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XL Notices respecting Next) Books, 
A Treatise on Crystallography , by W. H, Miller, F.R.S., Professor 
of Mineralogy in the University of Cambridge. 
J T is well knowTi to those who have attended to the subject of cry- 
stallography, 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culating their relations, have been in a great measure superseded by 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 sy sterns 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, Kuplfer, 
Kohler, Naumann, Neumann, Grassmann, Hessel, and others, in Ger- 
many, and by Mr. Levy, Mr. Brooke, and Mr.|Whewell 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 wniters ; 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 w^hich 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 Kdnigsberg {Beitrdge 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, IS'lO. F 
