The American Naturalist. 



[January, 



York : MacMillan & Co. Pp. xii and 512 ; figs. 597, pi. viii : price 



This "Crystallography" is a real addition to the literature of the 

 subject that it treats. Its appearance reminds one strongly of Groth's 

 " Physiographische Krystallographie," although the book is by no means 

 a reproduction of the German treatise. The latter discusses the sub- 

 ject from the side of solid symmetry, whereas the former deals with it 

 rather from the analytical point of view. The first 187 pages of the 

 volume treat of the general relations of crystal planes and of zones. 

 The next 200 pages take up the six crystal systems beginning with the 

 cubic, and discuss in order the holosymmetrical and the merosymme- 

 trical forms, combination of forms and twinned forms. Chapter VIII, 

 embracing pages 388-463, is devoted to crystal measurements and cal- 

 culations, and the final chapter to the projection and drawing of crys- 

 tals. The plates show the projection of the poles of the most general 

 form and of its derived hemihedral and tetartohedral forms in each 



It is almost needless to state that the work of the author is based ex- 

 clusively on the system of indices, known generally as the Miller sys- 

 tem. Not only are the faces of crystal forms studied through the aid 

 of the spherical projection, but the individual planes are discussed 

 solely in terms of their normals. No reference is made to other sys- 

 tems of notation, nor to other methods of projection than those elabora- 

 ted. The book might have been of a little more practical value had 

 the author at least referred to other systems, but its unity might have 

 suffered. As it is, the volume is a very complete exposition of crystallo- 

 graphy from the Miller standpoint, and it will, without doubt, prove 

 of inestimable value in popularizing this— the most beautiful method 

 of studying the subject. Of course, the treatment is purely mathemat- 

 ical, but the mathematics used are simple enough to be understood bv 

 any one acquainted with the methods of spherical geometry. To the 

 student of minerals too much emphasis will seem to be placed on the 

 theoretical aspect of the development of crystal forms, but to the 

 specialist in crystallography, the emphasis will appear to be placed 

 just where it belongs— on the possibility of deriving all possible sym- 

 metrical polyhedrons from certain simple abstract notions concerning 

 pairs of planes, at the basis of which is the principle of the rationality 

 of the indices. 



to the student of fori 

 Nevei 



doubt that the treatise before us will appeal less strongly 



by the former, if, for r 



alytical proclii 



