122 



system only an oblique parallelepiped cell being possible, for the 

 monodinic two kinds of cells, for the rhombic four, for the trigonal 

 only one rhombohedral cell, for the tetragonal system two kinds of 

 cells, for the hexagonal only an equilateral trigonal prism, of which 

 six contiguous ones are shown in the figure, -- and for the cubic 

 system three kinds of cells. The cells of the rhombic, tetragonal 

 and cubic system which have a point in the centre of the parallele- 

 piped cells drawn in fig, 107, can be also chosen in such a way, 

 that no point lies within the cell; in the cubic system for instance, 

 the elementary cell would then have an octahedral form, with a 

 point at each corner of the octahedron, etc. 



7. In connection with this we shall at the same time draw 

 attention to a fact which will appear of interest to us in future for 

 the understanding of special groups of phenomena. It concerns 

 the existence of so-called elements of pseudo-symmetry in such space- 

 lattices, a fact which finds its explanation in the special circum- 

 stance that there may exist a gradual passage of form from the one 

 kind of unit-cell to the other. 



Thus, comparison of the elementary cells of both the tetragonal 

 cells with the types a and b of the rhombic and the cubic system, 

 will make it clear at once, that a suitable change of the principal 

 dimensions in one or two directions will make their form approach 

 as closely as desired to that of a cubic cell. In the same way, if the 

 dihedral angle of the oblique monoclinic cell, differing from 90, 

 approaches very closely to this value, the cell becomes almost that 

 of a rhombic space-lattice. 



When the principal ternary axis of the rhombohedral cell is suitably 

 lengthened or shortened, the polar dihedral angles can approach 

 as closely as possible to 90, the rhombohedral cell being, therefore, 

 converted almost into a cube. Indeed, the rhombohedron is a dis- 

 torted cube, namely, if the latter be compressed or dilated in the 

 direction of one of its fo'ur trigonal symmetry-axes. 



If the prism-angle of a rhombic prismatic cell is almost 60 or 

 120, it approaches very closely to the equilateral triangular cell 

 of the hexagonal space-lattice, etc. 



In all such cases the lower symmetrical space-lattice exhibits 

 a greater or smaller approximation to a space-lattice of higher 

 symmetry. It is said to possess a limiting or pseudo-symmetry: the 

 space-lattice is called pseudo-cubic, pseudo-hexagonal, etc., to indi- 

 cate that, although having truly a lower degree of symmetry, - 



