DECEMBER 17, 1903] 
NATROL, 
147 
to develop along divergent lines. Thus for art 
students one section of geometry to which great atten- 
tion is paid is that relating to decorative geometrical 
designs, the study of which requires the drawing of 
many inscribed and circumscribed figures, patterns, 
&é. For science students this branch is of compara- 
tively little interest. On the other hand, the geometry 
of vectors, a subject of first importance in science, has 
little attraction for the artist. Again, a student of 
science finds great use for his graphical constructions 
in the making of numerical computations, and the sub- 
ject for him is becoming more quantitative in 
character. It is thus inadvisable to compile a text- 
book which shall endeavour to meet the wants of both 
classes of students; the first two books under review 
are written for science classes, and are adapted to the 
first stage of the revised South Kensington syllabus 
in Science Subject I. 
The text-book by Messrs. Morris and Husband con- 
tains a large number of problems (more than 300) in 
plane and solid geometry, the solution of each being 
described in detail. The diagrams are clear and well 
printed, and are conveniently arranged to face the text. 
Each chapter closes with a useful collection of 
exercises. The syllabus is very completely covered as 
regards the matter, but the method of treatment cannot 
be said to correspond with its spirit. The student is 
told everything in minute detail. He is not sufficiently 
encouraged to thinlk and invent for himself, and it is 
difficult to see how his interest can be maintained and 
his mental faculties properly developed. The method 
employed in problem 123 is obviously incorrect, and 
will no doubt be altered at the first opportunity. 
In the volume by Mr. Burn, it is evident that the 
author’s main interest centres in solid geometry, and 
he teaches this branch of the subject well, the student 
being instructed how to make simple models for him- 
self, these being effectively used along with drawing 
in order to obtain a good grasp of this somewhat 
difficult subject. Too little attention seems to be given 
to plane geometry, and the student is not well 
grounded therein. The treatment of vectors is also 
meagre, and displays an inadequate conception of the 
scope and importance of this portion of the subject. 
Unfortunately some of the diagrams are needlessly 
small, and are trying to the eyesight. 
The remaining five volumes are concerned principally 
with theoretical geometry. The book by Messrs. 
Marshall and Tuckey is a collection of nearly 550 ex- 
amples arranged in groups. ‘‘The examples on 
practical geometry are intended primarily to lead up 
to geometrical reasoning, and only secondarily to give 
manual dexterity.’’ Many of the examples are associ- 
ated with a rider (distinguished by italic type), the 
truth of which will become evident as the figure is 
drawn, and which the reader is asked to establish by 
deductive reasoning. We notice with satisfaction that 
Euclid’s method for the common tangents to two circles 
is discarded as unpractical. The examples in mensura- 
tion might with advantage have been a little more 
experimental. For instance, it would have been a 
satisfaction to a student to verify the numerical value 
of 7; and an example might have been inserted asking 
NO. 1781, VOL. 69] 
for the area of a circle, to be obtained by the method 
of counting squares. The table of four figure 
logarithms which the authors give will prove very 
useful. We think that a simple table of functions 
of angles should also have been inserted and made 
use of in connection with some of the examples, 
especially those in mensuration. Teachers will find 
this large collection of examples very convenient, but 
its value would be enhanced by a further development ~ 
on modern lines. 
The second instalment of Mr. Barrell’s ‘‘ Elemen- 
tary Geometry ’’? comprises portions of Euclid ii., iii., 
iv. and vi., with some additional matter. In few of 
the recent text-books on the subject are the advantages 
of the reform in geometrical teaching more con- 
spicuous than in this volume. While adhering to a 
strictly logical sequence, the author uses his new 
freedom to very good purpose, illustrating the pro- 
positions by experimental work, by well selected con- 
crete examples, and by the employment of arithmetic, 
algebra and trigonometry. The introduction of the 
sine, cosine and tangent in the admirable chapter on 
ratio and proportion, and the subsequent judicious use 
of these functions, is a very good feature. The book 
deserves to be extensively used, and the appearance of 
section iii. of the work, which is in preparation, will 
be awaited with interest. 
The first part of Mr. Allcock’s geometry (correspond- 
ing with Euclid i.) was published in the early part of 
the year. The work is now continued, and the pre- 
sent part contains the equivalent of Euclid iii., 1-34, 
and iv., 1-9, with some additional propositions, such 
as the properties of the nine-point circle, and some 
practical applications and exercises. The title of the 
book correctly describes its contents and scope, com- 
paratively little attention being given to quantitative 
and experimental graphical work. For those who do. 
not wish to be tied to Euclid’s sequence, and yet who 
desire to retain a strictly deductive system, the book 
will be found eminently suited. It is well written 
and beautifully printed; it contains a large number of 
easy deductive exercises distributed throughout its 
pages; and at the end of the volume there is a collec- 
tion of practical exercises requiring numerical answers, 
which are given. 
Mr. Clement Jones’s text-book is intended for 
students who, having already taken an ordinary course 
in elementary analytical conics, wish to continue their 
studies and to obtain a good working knowledge of 
the methods of analytic research. In establishing the 
numerous properties of conics, the elementary theory 
of equations is applied in a systematic and thorough 
manner, in connection with which extended use is 
made of the single variable in the equations to the 
lines and curves. In a final chapter an account is 
given of cubic curves, the same powerful and illumin- 
ating method being employed. At the end of the 
volume the student will find a very useful collection 
of more than 200 examples, mostly taken from uni-~ 
versity examination papers, and the answers to these, 
with hints for solution, are appended. 
The use of squared paper by schoolboys is becoming 
universal, and Messrs, Baker and Bourne have done 
