wherry: crystal form and optical properties 285 



oxygen or nitrogen atoms are present in all the layers and the 

 planes of the layers are therefore regarded as approximately 

 equally spaced. In the vertical direction, however, there are 

 layers containing hydrogen + carbon atoms, alternating with 

 others made up of oxygen and of nitrogen alone. In the first 

 kind the carbon atoms lie over vacant spaces in adjoining layers, 

 into which they can extend, so that the space occupied by these 

 layers is determined by the hydrogen atoms, which are distinctly 

 less in diameter than any of the others. The reason that urea 

 has a negative axial ratio is thus evidently the presence of layers 

 containing hydrogen atoms alternating with others made up of 

 thicker nitrogen and oxygen atoms in the vertical direction, while 

 all the layers contain the latter atoms in the horizontal one. 

 The next step is to calculate the spacing of the planes in centi- 



^ / x X W X m 

 meters, which may be done by the formula da = % 



^ y X p X c 



where da is the distance between the planes in the horizontal 

 direction, x the number of chemical molecules in the portion of 

 the space-lattice studied, W the molecular weight referred to 

 hydrogen, m the mass of an atom of hydrogen, y the number of 

 unit cells in the larger one, p the density, and c the vertical 

 crystal axial value. In the case of urea the values are: x = 4, 

 W = 59.57, m = 1.64 X 10-^^ gram, y = 64, p averages 1.33, and 

 c = 0.833. Substituting, da = 1.77 X 10-^ cm., which is very 

 slightly greater than the average diameter of the atoms concerned, 

 in hquids. Correspondingly, c?c = c X (ia = 1.47 X 10 -^ cm. 

 In the cell figured there are vertically 1 N layer, 2 H layers, and 

 2 half O layers; the total d = 4 X 1.47 = 5.88 X 10-« cm. If 

 the vertical thickness of an O layer is 2 per cent greater than in 

 liquids, or 1.63, and of N 1.73, total 3.36, the thickness of an H 



r CO Q «^g 



layer = — '- — = 1.26; this barely exceeds the diameter of 



a hydrogen atom adopted above. The structure assigned to 

 urea thus agrees quantitatively with all available data. 



