f^SO Professor WiUiam J. Pope [April 15, 



been shown fertile in the case of the crystalline elements can be 

 immediately applied to the binary compounds ; as before, each atom 

 will be represented by forces emanating from a centre, and equilibrium 

 will demand closest packing of the spheres used, just as in the 

 previous case. The atomic centres will now, however, be of two 

 kinds, and the question arises as to whether the domains of atomic 

 influence to be described about them will be all of the same magnitude 

 or whether two magnitudes of spheres must be employed, one for 

 each element present. This question is difficult to answer by refer- 

 ence to the facts already reviewed above ; probably the only indica- 

 tion which the latter afford in this connection is that closest-packing 

 of a considerable variety of different magnitudes would certainly be 

 most unlikely to lead to the close similarity of crystal form observed 

 as between the elements and the binary compounds. A direct 

 answer is, however, provided as the result of investigating the 

 crystalline forms of organic substances, to which reference will 

 presently be made ; this investigation has led to the discovery of a 

 definite law which governs the magnitudes of the several kinds of 

 atomic domain concerned in any crystalline compound substance. 

 It is found that the magnitudes of the atomic domains in any 

 crystalline compound are very approximately in the ratio indicated 

 by the fundamental valencies of the corresponding elements. Since 

 the molecules of nearly all the binary compounds which have been 

 crystallographically examined contain in the molecule one atom each 

 of two elements of the same valency, the polyhedral cells from which 

 a crystalline binary compound must be supposed built up are all, in 

 general, of approximately the same magnitude. The fact that most 

 binary compounds, like most elements, crystallise in either the cubic 

 or the hexagonal system, represents one of the simple results of this 

 law of valency volumes. 



The binary compounds thus, in general, affect crystalline struc- 

 tures which are derived from the cubic or the hexagonal closest- 

 packed assemblage of equal spheres ; one-half of the spheres, selected 

 homogeneously, represent atoms of the one element and the remainder 

 atoms of the second element. The mode in which the necessary 

 homogeneous selection may be made in the cubic assemblage, without 

 altering the values of corresponding dimensions in three rectangular 

 directions, is shown in a model. 



The crystalline forms of the binary compounds are in accordance 

 with what has been above foreshadowed. Table I. indicates that in 

 geometrical respects the crystalline binary compounds closely resem- 

 ble the elements; 68*5 percent, of those examined are cubic and 

 19 • 5 per cent, hexagonal, the remaining 12 per cent, crystallising in 

 systems of lower symmetry than these. The axial ratios, « : c, of all 

 the hexagonal binary compounds known are stated in Table II.; all 

 approximate closely to the value, a:c = 1 : 0-8165, for the model 

 hexagonal closest-packed assemblage of equal spheres. 



