242 HISTORY OF MINERALOGY. 



tion of deducing their consequences is made more 

 and more general and symmetrical : which we have 

 seen already exemplified in the history of celestial 

 mechanics after the time of Newton. It does not 

 enter into our plan, to dwell upon the various steps 

 in this way made by Levy, Naumann, Grassman, 

 Kupffer, Hessel, and by Professor Miller among our- 

 selves. I may notice that one great improvement 

 was, the method introduced by Monteiro and Levy, 

 of determining the laws of derivation of forces by 

 means of the parallelisms of edges; which was 

 afterwards extended so that faces were considered 

 as belonging to zones. Nor need I attempt to 

 enumerate (what indeed it would be difficult to 

 describe in words) the various methods of notation 

 by which it has been proposed to represent the 

 faces of crystals, and to facilitate the calculations 

 which have reference to them (L). 



Confirmation of the Distinction of Systems by 

 the Optical Properties of Minerals. Brewster 

 I must not omit to notice the striking confirmation 

 which the distinction of systems of crystallization 

 received from optical discoveries, especially those of 

 Sir D. Brewster. Of the history of this very rich 

 and beautiful department of science, we have already 

 given some account, in speaking of optics. The first 

 facts which were noticed, those relating to double 

 refraction, belonged exclusively to crystals of the 

 rhombohedral system. The splendid phenomena of 

 the rings and lemniscates produced by dipolarizing 



