1913] 



on Great Advance in Crystallography 



699 



on the values of the five fundciineiital angles which, in general, 

 characterize the crystals of any specific substance. A cubic crystal 

 has definite angles which are entirely fixed and rendered invariable 

 by reason of the perfect symmetry. At the other extreme come 

 tricliuic crystals, the general case, in which all five fundamental 

 angles are dilferent and quite independent of each other. On mono- 

 clinic crystals there are three independent angles, from which the 

 other two can be calculated. Rhombic crystals have only two inde- 

 pendent angles, which, if measured, enable the other three to be 

 calculated. Hexagonal, tetragonal, and trigonal crystals possess only 

 one angle independent of the symmetry, determinative of the relative 

 length of the unique axis of hexagonal, tetragonal, or trigonal 

 symmetry. 



The first object of von Fedorow in order to arrive at the correct 

 setting, is to decide which are the primary axial-plane and parametral 

 faces ; and he is wonderfully aided here by the discovery of the fact 



Fig. 21. — Crystal of Ammonium 

 Ferrous Sulphate. 



Fig. 22.— Crystal of Potassium 

 Nickel Sulphate. 



that the faces most extensively developed under ideal conditions of 

 growth are those over which the points of the space-lattice are most 

 densely strewn. Hence, von Fedorow tries to discover the faces of 

 greatest reticular density by calculation. For it is a well-known 

 fact that the most diverse habits — due to different faces being most 

 prominently developed under different conditions of environment — 

 are shown by the crystals of the same substance. A capital example 

 is afforded by the double sulphates of the monoclinic series crystal- 

 lizing with GHoO. One of the conimonest of these salts, ammonium 

 ferrous sulphate, (NH^)2Fe(S04)o.6H20, exhibits a particular form 

 (consisting of a pair of parallel faces), r'{201}, not really a primary 

 one, so prominently, the ciTstals being tabular upon it as illustrated 

 in the lantern slide (Fig. 21), that Wulff has actually taken it as the 

 basal plane, rather than the form c{001}, which is considered by the 

 lecturer, following older observers, to be the true basal plane for this 

 whole series of isomorphous salts. For the very large development 



