656 
NATURE 
[AuGUST 29, 1912 
worl, There is very little explanatory text in the 
pupil’s edition, which consists of a series of care- 
fully graduated sets of examples; but the volume 
designed for the teacher contains not only the 
answers and additional oral exercises, but also 
illustrations of the methods recommended for use 
and a large number of useful hints and cautions, 
the full value of which will be realised only by 
those who are acquainted with the varied difficul- 
ties of the beginner. The teaching of elementary 
arithmetic is a harder task than many people 
admit, and requires more skill and care than is 
often recognised. Success can be achieved only 
by a careful formulation of the scheme of work 
and of the methods to be employed. In this, the 
teacher’s edition should be most useful. It is 
thoroughly sound and trustworthy, and full of 
excellent suggestions. 
(2) The contents of this volume are best ex- 
plained by enumerating the headings of the six 
parts into which it is divided. These are (1) Intro- 
duction; (2) Kinematics; (3) Kinetics; (4) Statics; 
(5) Hydromechanics ; (6) Elasticity. It is assumed 
that the reader possesses an elementary knowledge 
of the methods of the calculus, and is not entirely 
unacquainted with the ideas of mechanics; the 
more elementary parts of the subject are therefore 
treated in outline, and are intended mainly for 
revision or reference. 
The section on kinematics opens with a discus- 
sion of the properties of vector quantities. This 
is followed by chapters on rectilinear motion, which 
includes the case of variable acceleration, motion 
in a curve subject to a central acceleration, analy- 
sis of plane rotations, motion in space with fixed 
and moving axes, consideration of different forms 
of linkages, and a brief but lucid account of the 
theory of strains. The treatment of kinetics is 
prefaced by a valuable and most interesting 
account, mainly historical, of the physical con- 
ceptions upon which the theory is based. The 
discussion of the motion of rigid bodies in this 
section and of the theory of attraction and general 
conditions of equilibrium in the next follows the 
customary lines. Only forty pages are devoted to 
hydrostatics and hydrokinetics, and about twenty 
pages to elasticity. There is an admirable collec- 
tion of miscellaneous examples at the end of the 
book. 
(3) This book is intended for use with beginners; 
but either thesauthor is not in sympathy with the 
recent changes in connection with the teaching of 
elementary trigonometry, or else he is writing for 
students who take up the subject at a late stage in 
their course. Now that it has become the custom 
for boys in the middle divisions of public schools to 
start trigonometry at a time when formerly they 
NO. 2235, VOL. 89] 
would have still been occupied with complicated 
arithmetical problems and algebraic manipulation, 
it is both necessary and instructive to lay great 
emphasis on the numerical aspect. Identity work 
and applications to the geometry of the triangle 
are unsuited to the purpose which this change in 
the curriculum serves. The present volume opens 
with a chapter on contracted arithmetic; the second 
chapter defines the trigonometric ratios, and gives 
rather more than thirty identities as examples on 
the fundamental formule; this is followed by the 
ratios of special angles and the solution of equa- 
tions; numerical applications to the right-angled 
triangle are consequently postponed to the fourth 
chapter, and even here the examples are far from 
adequate. Part i. closes with chapters on 
logarithms and the solution of oblique triangles. 
The subjects dealt with in the second part are 
circular measure, ratios of obtuse angles, addition 
formule, and applfcations to the triangle. The 
concluding part deals with the general angle, 
methods of proof by projection, and properties of 
the triangle and quadrilateral. The author has 
the gift of writing simply and clearly, and the 
printing is well up to the high standard of the 
Cambridge University Press. 
(4) The authors have followed the suggestions 
made in the Board of Education’s circular on the 
teaching of geometry. The fundamental concepts 
and theorems of geometry are illustrated by ex- 
perimental methods, and a varied collection of 
numerical exercises is supplied. | Formal proofs 
are reserved for the second volume, which contains 
the substance of Euclid I. 1-34. In our opinion, 
the value of this method of exposition is seriously 
affected if riders of a simple character are excluded 
{rom the preliminary stage. If the student is 
restricted to numerical work, he will be slow to 
appreciate and assimilate the elementary proper- 
ties of geometry. The disadvantage of opening 
with a formal course lies in the inherent difficulties 
of the proofs of the early theorems. But if the 
results of these are assumed, a very numerous 
set of applications can be made. 
(5) This volume contains in rather less than a 
hundred pages a brief account of the elements of 
plane and spherical trigonometry. It is written 
for the student who requires only a practical know- 
ledge of the methods of the subject. No attempt 
is made to give analytical dexterity, and all dis- 
cussion of geometrical applications is omitted. 
But great care is taken to impress on the reader 
the supreme importance of methodical arrange- 
ment of numerical work. Tables of logarithms 
and the trigonometric functions occupy the second 
half of the book. It is both curious and regret- 
table that spherical trigonometry is included in 
rata ee 
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