SYSTEMS OF CRYSTALLIZATION. 235 



a necessary geometrical identity between the results 

 of division and the elements of composition, which 

 is the sole foundation of the supposition that cry- 

 stallography points out the actual elements, disap- 

 pears on being scrutinized : and when Haiiy, pressed 

 by this difficulty, as in the case of fluor-spar, put 

 his integrant octohedral molecules together, touch- 

 ing 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 derivation 

 was made more general and simple by Weiss and 

 others. 



"When, in 1809, I 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 ex- 

 pression. 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 gra- 

 dually unfolded to my hands, that which really 



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



