488 SCIENCE PROGRESS. 



alter the shape of the elementary cell in various ways by 

 supposing the distances between the lines to be unequal, 

 or by imagining the lines of descending hailstones to slope 

 in one direction or the other as they would do under the 

 influence of a wind. In this way we may obtain different 

 cells having the forms known as the square prism, the 

 oblique prism, the rhombohedron, etc., of crystallography, 

 and a different lattice corresponding to each of these. 



Now the most important and remarkable of all the 

 characters of a crystal is its symmetry. As is well known, 

 crystals are almost always symmetrical in shape, and accord- 

 ing to the nature of their symmetry they are grouped into 

 seven types or "systems". The grouping is sometimes 

 expressed according to the lengths and directions of the 

 three axes to which a crystal is referred ; but it will be seen 

 on reflection that these axes are nothing more or less than 

 the three sides of the elementary cell of the lattice. A 

 variation of the lengths and directions of the axes corre- 

 sponds exactly to a variation of the form of the elementary 

 cell, and by either process we obtain geometrical figures, 

 which generally possess a certain symmetry. 



Bravais, therefore, proceeded to investigate all the 

 possible forms of space-lattices and the nature of their 

 symmetry ; and the result at which he arrived is surpris- 

 ingly simple. 



He found that there are only fourteen different sorts of 

 lattices, and that these, if classed by their symmetry, fall 

 into seven groups, which have precisely the same symmetry 

 as the seven systems into which all known crystals had 

 already been grouped. 



The lattice structure, however, fails to explain the form 

 of what are commonly called hemihedral or merohedral 

 crystals, i.e., those which only partially possess the symmetry 

 of the system to which they belong ; it gives us, for example, 

 the form of the cube and octahedron of fluor-spar and other 

 substances, but it does not account for the form of the 

 tetrahedron of zinc-blende, or the common deltoid dodeca- 

 hedron of iron pyrites. For all these merohedral forms (and 

 they perhaps constitute in reality the majority of crystals), 



