314 



EEPORT — 1901. 



Hence the points of the Sohncke-systera may always be grouped together 

 in sets such that the centres of gravity of the sets constitute some space- 

 lattice. The law of rational indices is, therefore, applicable to a Sohncke- 

 system as well as to the space-lattice. 



Fig. 5, for example, represents a Sohncke-system of points possessing 

 screw-axes of hexagonal symmetry at B, C, D (No. 46 of Sohncke's 

 treatise). A point is brought into coincidence with a neighbouring 

 point by giving the system a rotation of 60° about one of these axes, 

 accompanied by a transla.tion along the axis. 



If every set of six points, such as c,, c.,, C3, c/, c./, c^', be regarded as 



grouped about a single point at their centre of gravity, y, the Sohncke- 

 system of fig. 5 can be treated as composed of groups of six points whose 

 centres form the space-lattice of fig. 6, in which the points all lie at equal 

 intervals on .straight lines.' (The lattice of fig. 6, like that of fig. 2, 

 possesses trigonal axes.) The Sohncke-system may therefore be regarded 



Fig. 5. 



as consisting of six similar lattices constructed from c,, c.2, C3, c/, c.^', c^' ; 

 the planes whose directions are given by any such points as /3, y, c form 

 a crystalline system of planes which obey the law of rational indices. 

 They may, therefore, be taken to represent the faces of the crystal. 



In such systems, and in others to be described below, it must be 

 remembered that the points of the figure may represent merely homologous 

 points in the material of which the crystal consists, whatever may be 

 the nature of that material ; it is not necessary to regard them as repre- 

 senting atoms or molecules, or as presupposing anything relating to 

 atoms or molecules. 



' A lattice formed of points verticallj'' midway between the points of the one 

 figure applies equally well, since the points of the Sohncke-system can just as 

 symmetrically be allotted to form groups having these other points as centres. 



