MOLECULAR ARCHITECTURE 363 



parameters than the topic axial ratios ? This we shall proceed 

 to explain. 



In the first place, we know that the equivalence parameters 

 represent definite translations in the assemblage of spheres 

 of which the crystal is built up ; that is to say, they are the 

 distances between adjacent similarly situated points of the 

 homogeneous structure in the three selected directions. It 

 is of great significance that models of quite a number of 

 crystal structures have been built up from spheres of appro- 

 priate sizes ; these models not only conform in symmetry to 

 the crystals whose structure they represent but the transla- 

 tions of the model correspond in dimensions to the equivalence 

 parameters calculated for the crystal. In such cases as these— 

 notably in that of benzene, with which we shall subsequently 

 deal more fully — the architecture of the crystal can be regarded 

 as very fully elucidated and the equivalence parameters, having a 

 perfectly definite physical meaning, must in all cases be of great 

 value for comparing the structures of different substances. 



We have already referred to the minerals of the chondro- 

 dite group as exhibiting among themselves a most interesting 

 morphotropic relationship. The minerals prolectite, chon- 

 drodite, humite and clinohumite differ in composition each from 

 the preceding one by the increment Mg^iO^, their respective 

 compositions being given by the formulae MgSi04 2Mg(E, OH) ; 

 Mg3(SiO,).2Mg(F, OH); Mg,(SiO,)32Mg(F, OH) ; and Mg,(SiO,), 

 2Mg(F, OH).^ The axial ratios of the four minerals are related 

 in such a way that a : b is practically the same for each, whilst 

 the ratios c : b are in the proportion 3:5:7:9. No explanation 

 of this well-known relationship has hitherto been forthcoming. 

 But if the equivalence parameters for the four minerals be 

 calculated and compared, it is found that hvo of these dimensions 

 are practically constant for each mineral and that the addition 

 of the increment Mg^SiO^ leads in each case to a constant increase 

 of the dimension z. 



' In these compounds the fluorine and hydroxy] are isomorphously mutually 

 interchangeable. 



