WHERRY : CRYSTAL FORM AND OPTICAL PROPERTIES 283 



and (3) the axial ratio of the substance. The two ratios are 

 ahvays used in the opposite order; that is, if the one refers to 

 a/c, the other is taken as cla. 



The agreement of the two ratios is very exact, and indicates 

 that in urea the standard axial ratio is identical with the true one, 

 all of the atoms having a part in determining the position of the 

 unit' sphenoid. 



The information at hand now seems sufficient to warrant the 

 working out of the probable space-lattice of the substance, which 

 may be accomplished by bearing in mind the following points : 



Since no change from one isomer into another is ever caused by 

 crystallization, molecules must be preserved in crystalhzed 

 organic compounds better than in most of the inorganic ones that 

 have been studied with X-rays. The chemical molecule should 

 therefore be retained as far as possible. It should be spread out 



H ^ TT 



in one plane, somewhat like this: N C N ^^^^ partial 



H H 



interpenetration of these groups is likely to occur. 



Since urea shows cleavage in three directions at right angles, the 

 lattice should have a general cubic plan. But since the crystal 

 class is scalenohedral, there must be some alternation of group- 

 ings, corresponding to that shown by the sulfur atoms in the 

 tetrahedral mineral sphalerite. The lattice should possess 

 a vertical axis of alternating four-fold symmetry, two horizontal 

 axes of two-fold symmetry, and two symmetry planes. The 

 atoms must be equally represented in the layers in all three 

 directions in space, and the average distance between their 

 planes vertically be 0.833 times that horizontally. Some explan- 

 ation of this difference in spacing should be seen in the atomic 

 arrangement. 



A space-lattice fulfilling these requirements proves to be very 

 easy to construct; and a portion of it containing five layers of 

 atoms in each direction is shown in figure 1. Four chemical 

 molecules are represented in this cell, as may be seen when it is 

 remembered that of each atom lying on outer surfaces only half 

 belongs to it. The oxygen atoms in the top and bottom layers 



