398 Dr. L.Vegardcm 



The tetrahedron itself has a hemihedral form ; but this 

 does not mean that the structure of the whole lattice is 

 hemihedral. The structure will be holohedral provided the 

 following conditions are fulfilled: — 



(1) The tetrahedra must form two groups. The tetra- 



hedra of each group may be brought to coincidence 

 with one another by a translation only, and a tetra- 

 hedron of one group may be made to cover one of 

 the other one by a translation and a rotation of 90° 

 about an axis parallel to one of the sides of the 

 cube. 



(2) The centres of the tetrahedra of any one of the 



groups must be arranged with holohedral symmetry. 



We easily see that these conditions cannot be fulfilled if 

 we suppose hydrogen to have an elementary lattice of the 

 same size as those of I and N. For in that case all the 

 tetrahedra belonging to the same elementary lattice of 

 N atoms must be parallel. Now the whole structure only 

 contains four elementary lattices of N atoms, and one of 

 the groups of tetrahedra should have their centres in two 

 elementary lattices ; but two elementary lattices forming- 

 part of a face-centred lattice cannot be arranged with cubic 

 symmetry, and thus the second condition cannot be fulfilled. 

 If, then, hydrogen has elementary lattices of the same size 

 as those of I and N, all tetrahedra must be parallel and the 

 symmetry of the lattice will be hemihedral (hexakistetra- 

 hedrical) of the class 31. 



A holohedral symmetry we could get if the side of the 

 elementary lattice of H was twice that of N and I. Then 

 the tetrahedra belonging to each single elementary lattice of 

 nitrogen could be arranged in two different positions in such 

 a way that the conditions (1) and (2) were fulfilled. 



Thus our considerations have Jed to the result that the 

 structure must either be holohedral or possess the symmetry 

 of the hexakistetrahedrical class. The latter arrangement, 

 which would make the elementary lattice of H equal to that 

 of N, is very simple and should seem the more probable. 



With regard to the symmetry of the crystal, it is supposed 

 to be hemihedral ; but the kind of hemihedrism is not quite 

 certain. Groth put it down as pentagonikositetrahedrical. 

 Which of the two possible arrangements of the hydrogen 

 atoms is the one which is able to explain the symmetry of 

 crystal, further investigation must decide. There is, how- 

 ever, very little hope that the Rontgen-ray analysis can give 

 us the exact position of the H atoms. 



