614 

MATHEMATICAL CRYSTALLOGRAPHY. 
An Amateur’s Introduction to Crystallography 
(from Morphological Observations). By Sir 
W. P. Beale, Bart. Pp. vii+220. (London: 
Longmans, Green and Co., 1915.) Price 
4s. 6d. net. 
HIS exposition of crystallography has been 
written by “an amateur” with the inten- 
tion to help “other amateurs.” Amateurs differ, 
however, very widely in the variety and extent 
of their interests and also in their keenness. The 
author has evidently had a mathematical training, 
and it is this aspect of the subject that specially 
appeals to him. Very few amateurs, such as 
those possessing a collection of minerals, would, 
we imagine, be anxious to begin by calculating 
the axial ratios of their crystals. They would 
rather wish to gain some insight into the general 
relations of the external forms and symmetry of 
crystals; and they would be repelled by pages of 
mathematical discussion and formule. Having 
produced such a work on crystallography, the 
author must no longer regard himself as a mere 
amateur, but as a serious crystallographer. For 
these reasons the book cannot be recommended to 
amateurs; it should, in fact, be carefully kept out 
of the reach of anyone who displays the slightest 
curiosity respecting crystals, otherwise the spark 
will surely be extinguished. On the other hand, 
the book will be of real value to the serious 
student who has already made some start in 
crystallography, for it will present the subject to 
him in a somewhat different light from that given 
in the ordinary text-books; and taking the two 
together the subject will no doubt be studied more 
intelligently. 
The author plunges into his theme by regarding 
a crystal as a geometrical polyhedron, and select- 
ing three edges as axes of reference, he explains 
clearly how the positions of all the other surfaces 
of the solid are fixed in terms of the Millerian 
system of notation. Commencing with the most 
general (and difficult) case, namely that of the 
anorthic system, he leads the unfortunate 
reader through the maze of spherical triangles 
necessary for the calculation of the. angles of 
inclination and the relative lengths of the axes of 
reference. The remaining systems of crystals are 
logically treated in turn, ending with the cubic. 
Here the important idea of symmetry is only inci- 
dentally touched upon. This is, however, treated 
rather more fully in the succeeding description 
of the merohedral forms belonging to each system. 
There is a long appendix on methods of calcula- 
tion, and another on the drawing of crystals from 
the calculated elements. 
NO. 2388, VOL. 95] 
NATURE 

[AUGUST 5, I9I5 

The 136 illustrations (several of which are 
repeated for convenience of reference) are a special 
feature and are entirely original. These are well 
and clearly drawn, and the method of giving the 
axes of reference in red adds still more to their 
clearness. There is a slight slip in fig. 64, whilst 
fig. 65 is quite wrong. The book is clearly 
printed in large type, and there are but few 
misprints; {hko}, etc., instead of {hko}, etc., 
however, recurs throughout the volume. 
Liwees: 

OUR BOOKSHELF, 
The Medical Annual. A Year Book of Treatment 
and Practitioner’s Index.  Thirty-third year, 
1915. Pp. cxx+830. (Bristol: J. Wright and 
Sons, Ltd.; London: Simpkin, Marshall and 
Go: Ltd, 1915-)) Pricejitossinet: 
Tuts, the thirty-third annual issue of this publica- 
tion, contains a summary of the year’s (1914) con- 
tributions to medicine and surgery by a number of 
competent authorities. The exceptional lateness 
of the isue is accounted for by the strain and 
distraction of a great war, all the contributors, 
fully occupied as they are in normal times, having 
been working under exceptional stress from mili- 
tary duties and contingent work. The list of 
contributors is a sufficient guarantee of the 
accuracy and up-to-dateness of the information 
given. Thus we find an account of the latest 
work on typhus and cerebro-spinal fevers, both 
of topical interest at the present time. Trypanoso- 
miasis is dealt with by the competent hand of Sir 
Leonard Rogers, and the article gives full informa- 
tion of the latest work on the parasitology and 
treatment of this important condition. About 
twenty pages are devoted to the important sub- 
jects of radio-activity, X-rays, and electro-thera- 
peutics, and useful sections deal with the changes 
in the new British Pharmacopeeia of 1914. Special 
articles on naval and military surgery are in- 
cluded, together with references to personal ex- 
perience in the treatment of wounds. A number 
of full-page and other illustrations are included, 
and form a special feature of the volume; they 
illustrate various disease conditions, details of 
surgical technique, surgical appliances, patho- 
logical features, etc. The two plates of skin 
eruptions in pellagra are beautiful examples of 
colour photography. The “Medical Annual” is 
a book eminently suited to the needs of the busy 
practitioner who desires to keep abreast with 
modern progress. 
Wisconsin Geological and Natural History 
Survey. Bulletin No. xxxiv. Economic Series, 
No. 16. Limestone Road Materials of Wis- 
consin. By W. O. Hotchkiss and E. Steidt- 
mann. Pp. vili+137. (Madison, Wis. : Pub- 
lished by the State, 1914.) 
Tuis bulletin has been published for the purpose 
of helping to conserve the expenditure of the “vast 
