MOLECULAR ARCHITECTURE 351 



four elements of symmetry referred to. When the elements 

 of symmetry of the types of homogeneous structures are 

 compared with those of the crystallographer just referred to, 

 it is perceived that the simplification introduced by the con- 

 ception of the geometrical centre of the crystal is artificial ; 

 some of the coincidence movements characterising homogeneous 

 structures possess no such centres, e.g.^ the screw movements. 

 In the case of movements referable to no centre of symmetry, 

 the change of orientation or effect of the movement on 

 direction produced by the less regular movement of the 

 homogeneous structure is identical with that brought about 

 by some centred movement. 



The Phenomena of Polymorphism, Isomorphism and other 

 MoRPHOTROPic Relationships 



From this necessarily brief sketch of the mathematical 

 theory of crystal structure, we may now pass to the considera- 

 tion of the mode in which the theory serves in the interpre- 

 tation of problems which arise in the practical study of 

 crystals. The net result of the work which has been described 

 above is to show that an intimate relationship exists between 

 the number of possibilities of homogeneous distribution of 

 points in space as determined geometrically and the classes 

 of symmetry observed in crystals. The conclusion to be drawn 

 from this result is that crystals are homogeneous structures ; 

 a conclusion amply justified by many physical facts, some of 

 which have already been cited. It is possible to imagine the 

 crystal units distributed so as to form a homogeneous structure 

 corresponding to one of the 230 types ; but it must be 

 observed that this purely geometrical conception does not 

 restrict or define either the shape or size of the crystal unit 

 in terms of the chemical molecule. No reason is offered for 

 the adoption by the units of a particular type of symmetry 

 and there seems to be no reason why the same units should 

 not be able to arrange themselves in more than one way. 

 That they can do so we have ample evidence, for many cases 

 are known of a chemical substance assuming more than one 

 crystalline form. This phenomenon is known as polymorphism. 

 Sulphur affords a good example of a polymorphous substance : 

 it is known in four modifications, one possessing orthorhombic 



