120 



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 wo 

 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 certain 

 symmetry, and the ques- 

 tion may arise: what rela- 

 tions exist between the 

 symmetry of the pattern 

 and that of its characteris- 

 tic net-plane? 



In fig. 1 06 and IQJ 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 jig. 1 06 a repeat is placed round each point of the described 

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

 in fig. 107 however a motif is chosen in which only the quaternary 

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

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



