266 
NATURE 
[May 16, 1912 
main argument, with chapters on variation and 
heredity. 
A general criticism, applicable not only to this 
but to many other American books, is that too 
little is made of the classical researches that have 
created the subject and too much of the latest 
results of the latest bulletin. To some extent this 
defect is remedied in the lists of papers given at 
the end of each chapter, where the classical papers 
are usually included, but there are some omis- 
sions; for instance, at the end of the chapter 
dealing with nitrogen fixation by bacteria there is 
no reference to Winogradsky’s papers. This is a 
defect that the teacher will have little difficulty in 
remedying if he wishes to do so, while the in- 
clusion of newer work has, at any rate, the 
advantage of familiarising the student with the 
work going on at the various experiment 
stations. 
At the end of each chapter a number of practical 
exercises are given, bearing on the work that has 
been discussed. The experiments are simple and 
convincing, and cannot fail to be helpful to the 
student. References are also given to larger 
works so that any particular point can be looked 
up. The illustrations are numerous and very 
good. 
Probably few teachers of plant physiology 
realise how many practical applications of their 
subject there are, or how much is added to the 
interest of the discussions by bringing in a few 
illustrations from agricultural or horticultural 
Particularly in these latter days, when 
numbers of botanists and mycologists in different 
parts of the world are applying science to crop 
production, is there a great amount of material 
accumulating which must soon react on the study 
of plant physiology. The teacher, at any rate, 
wiil be well advised to look through this volume in 
search of illustrations, and he may find it worth 
while to adopt some of the methods. 
practice. 
NON-EUCLIDEAN GEOMETRY. 
Bibliography of Non-Euclidean Geometry, includ- 
ing the Theory of Parallels, the Foundations of 
Geometry, and Space of N Dimensions. By 
Dr. D. M. J. Sommerville. Pp. xii+ 404. 
(London : Harrison and Sons, St. Martin’s Lane, 
1911, for the University of St. Andrews, Scot- 
land.) Price 10s. net. 
Ca its subject, this bibliography 
seems at first sight extraordinarily large; 
but there are several reasons why it is not so 
formidable as it looks. The actual list of titles 
occupies pp. 1-261; this is arranged chronologi- 
cally, each year’s titles being indexed by the 
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authors’ names. ‘Then (pp. 261-310) we have a 
subject index, an alphabetical list of subjects, and 
an author index. Finally, Mr. Sommerville has 
included various topics not strictly belonging to 
the subject, but more or less closely connected 
with it; for instance, quaternions, Cantor’s theory 
of aggregates, Minkowski’s ‘‘ Geometrie der 
Zahlen,’’ and so on. At the other extreme, we 
have reviews of books, references to the subject in 
fiction, and even “‘the realm of spirits.” 
In a work of this kind it is better to be inclusive 
than exclusive; so long as the list is reasonably 
complete, and the subject-index arranged on sound 
principles, the compiler has done his duty. There 
is every reason to believe that, in both respects, 
Mr. Sommerville has achieved success. As a few 
examples out of many that could be given, we may 
note the entries under “time of two or more 
dimensions,” and “‘time as the fourth dimension,” 
the latter including a reference to Lagrange; 
those on the philosophy of geometry, significantly 
headed by Bergson; and, on the lighter side, those 
on the extension of magic squares and cubes to 
n dimensions. 
After making all deductions, we cannot fail to 
be impressed by the astonishing growth of this 
theory in recent times. Most remarkable of all, 
perhaps, is the fact that some eminent men of 
science are seriously suggesting time as, in a 
sense, a fourth dimension, the effect of which is 
to bring the physical universe sub specie eterni- 
tatis as a given configuration, parallel sections of 
which are realised by us as successive events, or 
aspects, in time. How far this is a mere way of 
speaking, or how far it may lead to a radical 
change in our assumptions of the ultimate undefin- 
ables of physics, it is too early to attempt to 
decide. Meanwhile, attention may be directed to 
M. Bergson’s “‘ Creative Evolution,’’ in which a 
distinction on purely philosophical 
grounds, between time as a metaphysical notion 
and the ¢ of mathematical physics. This conten- 
tion is not to be lightly dismissed, urged as it is by 
a philosopher who differs from the bulk of his 
profession in really understanding the methods 
and results of physical, biological, and mathemati- 
cal science. 
It is to be hoped that Mr. Sommerville’s excel- 
lent index will help to arouse even wider interest 
in the subject, which is not only fascinating and 
educative in itself, but, as we have just seen, not 
unlikely to be of wholly unexpected importance in 
the applications of mathematics to physics. The 
very last entry that we find is that of Minkowski’s 
collected mathematical memoirs; could anything 
be more suggestive ? G: Bu MM: 
is drawn, 
a 
