrite from Traversella (fig. 24) is an illustration of the first. A large pentagonal dodecahedron hav ing been completed, a new ac cession of material has been attached, not uniformly spread over the pre-existent crystal, to enlarge it, but locally ar ranged, in equal amount, at the poles of O. But here the special method of the arrangement has determined the formation of a number of small crystals of the same form as that originally projected. An alternation, as it were, in plan is shown in such a crystal of calcite as that in fig. 25. Here a scalenohedron is seen in the centre of the figure ; then a rhombohedron has been perched upon its summit, and lastly both have been sheathed in a six-sided prism with trihedral summits. Different as these three forms are, it is found that they all here stand in a definite position one to the other; that definite position is the relation which they bear to one of the sets of axes, and this set may be assigned, not only to all the three crystals here combined, but also to all the crystals be longing to the same mineral, wherever occurring. This general applicability constitutes one of the respects in which one special set of axes is, in each of the systems, preferred to the others. Fig. 24. Fig. 25. Another respect is the intensity with which the molecules cohere Coher- in the different parts of the crystal, as referred to these axes, and ence of the resultant different hardness of certain parts of crystals. It particles will be afterwards found that this obtains in a very limited uc-tequal manner in the crystals which belong to the first of the follow- j n a n di- ing systems, on account of its regularity and sameness as a whole. rec tioiis It may be laid down as a general rule that the edges of crystals are harder than the centres of their faces, and the solid angles harder than the edges. This is markedly the case in the diamond. But, apart from this, there is no distinctive hardness in any one part, side, or end of the crystals of the first system. It is otherwise with the crystals which fall to be considered in all the other systems. So different is the hardness of the various portions of these, so diverse the appearance of their parts in lustre, colour, polish, &c., so varying the amount of the recoil of these when struck, so unequal their power of conducting heat, so dissimilar their power of re sisting the agencies of decay, and so irreconcilable their action upon transmitted light, that we cannot but conclude that the molecules which build them up are packed with greater force, if not in greater number, in certain directions in preference to others. There thus remains no question that these nature-indicated sets of axes are those along which there has been a specially selective or " polar" arrangement. The six systems are founded upon the relationships of Systems of the axes in number, in length, and in angular inclination, crystals. All crystals may be divided into " orthometric " or erect forms and " clinometric " or inclined forms ; and in similar manner may the systems be, through a consideration of the relative lengths of their axes, divided into three classes. In the first, or most regular, of these the axes are all equal, that is, they are of one length ; in the second there is one axis which differs in length from the others, and therefore they are of two lengths ; while in the third the axes are all unequal, and therefore they are of three lengths. Of the six systems one belongs to the first class, two to the second, and three to the third. Hence they are thus classed : Monometric. Cubic. Diinctric. Tetragonal. Hexagonal. Tr {metric. Right Prismatic. Oblique Prismatic. Anorthic. Though the grouping of the systems into three classes in virtue of axial dimensions is markedly borne out by optical and other properties, yet it is altogether insufficient for determining the relationships of the myriad forms in which bodies crystallize. Such knowledge is only attained by combining the consideration of axial length with axial inclination ; and it is through a due regard of both of these that the six systems are instituted. The above table may be read in two different ways, either across or consecutively up and down the page.
The six systems may be treated of in either of these ways;