OcTOBER 20, 1899.] 
ical processes in plants and is here presented. 
Following the treatment of the Spermatophytes 
in the manner indicated is work on the great 
groups of plants. There will be some who will 
take exception to the choice of types. March- 
antia, for example, is a very antiquated and 
highly respectable laboratory type and possesses 
historical inertia, but it is hardly the best possi- 
ble representative of the Hepatic. Concern- 
ing these outlines it may be said that only the 
broad lines are laid down, and plenty of work 
is left for the teacher to do in intelligently 
planning the details of the laboratory work. 
The most valuable and distinctive feature in 
this portion of the book is the discussion of the 
pedagogics involved in each stage of the course. 
These must be passed with bare mention, though 
they deserve full treatment. 
It is satisfactory to know that morphological 
study is considered of great value in the training 
of students and that the diagrammatic rather 
than the artistic representation should be re- 
quired. 
A few inadvertencies have crept in. Longi- 
tudinal sections of a Scilla or Hyacinth flower 
passing through two stamens will not give an 
appearance of the ovary as represented in pages 
239 and 240, assuch sections would pass through 
one of the partitions. It is not at all certain that 
the willow flower is theoretically primitive, and 
much more uncertain is it that ‘ color develops 
* * * to show where the nectar is.’ Insects at 
least, it appears, are probably color-blind, but 
possess a keen sense of smell. And it is to be 
hoped that the essay on page 175 will not be read 
as an example without drawing attention to the 
incorrect use of the word ‘endosperm,’ for which 
‘food materials’ would better be substituted. 
Altogether, however, we have in Professor 
Ganong’s book a very useful and timely work, 
which will surely doa great deal towards the 
bettering of botanical teaching in the schools, 
and one, moreover, as unique as useful. 
FRANCIS E. toy. 
TEACHERS COLLEGE. 
Reye’s Geometrie der Lage. Lectures on Geometry 
of Position. By THEODORE REYE, Professor 
of Mathematics in the University of Strass- 
burg. Translated by THomas F. Hoieats, 
SCIENCE. 
577 
M.A., Ph. D., Professor of Applied Mathe- 
matics in the College of Liberal Arts in 
Northwestern University. New York, The 
Macmillan Company. 1898. Part I., 8vo. 
Pp. xix + 248. 
As is well known this book, of which the first 
edition was published not more than thirty 
years ago, is the outgrowth of lectures delivered 
before the engineering students in the Polytech- 
nic school at Zurich. These students were later 
to take lectures on Graphical Statics by Profes- 
sor Culmann who, in the treatment of his sub- 
ject, made free use of Von Staudt’s ‘ Geometrie 
der Lage.’ To get the most out of Culmann’s 
work it was necessary that the student should 
not only be well acquainted’ with the conics, 
quadric surfaces, etc., but that he should also 
have what may be called a well-cultivated geo- 
metric imagination, in order that he might 
easily realize for himself a clear mental picture 
of the space figures which play such an impor- 
tant part in the engineer’s work. 
It is hardly too much to say that for the spe- 
cial purpose he had in view, no better means 
than the projective geometry could have been 
employed by Professor Reye ; and one who has 
read his masterly treatment of the subject must 
always be grateful to him for the pleasure and 
profit derived therefrom. 
It seems to us that there is a rapidly growing 
interest in pure geometry in this country, and 
that its real merit as an instrument of education 
is coming to be more fully recognized. Rightly 
presented, the charm of the subject itself, which 
is free from the trammels of the metric geom- 
etry of Euclid, is immediately experienced by 
students. 
Although the geometry of position is often in- 
troduced by means of cross ratios, which (at least 
apparently) involve measurements, yet Reye’s 
treatment is entirely free, even at the beginning, 
from any dependence upon metric relations. He 
has, however, beautifully shown that metric re- 
lations, especially those connected with the conic 
sections, present themselves very naturally as 
special cases of general non-metric theorems. 
This, of course, may also be said of two other 
excellent books, viz., Cremona’s ‘Projective 
Geometry’ and Von Staudt’s ‘Geometrie der 
Lage’ ; but Von Staudt is too brief to be easily 
