NovEMBER 22, 1906 | 
parallels, triangles, parallelograms, and circles, with 
areas, loci, and symmetrical figures. There is a 
short introductory course of experimental geometry, 
followed by a preliminary chapter on the “‘ science 
of geometry,” in which fundamental concepts, 
axioms, and deductive processes are discussed. Thus 
prepared, practical work and logical development pro- 
ceed together. There are exercises in abundance of 
all types, theoretical, constructive, and numerical, the 
answers to the latter being given. There is a useful 
index of terms, and a collected list of propositions 
very convenient for reference. The book should prove 
of great value to teachers and pupils alike, and seems 
altogether good. 
(3) The new volume by Messrs. Baker and Bourne 
deals with the geometry of three-dimensional space. 
Book vi. corresponds with Euclid xi., and Book vii. 
gives the mensuration of the simple geometrical 
solids. The high standard of the authors’ previous 
work is maintained. The treatment is clear and con- 
cise, the printing is excellent, and useful sets of 
exercises are provided for class work. 
(4) The ‘Shilling Arithmetic’? by Messrs. Loney 
and Grenville is a handy little volume intended more 
especially for use in secondary schools, and consist- 
ing mainly of a very large collection of graduated 
examples with explanatory notes. Physical as well 
as commercial arithmetic is represented, though ex- 
amples of the latter type predominate. Answers are 
given at the end, and altogether the book is very 
suitable for its purpose. 
(5) Mr. Borchardt’s ‘‘ Junior Arithmetic”? is very 
like the one just noticed, but more use is made 
of graphs, the commercial type of exercise is less 
prominent, and the treatment follows more closely 
the scheme of the committee of the Mathematical 
Association. A special feature of the book is a set 
of 385 examples arranged as a graduated set of fifty- 
five test papers covering the whole subject. The 
course will form a good preparation for the Oxford 
and Cambridge locals, the London matriculation, and 
similar examinations. 
(6) The ‘ Junior Arithmetic’? by Messrs. Pendle- 
bury and Robinson is very similar in character to the 
two just mentioned, and is well suited for use under 
similar conditions. In all three there are too many 
exercises of the kind ‘‘ If 120 men can build a house 
60 feet high in 15 days, how many men will it take 
to build one 55 feet high in 10 days?’’ But the 
teacher can delete these and still have ample choice. 
The book can be obtained with or without answers. 
(7) Many students rightly wish to acquire an 
elementary working knowledge of the calculus at a 
comparatively early stage. By such the preliminary 
course of Mr. Angus will be appreciated. The author 
confines himself to the algebraical, trigonometrical, 
and exponential functions, and has thus space avail- 
able for ample illustration. There seems to be a 
want of clearness in the author’s notion of a rate; 
for instance, on p. where in the expression 
dV /aD=zD*/2, relating to a sphere, V denoting 
volume, he puts dV equal to 7.5 cubic inches per 
second, a statement which must perplex a thoughtful 
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NATURE 
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7 
student. 
be recommended to beginners who have some know- 
ledge of squared paper work. 
(8) The ‘‘ College Algebra’ by Mr. Fine is a very 
masterly and fascinating treatment of the subject, 
However, the book is a good one, and can 
whether from the standpoint of logical completeness 
or of practical computation. The books is divided into 
two parts, the first and smaller of which establishes 
the fundamental for numbers, 
rational and irrational, imaginary and complex, the 
discussion being based ‘‘on the notion of cardinal 
number and the notion of order, as exhibited in the 
first instance in the natural scale 1, 2, 3,... 
The second and main part of the work deals most 
thoroughly with the successive developments, and 
carries the subject so far as to include, in the later 
portions, the theory and solution of cubic and _ bi- 
quadratic equations, determinants, the binomial, ex- 
ponential, and logarithmic series, the properties of 
continuous functions, &c. The volume is beautifully 
printed, and whether adopted or not as a text-book 
in this country, so excellent a treatise should be found 
in the library of every teacher of mathematics. 
(9) As a first course of trigonometry for beginners 
the elementary text-book of Mr. D’Arcy is well con- 
ceived, the work being closely associated with quanti- 
tative practical geometry, and being carried only so 
far as problems on heights and distances and the 
solution of triangles, complex trigonometrical trans- 
formations being wisely absent. At the same time 
the idea of the book is not well carried out in detail. 
The style is unattractive, and the illustrations are not 
very illuminating. The figures are badly printed, and 
sometimes are scarcely legible. More attention might 
well have been given to the solution of triangles by 
means of right-angled triangles, and it seems a mis- 
take to have omitted to include the four-figure tables 
in the text. The book is designed for candidates 
taking the Cambridge previous or the Cambridge 
general examination, and test papers at the end con- 
tain many questions selected from these examination 
papers. 
(10) The ‘* Descriptive Geometry ’? by Mr. McLeod 
is intended as a minimum course for engineering 
students. It deals in a simple and straightforward 
manner with elementary problems on points, lines, 
and planes, polyhedra, curved surfaces and tangent 
planes, including several skew surfaces, sections, 
envelopes and developments, trimetric projections, and 
shadows. 
laws of operation 
” 
PHOTOGRAPHIC TOPICS. 
The Complete Photographer. By R. Child Bayley. 
Pp. xv+ 410. (London: Methuen and Co, n.d.) 
Price 10s. 6d. net. 
FTER having read this volume, the question that 
naturally presents itself to the reviewer is, to 
what class of readers will it appeal? The author, in 
his preface, states that he has made no attempt to 
compete with the many books on photography that 
have already been published, whether scientific trea- 
tises upon the principles underlying the practice or 
manuals of practical instruction. He states, further, 
