125 



of symmetry than its net-plane, the symmetry of the pattern as 

 a whole nevertheless does not possess a higher symmetry than its 

 net-plane. 



In fig. no the repeat is tetragonal, the net-plane rhombic ; and 

 the pattern as a whole is rhombic also. 



Bravais has made use of facts of this kind to explain the internal 

 structure of crystals which belong to the merohedral classes of the 

 seven crystal-systems. For, as we have seen, all the fourteen types 

 of possible symmetrical space-lattices have the symmetries of 

 the holohedral class of each system. If, however, round every point 

 of these space-lattices molecules be placed, which only possess a 

 certain part of the symmetry-properties characteristic of the space- 

 lattice under consideration, the molecular structure as a whole 

 can only exhibit the symmetry-elements which are common to 

 the space-lattice and the complex crystal-molecules. And precisely 

 because the space-lattice and its complex molecule still have some 

 symmetry-elements in common, these molecules will all remain 

 in parallel positions with respect to each other, in the same way 

 as the repeats of fig. 108, as well as those of jig. lop are parallel 

 to each other. All homologous atoms of these complex molecules 

 will, therefore, be arranged in similar and similarly oriented space- 

 lattices, which can be brought to coincidence with each other by the 

 characteristic symmetrical operations of the complex molecule l ). 



9. It is, however, evident that the solution of the problem of 

 homogeneous symmetrical arrangement as given by Bravais, 

 cannot be considered the most general and thus not a final one, 

 because the condition that all repeats of the stereometrical pattern 

 shall be parallel to each other, is quite an arbitrary factor in it, and 

 the deficiency of the theory in explaining the occurrence of lower 

 symmetrical dispositions than those of the space-lattices, is only 

 apparently eliminated by attributing to the repeats themselves such 

 qualities, as had to be explained by the principle of homogeneous 

 symmetrical arrangement alone. With respect to the explanation 



*) All that has been said above with respect to the "motif" or the"repeat" 

 of the endless pattern, is valid also for Bravais' "crystal-molecules"; etc. 



However, it should be mentioned here, that the word "motif", for instance in 

 the work of G. Friedel, has been used in a somewhat different significance, 

 namely in that of "fundamental domain" (cf. page 131 etseq.). If that definition 

 be adopted, our reasonings must be exchanged for such as are applicable to the 

 said "fundamental domains". In that case, for instance, the "motif" cannot be 

 more highly symmetrical than the crystalline system as a whole; etc. 



