NOTES TO BOOK XV. 279 



method, Prof. Miller has produced a work on Crystallo- 

 graphy remarkable for mathematical elegance and sym- 

 metry ; and has given expressions really useful for calpu- 

 lating the angles of crystalline faces, (A Treatise on Crys- 

 tallography. Cambridge, 1839.) 



(M.) p. 243. I have, as in the first edition, placed 

 Sir David Brewster's arrangement of crystalline forms in 

 this chapter, as an event belonging to the confirmation 

 of the distinctions of forms introduced by Weiss and 

 Mohs ; because that arrangement was established, not on 

 crystallographical, but on optical grounds. But Sir David 

 Brewster's optical discovery was a much greater step in 

 science than the systems of the two German crystallogra- 

 phers ; and even in respect to the crystallographical prin- 

 ciple, Sir D. Brewster had an independent share in the 

 discovery. He divided crystalline forms into three classes, 

 enumerating the Hainan "primitive forms'" which belonged 

 to each ; and as he found some exceptions to this classifi- 

 cation, (such as idocrase, &c.,) he ventured to pronounce 

 that in those substances the received primitive forms were 

 probably erroneous ; a judgment which was soon confirmed 

 by a closer crystallographical scrutiny. He also showed 

 his perception of the mineralogical importance of his dis- 

 covery by publishing it, not only in the Phil. Trans. (1818), 

 but also in the Transactions of the Wernerian Society of 

 Natural History. In a second paper inserted in this latter 

 series, read in 1820, he further notices Mohs's System of 

 Crystallography, which had then recently appeared, and 

 points out its agreement with his own. 



Another reason why I do not make this great optical 

 discovery a cardinal point in the history of crystallography 

 is, that as a crystallographical system it is incomplete. 



