Now the faces of the crystal parallel to each two of the three sets of parallel lines forming the space-lattice will be the three pairs of axial-plane faces, and any fourth face inclined to them must be got by removing parallelepipedal blocks in step-wise fashion, precisely like bricks, as already shown in Fig. 12 (page 28) in Chapter III., in order to illustrate the step by step removal of Haüy’s unit blocks. It will readily be seen that if one more cell be removed from each row than from the row below it, the line of contact touching the projecting corner of the last block of each row will be inclined more steeply than if two more cells were removed from each row. Moreover, the angle varies considerably between the two cases, and if three blocks are removed at a time the angle gets very small indeed. Hence, there cannot be many such planes possible, and we see at once why the indices of the faces developed on a crystal are composed of low whole numbers and why the forms are so relatively few in number. Owing to the minuteness of a chemical molecule, all the irregularities of such a surface are submicroscopic, and the general effect to the eye is that of a smooth plane surface. The space-lattice arrangement of the molecules in the crystal structure thus causes the crystal to follow the law of rational indices, by limiting and restricting the number of possible facial forms which can be developed. It also determines which one of the seven systems of symmetry or styles of crystal architecture the crystal shall adopt. It does not determine the details of the architecture, however, that is, to which of the thirty-two classes it shall conform, this not being the function of the molecular arrangement but of the atomic arrangement that is, of the arrangement of the cluster of atoms which form the molecule, and this leads us to the next step in the unravelling of the internal structure of crystals. The credit of this next stage of further progress is due to Sohncke, whose long labours resulted in the discrimination and description of sixty-five “Regular Point-Systems,” homogeneous assemblages of points symmetrically and identically arranged about axes of symmetry, which are sometimes screw axes, that is, axes about which the points are spirally distributed. Sohncke’s point-systems express the number of ways in which symmetrical repetition can occur. Moreover, the points may always be grouped in sets or clusters, the centres of gravity of which form a Bravais space-lattice. This latter fact is of great interest, for it means that Sohncke’s points may represent the chemical atoms, and that the stereometric arrangement of the atoms in the molecule is that which produces the point-system and determines the crystal class, while the whole cluster of atoms forming the molecule furnishes, as above stated, the representative point of the space-lattice.