MOLECULES IN A CRYSTAL. 489 



Bravais was compelled to introduce another assumption ; 

 the particles themselves were supposed to have an inherent 

 symmetry ; to be, not mere points, but symmetrical clusters 

 of atoms ; the symmetry of the crystal is then supposed to 

 be, not that of the lattice alone, but that which is common 

 to the lattice and to the molecules of which it is constructed. 

 Consequently, if the molecular cluster is less symmetrical 

 than the lattice, the crystal as a whole only possesses a part 

 of the symmetry of the system to which it belongs. 



For example : minute cubic particles placed at the 

 corners of a cube would be the elementary cell of a com- 

 pletely cubic lattice like that of fluor-spar ; but minute 

 tetrahedra placed at the corners of a cube would give rise 

 to a hemihedral cubic crystal like zinc-blende. 



This is, of course, all ancient history now, but it is 

 necessary for the correct appreciation of what follows. We 

 may note in passing that it is difficult to see why in the 

 Bravais theory each molecule, if its symmetry depends upon 

 the arrangement of atoms or chemical molecules within it, 

 should necessarily have only a symmetry deducible from 

 the lattice to which it belongs. Why, for instance, should 

 the molecule not be pentagonal in form, although this is 

 not admissible as a crystal form ? This objection cannot 

 be raised to the second theory, which we have now to 

 consider. 



THE SOHNCKE THEORY. 



The next advance, and a very important one, was made 

 independently by Wiener and Sohncke, who endeavoured 

 to solve a different problem, namely: In how many ways 

 can a set of points be arranged in space so that the 

 distribution round any one point is identical with that 

 round any other of the set? In other words : How many 

 possible homogeneous assemblages of points can be con- 

 structed ? This is a very natural structure to assume, for 

 it harmonises with the homogeneous physical nature of a 

 crystal ; the assumption made is, that the symmetry at any 

 one point of the structure is the same as at any other point. 



