ON THE STRUCTURE OF CRYSTALS. • 299 



that the mutual inchnations of corresponding faces of rock-crystal are 

 the same in different specimens. 



It was seen that the property of cleavage also points to the uniform 

 repetition throughout a crystal of a definite structure of some kind, and 

 various suggestions as to the forms of ultimate particles were based upon 

 the cleavage. Thus Guglielmini,' who also studied the forms of alum, 

 argued the existence of plane faces for these particles, and attributed 

 crystal forms to them. This observer, relying on the uniformity of 

 internal structure, was the first to affirm that crystals of the same sub- 

 stance must always cleave in the same directions. Westfeld ^ suggested 

 that calc-spar is composed of rhombohedral particles. The latter idea 

 was adopted and extended by Gahn and Bergmann,-* who thus anticipated 

 the general theory of crystal structure put forth by the Abbe Haiiy, 

 to which reference will be made immediately. 



Shortly prior to Haiiy we have the important discovery made by 

 Rome de I'Isle * that the various shapes of crystals of the same natural or 

 artificial product are all intimately related to each other, and can be 

 derived from a certain fundamental figure called the 2)ri7nitive forin, the 

 shape and angles of which are proper to the substance. The variety of 

 form is due to the variety of the secondary faces. De ITsle himself 

 seems to have supposed that the secondary faces have absolutely arbitrary 

 positions, except so far as they are fixed by symmetry of mere extei'nal 

 form. His work, by directing attention to the invariable nature of the 

 crystal substance, and to the striking contrast between this invariability 

 and the variety of external form which may be exhibited by the same 

 body, supplemented the evidence in the same direction afforded by 

 optical and physical properties.^ 



Haiiy. 



It is now rather more than a century since Rene Just Haiiy sug- 

 gested an intimate relation between the forms of crystals and the arrange- 

 ment of their ultimate parts, and thus placed the study of crystal structure 

 on a sure foundation. The stimulus given to research by his labours has 

 been enormous ; multitudes of facts supporting his principal conclusions 

 have been accumulating ever since his day ; and it is not too much to say 

 that nearly all the subsequent work on the subject has been but an expan- 

 sion or modification of the work done by him. 



Haiiy bases his conclusions as to the nature of the crystal unit, or 

 molecule, entirely on the phenomena of cleavage. In any given crystal 

 which displays this property he determines the shape of the similar poly- 

 hedra which would be obtained by separating the mass along cleavage 

 planes into a number of similar fragments, each set of parallel planes of 

 cleavage being equally spaced throughout. For example, cleavage 

 parallel to the faces of a cube leads to cubic fragments ; that parallel to 

 the faces of a hexagonal prism to fragments which are triangular prisms 



' Riflessioni filosofiche dedntte dalle figure de sali, Bonon. 1688, and De salibus 

 dissertatio epistolaris, Venet. 1705, 



- Mineralogisvhe AMandhingen, Stiick I. Gottingen u. Gotha, 1767. 



' ' Varia3 crystallorum formaj a Spato ortte ' in A^ov. Acta Meg. Soc. So. TTpsaL, 

 1773, i., and ' De formis crystallorum ' in Opusc. Upsala, 1780, ii. 



* Essai de CrisfallograjiJiie, Paris, 1772. Cristallographie, ou description des 

 former proprei a tous les corps du regne mineral, Paris, 1783. 



* SchiJnflies, Krystallsystevie u. Krystallstructur, p. 5. 



