MOLECULES IN A CRYSTAL. 499 



If we are to deduce the thirty-two groups from the 

 simple principle of homogeneity alone, without assuming 

 this law, we have at present to adopt a structural theory. 

 Now there is no direct evidence that the constituent par- 

 ticles of crystals are different in their nature ; zve are, there- 

 fore, driven to the theory of Schonflies and Fedorow. 



That theirs are purely geometrical structures in which 

 the particles are mathematical points may be a recommenda- 

 tion rather than an objection to the theory, for it serves to 

 remind us that the structure is to be regarded as merely a 

 model or representation of something of which we have no 

 nearer knowledge, and does not necessarily indicate the 

 relative positions of the molecules any more than the figures 

 of stereo-chemistry necessarily indicate the relative positions 

 of the atoms. 



The second remark relates to a point which is often 

 overlooked. The structure theories do not assume that a 

 crystal is necessarily symmetrical ; they acknowledge that 

 a crystal may be devoid of symmetry (calcium hyposulphite 

 and acid strontium tartrate are examples) ; they only assert 

 that a crystal must belong to one of thirty-two types, of 

 which one has no symmetry, but the remaining thirty-one 

 are symmetrical in various degrees ; similarly they indicate 

 that if a crystal is bounded by plane faces there is good 

 reason for believing that these should be the planes of a 

 Bravais lattice, that is, should obey the law of rational 

 indices. Why a crystal should be symmetrical, or why it 

 should be under certain circumstances bounded by plane 

 faces, they utterly fail to show. 



One objection which may be urged against the structural 

 theories may be considered- in conclusion. It may be said 

 that they are mere mathematical exercises which have no 

 physical meaning. 



In reality, however, as Schonflies is careful to point out 

 (20), what the structural theory does is this : it divides 

 space into fundamental cells, within each of which analogous 

 portions of matter must be distributed in an analogous 

 manner, leaving the chemist, physicist and crystallographer 

 to decide what are the characters of these portions of matter, 



