300 REPORT— 1901. 



(fig. 1). The units thus obtained, which he calls moUcules xntegrdnies} 

 belong, he finds, to one of three simple kinds : they are in some cases 

 tetrahedra, in others triangular prisms, in the remaining cases parallele- 

 pipeda,^ and their form is found by observation to be invariable for a 

 given kind of mineral.^ He considers that if the process in question does 

 not furnish the precise shapes of the actual crystal molecules, it at least 

 pictures to us a representative analysis of crystal structure which is 

 worthy to stand for the actual facts, and enables us to correlate them.'' 

 A further partitioning of the molecules inUgrantes is, indeed, suggested, 

 which would assign a definite relative position in space to the elements 

 forming a chemical compound,'' but the chemical atoms {molecules dlemen- 

 iaires) of various kinds thus supposed to have distinct places in the crystal 

 substance, and to be of definite and constant form, are not made the 

 subject of investigation. The molecules integrantes are supposed to result 

 from the regular combination of the latter to form a single kind of unit 

 or molecule, and these alone foi'm the basis of Haiiy's theory of crystal 

 structure. 



Adopting the idea put forward by Rome de I'lsle of the existence in 

 every crystal of a primitive form,'' or nucleus, Haiiy supposes that this 

 nucleus consists of a considerable number of niole'cules inte'gr antes,'' and 

 that the primary facea of a crystal are the outcome of regular accretion 

 upon the faces of the nucleus. Secondary crystal faces are those not 

 parallel to the cleavages, and these are explained by supposing that the 

 successive layers deposited on each face of the primary nucleus do not 

 overlap preceding layers sufficiently to yield merely an enlarged figure of 

 the same shape as the nucleus, but, falling short of this in a regular 

 manner, form by their boundaries planes which truncate the edges or 

 corners of the enlarged figure referred to.* He points out, however, that 

 since microscopic crystals have as complete a complement of faces as those 

 of larger growth, the modification by which the structure acquires new facea 

 must be an initial one, which takes place once for all, subsequent growth 

 being the result of accretion upon secondary and primary faces alike.° 



In cases where the molecules integrantes are parallelepipeda this 

 mapping out of secondary face directions by the edges bordering suc- 

 cessive layers where the boundaries of added layers fall short at edges or 

 corners in a regular manner, is easy to follow. In order to explain in a 

 similar manner the production of new faces, where the m.olecules in- 

 tegrantes are tetrahedra or triangular prisms, Haiiy regards these mole- 

 cules as aggregated to form parallelepipedal groups, which he calls 

 molecules soustractives.^^ This is, of course, merely a geometrical con- 

 ception, intended to elucidate the growth of secondary faces by regular 

 decrease in extent of succeeding layers, and does not refer to any physical 

 association of the molecules integrantes to form molecules soustractives ; 



' Traitc de 3Iiniralogie, Paris, 1801, i. pp. siv and 6. "^ Tb'ul., p. 30. 



3 Ibid., pp. xiv and 20, 29, and 32. ^ Ihid., pp. 7 and 31. ^ Ihul., p. 6. 



^ Traite de Mincralogie, i. pp. 20 and 28, also p. 481. Haiiy says in another place : 

 • La forme primitive parolt etre le r6sultat de la crystallisation la plus parfaite dont 

 un mineral soit susceptible ; mais ce n'est pas toujours celle qui se rencontre le plus 

 ordinairement ' {Fssai d'vne Thiorie sur la Structure des Crijstauw, Paris, 1784, 

 p. 50). 



' Traitc de Miniralo(]ie, i. p. 29. Thus he considers that the primitive form of 

 tourmaline is a rhombohedron, but that the molecule intt'fjraTite is a tetrahedron, 

 which is the sixth part of such a rhombohedron (see ibid., p. 30). 



* Ihld., p. 34 et serj., also p. 285. » Ibid., p. 08. '» Ibid., p. 97. 



