AuGusT 27, 1914] 
NATURE 
663 
acting outwards along the normal. We are glad 
to see that statics and dynamics are taken 
together, instead of, as often happens, being 
made to form distinct parts of the course. 
(3) Most of the subject-matter of this book is 
included in the ‘“‘Numerical Trigonometry” by 
the same authors, already noticed in these 
columns. There are additional chapters on solid 
geometry, multiple angles, and identities. 
(4) Following their usual custom, Macmillan 
and Co. publish in a single volume the collected 
mathematical papers for admission to Sandhurst 
and Woolwich for the years 1905-1913. All the 
diagrams are reprinted as set, and a complete list 
of answers is appended. The volumes of this 
series are invaluable for army class work. 
(5) The authors of this practical text-book have 
interpreted in an admirable manner the sugges- 
tions made in the Board of Education’s Circular, 
Number 807. The course is planned to cover five 
years, and deals with length, area, volume, 
weight, and time. In addition to setting out in 
detail the experiments to be made, there is a 
number of useful notes for the teacher, enumerat- 
ing such points as are likely to require special 
attention, detailing the requisite apparatus, and 
suggesting methods for organising the work of 
the class. Complete lists are also given at the 
end of the equipment that is (1) necessary and 
(2) desirable, together with useful information 
as to cost. The book is undoubtedly the work of 
eapable and enthusiastic teachers, and the variety 
of the exercises is evidence of the thought that 
has been expended in the selection of material. 
(6) The purpose of this book is to provide an 
account of the theory of proportion, suitable for 
elementary teaching. The main part of it is 
founded on an annual course of lectures given by 
the author in the University of London; but the 
concluding chapters are intended only for teachers 
or honour-students. 
One of the chief points of difference between the 
theoretical development adopted by Prof. Hill and 
that of Euclid is the establishing of properties 
of equalities of ratios by the use of Def. 5, Bk. v., 
instead of introducing Def. 7, Bk. v., which 
gives the test for distinguishing between unequal 
ratios. The author is of opinion that this greatly 
simplifies the difficulties students meet with. For 
the first nine chapters, which form the elementary 
course, little mathematical ability is required; 
and a clear idea should be obtained of the mean- 
ing and nature of irrationals. Part II. deals with 
geometrical applications of Stolz’s theorem on 
the test for equal ratios and further consideration 
of irrationals; and Part III. is historical, being a 
commentary on Euclid’s work. 
NO: 92339, VOL. 93] 
(7) This is the second volume of a treatise on 
mechanics, the first part of which deals with 
statics and has already been noticed in these 
columns. Together they form an excellent course 
of reading for scholarship divisions in secondary 
schools. In style, this volume closely resembles 
the first; the bookwork is cast in an interesting 
and refreshing form; the able student will find 
much that is highly stimulating, and the boy of 
ordinary capacity will appreciate the concentra- 
tion on the fundamental] processes required for the 
systematic solution of problems. Many boys are 
so easily bewildered by detail, that it is highly 
important to make them realise at the earliest 
moment how few and simple are the general 
principles of mechanics; and for this reason it is 
desirable to provide them with examples which 
require small analytical skill. In this respect, as 
in his volume on statics, Prof. Lamb has prce- 
vided exactly what is most needed. A certain 
number of the traditional problems are naturally 
included, but the main body have been selected 
to illustrate principles and clarify ideas. There 
is an interesting appendix on the relation of 
abstract dynamical principles to human experi- 
ence. 
(8) More than twenty-five years have passed 
since Prof. Klein’s classic treatise was first trans- 
lated into English, and the nature of its contents 
and the line of argument are so well known as to 
render any account at the present time super- 
fluous. In preparing this revised edition, Dr. 
Morrice has been fortunate in securing the 
assistance of Prof. Burnside. 
(9) If a set of n values of a slightly varying 
quantity are taken, the expression representing 
them most closely is obtained from a Fourier 
series. To assist numerical computation, these 
tables, arranged by Prof. Turner, give the values 
of terms of the type a,,, sin 70, a+,, cos70 to 
two significant figures, for values of n between 
8 and 22, where 0=27/n. 
OUR BOOKSHELF. 
India-rubber Laboratory Practice. By Dr. W. A. 
Caspari. Pp. viii+196. (London: Macmillan 
and, Cox, Jlatd’ te1oL4.) bnice cs? net. 
Ir must be a great temptation to any chemist who 
writes about rubber at the present time to devote 
a considerable amount of attention to the views 
that are in the air on the constitution of this ia- 
teresting substance, or substances, and to the 
bearing of recent developments in colloidal chem- 
istry on the problems presented by the prepara- 
tion and properties of rubber. Dr. Caspari has 
expressly omitted all reference to these subjects, 
and has limited himself entirely to the analytical 
problems which arise in the ordinary routine prac- 
