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XI. Notices 7'especting New Booh. 



A Treatise on Crystallography , by W. H. Miller, F.R.S., Professor 

 of Mineralogy in the University of Cambridge. 



T T is well known to those who have attended to the subject of cry- 

 -■ staUograph)^ that the classification of crystalline forms introduced 

 by Haiiy, as well as the methods of expressing these forms and of cal- 

 culating their relations, have been in a great measure superseded by 

 other modes of treating the subject. The distinction of systems of 

 crystallization proposed by Weiss and Mohs has been generally ac- 

 cepted among crystallographers ; and the angles made by faces, 

 edges, and the like, instead of being deduced by means of geome- 

 trical reasoning, have been obtained by the more general methods of 

 spherical trigonometry and analytical geometry. Weiss may be 

 looked upon as the person who first introduced this more general 

 mode of calculation ; and he has been followed by G. Rose, KupfFer, 

 Kohler, Naumann, Neumann, Grassmann, Hessel, and others, in Ger- 

 many, and by Mr. Levy, Mr. Brooke, and Mr.jWhewell in England. 

 Along with these different modes of calculation, different modes of 

 notation for crystalline forms have also been employed. The old 

 unsystematic notation of Haiiy has been modified and retained by 

 Mr. Brooke, Mr. Levy, and Mr. Phillips in England, and by several 

 French writers ; while Professors Mohs and Weiss have each intro- 

 duced his own method of notation. 



The notation of Mohs, in itself most superfluously cumbrous and 

 unsymmetrical, has been made the basis of a much improved system 

 of notation by Prof. Naumann ; and the symbols of Weiss, which 

 are really the most general, and depend upon a single convention, 

 have been somewhat simplified by Mr. Whewell. In this state of 

 the subject, we turn with great interest to the treatise of Professor 

 Miller, who from his familiarity with analysis is able to give to cry- 

 stallographical methods all the generality and simplicity of the 

 best school of mathematics, and who likewise, from his acquaint- 

 ance with special minerals, is not likely to fail in furnishing abun- 

 dant exemplifications of his general methods. We may state in Pro- 

 fessor Miller's own words the selection which he has made of a 

 notation and mode of calculation. " The crystallogi-aphic notation 

 adopted in the following treatise is taken, with a few unimportant 

 alterations, from Professor Whewell's memoir on a general method 

 of calculating the angles of crystals, printed in the Transactions of 

 the Royal Society for 1825. The method of indicating the posi- 

 tions of the faces of a crystal by the points in which the radii drawn 

 perpendicular to the faces meet the surface of a sphere, was invented 

 by Prof. Neumann of Konigsberg (BeitrUge zur Krystallonomie), and 

 afterwards, together with the notation, re-invented independently by 

 Grassmann (Zur Krystallonomie und geometrischen Combinations - 

 lehre). The use of this method led to the substitution of spherical 

 trigonometry for the processes of solid and analytical geometry in 

 deducing expressions for determining the positions of the faces of 



Phil. Mag. S. 3. Vol. 16. No. 100. Jan. 1840. F 



