123 



its dimensions and its whole character closely approach to those of a 

 really cubic or hexagonal space-lattice. In the case of such a rhombic, 

 but pseudo- trigonal or pseudo-hexagonal arrangement for instance, 

 the vertical axis is, of course, only a binary axis of symmetry; but its 

 direction is at the same time that of an approximately ternary or 

 senary axis. The space-lattice is said to have an axis of apparent 

 symmetry; and, as we shall see afterwards, such pseudo-ternary or 

 pseudo-hexagonal axes, - - although, properly speaking, being no 

 real symmetry-elements of the space-lattice, can occasionally have 

 some of the functions of true symmetry-axes. 



We will consider this fact more in detail in the next chapter of 

 this book, in connection with some remarkable phenomena met 

 with in crystalline matter. 



8. For the moment 

 we will return to our two- 

 dimensional patterns of 2, 

 the character of which, as 

 we have seen, is always 

 closely related to a certain 

 net-plane. Such pattern can 

 eventually possess a cer- 

 tain symmetry, and the 

 question may arise: what 

 relations exist between the 

 symmetry of the pattern 

 and that of its characteris- 

 tic net-plane? 



In fig. loS and /op two 

 patterns are reproduced whose net-planes are essentially identical, 

 namely a net-plane with ordinary quadratic meshes. This net-plane 

 can, therefore, be considered as having an infinite number of quater- 

 nary axes perpendicular to the plane of drawing,- and four sets of 

 symmetry-planes passing through those axes; moreover, their inter- 

 sections with the plane of the figure are binary axes, and, of course, 

 there is also an infinite number of symmetry-centres. 



In fig. 1 08 .a repeat is placed round each point of the described 

 net-plane, which has itself precisely the same set of symmetry-ele- 

 ments; in fig. 109, however, a motif is chosen in which only the quater- 

 nary axis has remained, while all other symmetry-elements of the 

 quadratic net-plane are lacking in it. Now from these figures it can 



Fig. 108. 



