606 Notices respecting New Books. 
rotation. The theory of the point-groups is worked out in detail in 
Chapters IV., V.,and VI., and it is proved that there are 32,and only 
32, finite groups of movements consistent with the law of rational 
indices. ‘Two brief chapters on the relations between crystalline 
symmetry and physical properties and on the growth of crystals 
complete Part I.; and the rest of the book is devoted to the structure 
theory of crystalline matter. There is thus presented for the first 
time to English readers in connected form the geometrical theory of 
crystal structure. The 230 space groups capable of representing 
crystalline form are worked out in sufficient detail, and are pro- 
fusely illustrated by diagrams drawn on the lines suggested by 
Federow. Mr. Hilton lays no claim to originality, but aims at 
reproducing mainly the system developed by Schoenflies. He has, 
however, laid other writers under contribution; and his own 
powers are in evidence in the clearness of exposition and compact- 
ness of demonstration. The argument is frequently very con- 
densed, and every line demands the closest attention on the part 
of the reader if he wishes really to follow the demonstration. 
There is a steady strain upon the geometrical and kinematical 
imagination, a strain which comparatively few of those who are 
practically interested in crystallographic questions will care to 
undergo. But the mathematical student interested in the theory 
of groups will be greatly benefited by a careful study of Mr. Hilton’s 
pages. Towards the close of the book reference is nade to dynamic 
possibilities of .crystalline structure as distinguished from geome- 
trical possibilities. Here, of course, we encounter questions of 
molecular stability which can hardly at present be stated, far less 
solved. 
Thermodynamics and Chenustry : A non-Mathematical Treatise for 
Chemists and Students of Chemistry. By P. DunEem, Professor of 
Theoretical Physics at the Unwersity of Bordeaux. Authorized 
translation by George K. Burgess. New York: John Wiley & 
Sons. 1903. Pp. xxi+ 445. 
A LARGE number of chemists and students of chemistry find it 
difficult, if not impossible, to follow the modern developments of 
the theory of chemical equilibria, by reason of their insufficient 
knowledge of the mathematical processes whose aid must be 
invoked in a thorough discussion of the subject. To such the 
translation of Professor Duhem’s book will be a welcome addition 
to their scientific library, as the author deals with the subject 
withovt the use of analysis. Such a method must necessarily have 
its shortcomings, and the reader must now and then be asked to 
take certain things for granted which could readily be demonstrated 
were the use of mathematical analysis not forbidden. On the other 
band, the non-mathematical reader has the satisfaction of knowing 
that, having consented to take certain statements on the authority 
of the mathematicians, he will not, in this book, have to wade through 
pages of, to him, unintelligible symbols. 
