736 The American Naturalist. lAs; 
The appearance of this edition of Professor Groth’s work marks an 
epoch in the history of crystallography, and there can hardly be a 
doubt that all the essential features of his treatment will soon be in- 
troduced at least in all advanced courses in the science. Crystallo- 
graphers will look forward with anticipation to the appearance of the 
great work on chemical crystallography on which Professor Groth is 
now engaged. 
Tables of the Thirty-two Classes of Crystal Forms.—In 
1892 Groth’ issued a table giving the stereographic projection to indicate 
the most general form of each of Gadolin’s classes of crystal forms, to- 
gether with the position of the crystallographic axes and the axes and 
planes of symmetry of the class. These differ from those of his later 
published text-book only in that the trigonal crystal system is not in- 
troduced in the secondary classification. This table has the great ad- 
vantage of bringing all the projections together on a single plate so 
that mutual relations may be made out. Wiilfing* has very recently 
issued a series of seven plates with explanatory text which give not 
alone the stereographic projections to illustrate the kind of symmetry 
of each class, but also sketches to indicate the character of all the 
kinds of crystal forms which can possibly occur with that kind of sym- 
metry. They constitute an introduction to or a synopsis of the subject 
of geometrical crystallography, much as it is treated by Groth, and 
will be of service in making the subject clear to a beginner, particu- 
larly one who cannot easily bring his mind to the condition of pictur- 
ing geometrical forms. Wiilfing has, however, unfortunately adhered 
to the old arrangement, and treats the classes of highest symmetry first ; 
and, moreover, has not utilized the abbreviated nomenclature adopted 
by Groth. This and the different numeration of the classes which the 
old arrangement involves, will introduce confusion, and are the serious 
mistakes of the little book. In his preface Wiilfing recalls an interest- 
ing passage in Goethe, which brings out so well the difference between 
the position now held by the science of crystallography and that which 
it occupied at the time the words were written (they were first printed 
in 1829) that I am inclined to introduce it here. Goethe wrote refer- 
ring to the science of crystallography as follows: 
3 Uebersichtstabelle der 32 Abtheilungen der Krystallformen mit Erlaiiterung- 
en, Beispielen, und graphischer Darstellung nach Gadolin zusammengestellt von 
P. Groth. Engelmann, Leipzig, 1892, 1 Mark. 
* Tabellarische Uebersicht der einfachen Formen der 32 krystallographischen. 
Symmetriegruppen zusammengestellt und gezeichnet von Dr. E. A. Wiilfing. 
Koch, Stuttgart, 1895. 
