146 MOLECULAR GROUPING 



with an obtuse edge horizontal (best by fitting it into a 

 corresponding cut in a board), so that the long diagonal ce 

 of the right end-face c d ef is also horizontal, put the blade 

 of a knife at a at right angles to the upper edge, and press 

 it gradually into the crystal; then 

 the part of the crystal to the right of 

 the knife will be deformed in such 

 a way that when the knife reaches the 

 middle edge it will have assumed ex- 

 actly the form of an oppositely-placed 

 - 3i half-rhombohedron. The part of the 



calcite occupying the new position is 



quite homogeneous physically, but has its plane of cleavage 

 parallel to c e g instead of c e d as formerly. 



Taking into account this possibility of an arrangement 

 which is similar round each molecule, but not parallel, 

 Sohncke arrived at 65 regular point systems (extended 

 by Schonflies and Fedorow to 230) which in general consist 

 of several congruent interlaced spatial 'gratings/ They 

 fall, according to their symmetry, into seven systems, like 

 the spatial gratings, and yield exactly the 32 classes of 

 possible crystallographic forms given by the fundamental 

 law of geometrical crystallography 1 . 



5. The Fundamental Law of Physical Crystallography. 



If Sohncke's theory corresponds, on the one hand, to the 

 geometrical relationships of crystals, it allows, on the other, 

 an attempt at explanation of their physical behaviour. 

 Symmetry of external form is referred to that of the 

 internal structure, and explains at once why symmetry 

 of physical properties coincides with that of the external 

 form, which, it is well known, is the content of the funda- 

 mental law of physical crystallography. 



Take, as example, the hardness of rock salt. This shows 



1 Groth, Physikalische Krystallographie, pp. 268, 277. 



