142 MOLECULAR GROUPING 



indices restricts the possibilities of symmetry. In the first 

 place, by reference to Fig. 28 we see that there need be no 

 symmetry at all, in which case we have the unsym metric 

 (tri clinic) system. 



One plane of symmetry may be present, but it is limited 

 as to position; if e.g. it passes through zox, then the 

 plane symmetrical to ABC would have rational indices 

 with respect to ox and oz, but not in general with respect 

 to OY ; it is therefore a subsidiary condition that OY 

 should be perpendicular to the plane of xoz. These are 

 the conditions for the non- symmetric system. 



One axis of symmetry may be present, i. e. a line such 

 that rotation about it through an angle less than 360 

 brings the crystal into a position identical with its 

 original position. If e.g. the axis occupies the position 

 oz (Fig. 28), the law of rational indices is satisfied when 

 XOY = 90 and OA = OB ; such axes are therefore, for the 

 same reason, subjected to certain conditions; they can 

 only be double, triple, quadruple, or sextuple, i. e. the form 

 may recover its original position on rotation through 1 80, 

 120, 90, or 60, i.e. two, three, four, or six times in 

 a circle. These are the conditions for the rhombic, 

 trigonal, tetragonal, and hexagonal systems. 



A third possibility is that the crystal on rotation comes 

 into a position symmetrical to its original position ; it 

 is then said to have an axis and plane of compound 

 symmetry. 



In this way, taking into account the law of rational 

 indices, thirty-two classes, exactly corresponding to the 

 facts, are arrived at ; and these are grouped in the seven 

 crystalline systems : 

 I. Triclinic system. 



1. Holohedry. Example: calcium thiosulphate (CaS 2 O P> 

 . 6 H 2 0). 



2. Hemihedry : one double axis and one plane of com- 

 pound symmetry at right angles to it. Example : eZ-mono- 

 strontium tartrate (Sr(C 4 H 5 O e ) 2 . 2H 2 O). 



