1910] on the Chemical Significance of Crystal Structure. 831 



Table II. — Hexagonal Binary Compounds, 



In connection with the elements and binary compounds it is note- 

 worthy that the mode of treatment described appears practically to 

 eliminate molecular aggregation of the atoms as a factor in determin- 

 ing the crystalline structure ; that is to say, the distance separating 

 two neighbouring atom centres is the same whether those atoms 

 belong to the same or to different molecules. Another interest- 

 ing fact is that, whilst the elements and binary compounds for 

 the most part crystallise in the cubic or hexagonal systems, sub- 

 stances of greater molecular complexity rarely crystallise in these 

 highly symmetrical systems ; thus, of a great number of organic 

 compounds examined, 2*5 and 4*0 per cent, only belong to the 

 cubic and hexagonal crystalline systems respectively (Table I). This 

 observation is important as one of many indications that the cells 

 into which the crystal structure of a complex compound are par- 

 titionable are not, in general, all of the same volume. Further in- 

 vestigation shows that the volumes of the polyhedral cells representing 

 the atomic domains of the several elements present in a complex crystal- 

 line compound are governed by the law of valency volumes to which 

 reference has already been made. The correctness of this conclusion 

 concerning the proportionality between the numbers expressing the 

 fundamental valencies of the elements and the volumes of the corre- 

 sponding spheres of atomic influence has been abundantly verified, 

 not only by the laborious process of working out a large number of 

 cases, but in several other ways which may be more rapidly indicated. 

 The following are illustrations of the latter kind of verification. 



Table III. states the composition and axial ratios, a :b :c, oi a 

 series of four crystalline minerals which differ in composition by 

 the increment, Mg2Si04 ; the sums of the valencies of the atoms 

 composing the different molecular aggregates are stated under the 

 heading, W. The increment, MgoSi04, also occurs as the crystalline 

 mineral forsterite, of which the axial ratios have been determined. 

 It is evident that the ratio, a/b, has approximately the same value 

 of 1*08 for all four members of the series, and that practically all 

 differences in relative dimensions are expressed by the ratio, c/b. 

 On dividing the valency volume, W, by the corresponding value 

 for c/b in each case, the quotients 11 '7, 12*1, 12-3, 12-4 and 12*7 

 are obtained respectively for the substances prolectite, chondrodite, 

 humite, clinohumite, and forsterite. The relative dimension, c/b, is 

 thus roughly proportional to the sum of the valencies in this set of 



YoL. XIX. (No. 104) 3- 1 



