JANUARY 4, 1917] 
MATHEMATICAL TEXT-BOOKS. 
(1) A Shilling Arithmetic. By J. W. Robertson. 
- Pp. viilitigt. (London: G. Bell and Sons, 
Ltd.) 
(2) Revision Papers in Arithmetic. By C. Pendle- 
bury. Pp. xv+68+xviii. (London: G, Bell 
and Sons, Ltd., 1916.) Price 1s. | 
(3) Preliminary Geometry. By F. Rosenberg. 
Pp. vi+220. (London: University Tutorial 
sseress, Lid., 1916.) Price as. 
(4) Statics: a First Course. By C. O. Tuckey 
and W. A. Nayler. Pp. 299. (Oxford: At 
' the Clarendon Press, 1916.) Price 3s. 6d. 
(5) Exercices Numériques et Graphiques de 
Mathématiques. By Prof. L. Zoretti. Pp. xv+ 
124. (Paris: Gauthier-Villars et Cie, 1914.) 
Price 7 francs. 
(6) Ruler and Compasses. 
Pp. 148. 
1916.) 
By Hilda P. Hudson. 
(London: Longmans, Green and Co., 
Price 6s. net. 
(x) ME ROBERTSON’S “Shilling Arith- 
metic’? deserves the attention of the 
teacher if only for the collection of carefully 
devised and arranged original examples. It is 
not overloaded with text, nor is undue space 
given to illustrative examples. Stress is laid 
upon the use of rough checks. No use is made 
in H.C.F. of the principle matnb. In finding 
prime factors the child is told to begin by re- 
moving the lowest factors first, a practice which 
does not make for speed, especially as the tests 
for divisibility by 11, 9, etc., are supposed to be at 
the service of the student. In the sections on 
fractions the figures are too small, and in the 
copy that has reached us they are often of varying 
degrees of distinctness. It is nothing short of 
criminal for any publishing firm in these days 
to issue books for the young upon which any 
reproach of the kind can be cast. Numbers 24 
and 25 (p. 47) are instances of wickedly small 
type, and the strain to young eyes is greater 
still when the space between the lines is inadequate, 
€.g. compare numbers 26-40 on this page with 
numbers 41-43 on the next, and the relief is 
instantaneous. 
In the treatment of stocks we are glad to see 
that the author banishes the mischievous “ rool. 
stock” and uses “voucher” in its place. It is 
curious that in such questions as ‘“ Which is the 
better investment, 54 per cent. stock at 80, 
or 4 per cent. stock at 97?” few, if. any, 
text-books suggest the investment in each stock 
of the product of the prices—i.e. in the present 
case, 89ql.x97. This buys 97 bonds giving 
53]. each per annum or 8g bonds giving 
4l. each per annum. The difference is rapidly 
found with a minimum of fractional work. There 
is a useful set of forty test papers. As an instance 
of the practical tone pervading the book, we may 
take the warning that the percentage profit in 
actual commerce is reckoned as often on the cost 
as on the selling price. . 
(2) Mr. Pendlebury’s ‘Revision Papers in 
Arithmetic” provide “a well-graduated and com- 
NO. 2462, VoL. 98] 
NATURE 347 
prehensive examination course up to the standard 
of the Oxford and Cambridge Locals.” They 
seem excellently adapted for such a_ purpose. 
The Answer pages are perforated for removal if 
deemed necessary, and our only grumble is 
with the publisher as to the strain caused 
here and there by small faint figures to young 
eyes. 
(3) Mr. Rosenberg’s ‘Preliminary Geometry ” 
claims to be a judicious blend of the theoretical 
and practical. Where possible, “each important 
proposition . . . is. preceded by introductory 
analytical practical work, enabling the learner to 
discover for himself the law formally proved in 
the proposition.” Parallels follow the work on 
the angle and triangle, but otherwise the order 
followed is that of the Oxford and Cambridge 
syllabus. Where the book is not used by the 
private student the answers, which contain hints 
for the solution of many riders, should be detach- 
able. Boysand girls aremortal. The explanations 
are clear and precise. Such pages as 67—70, “ Hints 
on the Solution of Riders,” are invaluable to the 
private student, and throughout the book there 
is ample evidence that the author is familiar with 
every trap into which the unwary beginner may 
fall. The book enjoys all the devices of type, 
etc., that are common to works issued by the 
University Tutorial Press. 
(4) The “Statics” of Messrs. Tuckey and 
Nayler must be carefully examined by all who 
are not so satisfied as to scorn ingenious “tips” 
on points in the presentation of a subject which 
is always difficult to a certain type of youthful 
mind. The figures are large and clear. It would 
have cost very little more trouble to add 
the date to the sources—Army, Previous, etc.— 
from which the questions have been taken. The 
point is not immaterial, as considerable trouble 
to examiners might thereby be saved, as a recent 
trial in the courts may suggest to those who have 
to set papers. The young teacher will welcome 
chap. viii., on “The Connections between the 
Principles”; such pages as 242-243 will be a 
revelation to many who are inclined to take 
“Jaws” for granted, and whose historical instinct 
requires a gentle titillation. The manner in 
which couples are introduced is worthy of notice, 
as is also the chapter on geometrical methods, 
since it is “beginning to be recognised that the 
relations between three actual forces in equilibrium 
can be more readily grasped by the beginner than 
those between two actual forces and their hypo- 
thetical resultant.”” The book will be a great dis- 
appointment to those who share with Sir Peter 
Teazle a horror of principles. 
(5) Prof. Zoretti’s ‘‘Exercices Numériques ” 
represents the revolt in French educational circles 
against a system of teaching which leaves the 
student unable to use the tools at his disposal. 
The author’s experience as examiner has brought 
him fate to face with “bacheliers” in the land of 
the metric system who do not know the meaning 
of a decimal or a significant figure; who are 
checked by a change of units; to whom the real 
