100 On G-ystalhgraphj. 



of their principal angles, and showed (what was a very es- 

 sential point) that these angles were constant in each va- 

 riety. In a word, his crysrallocraphy is the production of a 

 very extensive and highly useful course of study. 



'the illustrious Bergman, bv endeavouring to penetrate to 

 the mechanism of the structure of crystals, considered the 

 different forms relative to one and the same substance as' 

 produced bv a superposition of planes, sometimes constant 

 and sometimes variable, and decreasing around one and the 

 same primitive form. He applied this primitive idea to a 

 small number of crystalline forms, and verified it with re- 

 spect to a variety of calcareous spar* by fractures, which 

 enabled him to ascertain the position of the nucleus, or of 

 the primitive form, and the successive order of the laminae 

 covering this nucleus. Bergman, however, stopped here, 

 and did not trouble himself either with determining the laws 

 of structure, or applying calculation to it. It was a simple 

 sketch, drawn en passant, of the most prominent point of 

 view in mineralogy, but in which we see the hand of the 

 same master who so successfully filled up the outlines of 

 chemistry. 



In the researches which T undertook about the same pe- 

 riod on the structure of crystals \, I proposed combining 

 the form and dimensions of integrant molecules with simple 

 and regular laws of arrangement, and submitting these laws 

 to calculation. This work produced a mathematical theory, 

 vhich I reduced to analvtical formulce, representing every 

 possible case, and the application of which to known forms 

 leads to valuations of angles constantly agreeing with obser- 

 vation. 1 shall explain the principles of this theory by the 

 help of reasoning alone, and of some projections which will 

 facilitate their explanation. Geometricians may acquire a 

 more correct and more detailed knowledge of the subject by 

 perusing the calculations which are given separately in this 

 work. 



THEORY OF THE STRUCTURE OF CRYSTALS. 



Primitive Forms. — The idea of referring to one of the same 

 primitive forms all the forms which may be assumed by a 

 mineral substance, of which the rest may be regarded as 

 being modifications only, has frequently suggested itself to 

 various naturalists who have made crystallography their study. 

 It was in consequence of having regarded it in a false point 



♦ This is wli.it has been called dent de aichon, but which I call metastatic. 



•f The members of the Academy of Sciences were acquainted with my first 

 Essavs on this subject, when they received Bergman's Memoir, which was 

 communicated to mc as being- interesting. 



of 



