JuLy 16, 1914] 
NATURE 
mathematical induction and the binomial theorem. 
The place assigned, as is usual in text-books, to 
mathematical induction shows how broad is the 
gulf between psychology and logic. The collec- 
tion should prove useful. ; 
(4) It is pleasant to read such a practical book 
as this one. The authors have dealt only with 
those parts of mathematics which seemed to them 
to be of real value in practical work, and the 
whole book is pervaded by the spirit of Prof. 
Perry. The very form of the questions is re- 
freshingly non-academic: we are concerned with 
the important things of life—with ‘ kilowatts, 
gearing, and Whitworth standard nuts. It would 
seem to be a mistake to give (as on p. 257) 
areas and volumes of certain figures, and then 
remark : 
“The formule are proved most conveniently by 
the aid of more advanced mathematics than need 
be given in this volume.” It warms one’s heart 
to see (p. 5): “A formula is practically the simple 
single statement in general terms of a whole series 
of particular facts.’ It seems to us that Prof. 
Perry and his school are doing much incidentally 
to help the development of mathematics by open- 
ing our eyes to the fact that what Boole called 
“‘a premature converse with abstractions” is 
ruinous for a boy’s whole mental life. 
(5) Is simply a reproduction of the second part 
of (6) with a new preface. Whereas the preface 
of (6) gives a list of the “distinctive features” of 
the book, (5) states somewhat ambiguously : 
“Whatever unusual merit the book possesses 
must be largely sought for in the following 
points: a.” 
In (6), then, we find that, -both in plane and in 
spherical trigonometry, triangles are solved in 
detail by graphical methods before analytical 
methods are presented, and there are many other 
innovations—thus, Napier’s rules are proved and 
the three fundamental formule for the spherical 
triangle are derived simultaneously. Having read 
(p. v.): “The references to algebra are limited 
to those with which every beginner may be reason- 
ably assumed to be familiar,” we are surprised 
to find (p. 278) the imaginary unit defined shortly 
as the solution of the equation x2+1=0, no evi- 
dence having been given that this equation has 
a solution. After this, we cannot be surprised 
that there is not the slightest attempt either to 
point out to the student the very great and funda- 
mental difficulties that there are in the theory of 
convergence (see especially p. 312) or even to treat 
the subject correctly. The historical references 
are sometimes faulty: Wessel was a Dane and 
not a German; the trigonometrical form of a 
complex number is due to Euler and not to Cauchy 
(p. 285). . 
NO. 2332, VOL. 93] 
505 
OUR BOOKSHELF. 
The Schools and the Nation. By Dr. Georg 
Kerschensteiner. Authorised translation by 
C.K. . Ogden... Pp. xxiv+351. ~“(London- 
Macmillan and Co., Ltd., 1914.) Price 6s. net. 
Tuis is a book of exceptional interest for all who 
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How Man Conquered Nature. By Minnie J. 
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THE style of this little book will appeal to children. 
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Man’s development is traced from the time when, 
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Tus wall map is constructed on a conical pro- 
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to an inch. It is provided with an inset map of 
