SYSTEMS OF CRYSTALLIZATION. 327 



portion of Haiiy's doctrine which most riveted popular attention and 

 applause, was his dissection of crystals, in a manner which was sup- 

 posed to lead actually to their ultimate material elements. Yet it is 

 clear, that since the solids given by cleavage are, in many cases, such 

 as cannot make up a solid space, the primary conception of a neces- 

 sary geometrical identity between the results of division and the 

 elements of composition, which is the sole foundation of the supposi- 

 tion that crystallography points out the actual elements, disappears on 

 being scrutinized : and when Haiiy, pressed by this difficulty, as in the 

 case of fluor-spar, put his integrant octohedral molecules together, 

 touching by the edges only, his method became an empty geometrical 

 diagram, with no physical meaning. 



The real fact, divested of the hypothesis which was contained in the 

 fiction of decrements, was, that when the relation of the derivative to 

 the primary faces is expressed by means of numerical indices, these 

 numbers are integers, and generally very small ones ; and this was 

 the form which the law gradually assumed, as the method of deriva- 

 tion was made more general and simple by Weiss and others. 



"When, in 1809,1 published my Dissertation," says Weiss, 1 "I 

 shared the common opinion as to the necessity of the assumption and 

 the reality of the existence of a primitive form, at least in a sense 

 not very different from the usual sense of the expression. While I 

 sought," he adds, referring to certain doctrines of general philosophy 

 which he and others entertained, " a dynamical ground for this, 

 instead of the untenable atomistic view, I found that, out of my 

 primitive forms, there was gradually unfolded to my hands, that 

 which really governs them, and is not affected by their casual fluctua- 

 tions, the fundamental relations of those Dimensions according to 

 which a multiplicity of internal oppositions, necessarily and mutually 

 interdependent, are developed in the mass, each having its own pola- 

 rity ; so that the crystalline character is co-extensive with these pola- 

 rities." 



The "Dimensions" of which Weiss here speaks, are the Axes of 

 Symmetry of the crystal ; that is, those lines in reference to which, 

 every face is accompanied by other faces, having like positions and 

 properties, Thus a rhomb, or more properly a rhomlohedron? of 



1 Mem. Acad. Berl. 1816, p. 307. 



2 I use this name for the solid figure, since rhomb has always been used foi 

 a plane figure. 



