ON THE STRUCTURE OF CRYSTALS. 



301 



for the purpose of explaining the production of secondary faces, it enables 

 all the structures formed by the mole'ctdes inte'grantes to be regarded as 

 composed of parallelepipedal units/ although these may be only geome- 

 trical fictions. 



The hexagonal structure of figs. 1 and 2 may be regarded either as 

 built up of the molecules inte'grantes ABC, which are triangular prisms, 

 or of the molecules soustractives ABDC, which are rhombic prisms of 

 120° and 60°. 



The crystal may then be regarded as consisting of molecules sous- 

 tractives, which are parallelepiped a packed together in parallel positions 

 so as to fill space (hg. 4, p. 305). 



The growth of the secondary faces by decrements consisting of whole 

 numbers of the molecules soiistractives leads directly to the great and 

 fundamental Law of the Rationality of Intercepts.^ (This Law will be 

 referred to below under its more familiar name, the Law of Rational 

 Indices.) The truth of this law Haliy himself established by the 

 measurement of a vast number of crystals, and it seemed to carry with 

 it the justification of his apparently arbitrary theory of their structure. 



Fig. 1. 



Fig. '2. 



It will, however, be found later that an hypothesis of a more general 

 character leads to the same results. 



Put concisely, the objections to Haiiy's conclusions as to the nature of 

 the ultimate particles of crystals are the following : — 



1. Haiiy has to suppose that crystal surfaces, apparently plane, are 

 actually corrugated,'^ and, if the same be admitted with regard to cleavage 

 planes, other forms for the molecules inte'grantes than those which he 

 deduces are possible. It is easy to picture a simple case in which the 

 directions of cleavage would prove a fallacious guide to the determina- 

 tion of the shape of the ultimate units of a body. 



Thus suppose that a number of equal regular hexagonal prisms of 

 some uniform material are fastened together in a close and regular manner 

 by a uniform but weak cement, so that the adhesion between the prisms 

 is much weaker than the cohesion of their substance. It is, then, evident 



' Traiti! de Hineralo/jfie, pp. 97 and 284. Comp. Bravais' conceptions (see below, 

 p. 306). 



- This law carries with it the exclusion of two of the five regular pol>hedra from 

 the forms possiole for crystals, i.e., of the regular pentagonal dodecahedron and the 

 icosahedron (ihid., p. 80). 



=> See his explanation of the occurrence of secondary faces just referred to aboVe. 



