AUGUST 29, 1912| 
very few school courses. The educational value 
of solid geometry is gradually becoming recog- 
nised, and it is not improbable that this change of 
attitude may affect the teaching of trigonometry. 
(6) This is a book which should prove of deep 
interest to all students of geometry. The author 
has been able, by confining himself to the methods 
of cross-ratio, to attain a thoroughness of treat- 
ment which has been impossible for previous 
writers, who have combined the theory of 
cross-ratio with other methods of projective 
geometry. There is much in this volume that is 
original, and numerous references are given to 
other works. One of the most valuable features 
is the insertion of copious historical notes. The 
author has made a special study of ancient 
geometry, and all who are interested in the 
development of the subject will value highly the 
results of his researches. 5 
The book falls into two parts: the first deals 
with pencils and ranges of the first order, and 
contains a comprehensive account of the theory 
of homography and involution, special attention 
being directed to the practicability of construc- 
tions; the second gives a selection of the applica- 
tions to the conic, in particular the theory of 
ranges of the second order and conics having 
double contact. There are, in addition, 
appendices, one of which gives Pappus’s account 
of the Porisms of Euclid, and the other a proof of 
Pascal’s theorem by the methods of Euclid and 
Apollonius. 
The treatment goes considerably beyond the 
requirements of the ordinary scholarship candidate, 
so that pressure of work will probably not admit 
of its being read at school. But we hope that 
it will find a place in the course of reading at 
the university, for it is essentially a scholarly 
treatise. 
(7) This volume contains an introductory treat- 
two 
ment of algebra and geometry, the latter pre- | 
dominating. The chief feature of the book is the 
admirable nature of the examples. There 
greater variety of form and freshness of character 
than we have seen in any other text-book of this 
kind. The intrinsic difficulties are few, the pupil 
being required to show common sense and self- 
reliance rather than technical skill. Probably the 
better plan would be to use it in conjunction with 
other text-books rather than by itself. We hope 
it will become widely known. 
(8) This is a text-book of the old-fashioned type. 
There is little numerical work, the general angle 
is introduced at an early stage, the formule for 
ig a 
sums and products and for multiple angles pre- 
cede the solution of triangles, and there is no 
NO. 2235, VOL. 89| 
NATURE 
! 
657 
simple work on heights and distances. The 
quality of the paper used is distinctly poor- 
(9) This volume presents in a fairly compact 
form a course of solid geometry, mainly practical 
| and descriptive; but some analytical work is also 
included. No claim is made to any originality in 
treatment. The book is divided into three parts: 
the first contains a discussion of the solid angle 
formed by three planes, the representation in plan 
and elevation of the regular solids in simple posi- 
tions and problems on sections; the second deals 
with plane and tortuous curves with special refer- 
ence to the helix; and the last with surfaces of 
revolution, cylinders, and ruled surfaces, the 
method of index notation being fully explained. 
Owing to the small size of the page, some of the 
figures are printed across the binding, but in other 
respects they are very clear. There are no exer- 
cises. 
(10) We cannot praise too highly this small 
volume; it is both simple and comprehensive. 
The subject of graphical statics is of real educa- 
tional value. To regard it as suitable only for 
engineering students is an error which is now 
generally recognised. The mathematical specialist 
and the boy who is devoting time to the subject 
for the sake of a general education will alike 
profit by a course of this character. But neither 
of them needs that developed technique which the 
engineer or architect must acquire. One hour a 
week for a single term for the specialist, and about 
twice as much for the amateur, is sufficient to 
cover the range of this book. The boy who needs 
it for professional purposes will, however, have to 
devote three or four terms to it. The text is 
clearly put and illustrated by a number of excellent 
diagrams. There is a_ first-rate collection of 
examples. 
(11) Dr. Besant’s treatise on Hydrostatics, 
which was published about forty years ago, is so 
well known that any comment upon it is super- 
fluous. It has now reached its seventh edition ; 
but the alterations and additions that have been 
made are comparatively few. In appearance it is 
now rather more attractive, owing to the use of 
a larger page and wider spacing. Among the 
additions may be noted a treatment of stability of 
equilibrium by the principle of energy, which 
occupies nine pages, the use of Weéierstrass’s 
/ notation in some of the capillarity results which 
involve elliptic integrals, and a more comprehen- 
sive account of the equilibrium of revolving 
liquids. The collection of examples has also been 
improved by the introduction of a large number 
of problems taken from recent university examina- 
tion papers. 
