1895.] Mineralogy. 735 
Bravais’s space lattice theory of molecular structure is treated compre- 
hensively, with addition of some of the modifications which have been 
made to it by Sohfiche, Federow and Schénflies. Professor Groth 
states in his preface, that “ the edifice of crystal knowledge is one of 
the best founded in theory of any in the entire realm of physics.” 
The second part of the work, that treating the geometrical proper- 
ties of crystals, bears but slight resemblance to the corresponding por- 
tion of the former editions. Instead of the primary classification of 
Naumann into six crystal systems with their partial forms, which is in 
general use, the differentiation of Gadolin into thirty-two classes of 
forms which represent all possible kinds of crystal symmetry, is adopted. 
This classification does away with hemihedral, hemimorphic and tetar- 
tohedral divisions, which cause so much difficulty in teaching, and is 
logically and scientifically superior to the classification in use. Profes- 
sor Groth thinks that the simplification of the nomenclature which this 
classification makes possible, will make the subject easier for the stu- 
dent, but it seems to us that the additional conceptions of symmetry 
(centre of symmetry, and 1, 2, 3,4 and 6 zahlige axes of symmetry) 
which are used will more than outweigh these advantages in simplicity, 
except for students who have what the Germans call raiimliche Vor- 
stellungsgabe highly developed. Of the thirty-two classes of forms, 
three have now no known representative, but when it is remembered 
that since 1887 representatives have been discovered for six classes 
which before lacked examples, the probability is great that examples 
will soon be found of all classes. The crystal systems are retained as 
a sub-classification to indicate relationships, and a seventh system—the 
trigonal system—is added to include those classes which have a 3-zählige 
axis of symmetry (rhombohedral, pyramidal, trapezohedral, etc., mak- 
ing in all seven classes). The word cubic is adopted for the isometric 
system. Another important change lies in the arrangement. The 
class of least symmetry is considered first, and the others in the order 
of increasing symmetry. 
The subject of the calculation and drawing of crystals, which in the 
former editions of the work was scattered under the different systems 
in the geometrical portion, is here brought together and expanded to 
over 60 pages in the beginning of part III. It is followed by a descrip- 
tion of the methods of crystal measurement, in which is contained what 
will be to many, new descriptions of recently devised apparatus. Such 
is a modification by Klein and Fuess of the Federow universal attach- 
ment to the microscope stage. 
