558 

employ a known principle as to friction in his 
famous submarine telegraph relay; he was the 
discoverer of the principle. The same may be 
said about the description of Brown’s mechanical 
relay. We think that Prof. Boys is occasionally 
misled by assuming that his own very intimate 
knowledge of phenomena shared by other 
people. Yer es 
is 

MATHEMATICAL TEXT-BOOKS. 
(1) Subjects for Mathematical Essays. By Dr. 
C. Davison. Pp. x+160. (London: Mac- 
millan and Co., Ltd., 1915.) Price 3s. 6d. 
(2) Junior Algebra. By A. G. Cracknell and 
A. Barraclough. Pp. vi+280. (London: 
University Tutorial Press, Ltd., 1915.) Price 
25 Od: 
(3) Papers Set in the Qualifying Examination for 
the Mechanical Sciences Tripos, 1906-1913. 
Pp. go. (Cambridge: At the University Press, 
1914:) Price 2s. net. 
(4) A Shilling Arithmetic. By W. M. Baker and 
A. A. Bourne. Pp. xiv+192. (London: 
G. Bell and Sons, Ltd., 1915.) 
(5) Practical Mathematics Second Year. By 
AC bs Young = bps sdeemo4e | (koudonmeGe 
Routledge and Sons, Ltd., 1915.) Price 2s. net. 
(6) The Laws of Algebra. An Elementary Course 
in Algebraic Theory. By A. G. Cracknell. 
Pp. vi+68. (London: University Tutorial 
IPTess, lids, 19ns:)/sbmce ars. 
(1) HIS collection of essays will be found of 
the greatest value in the training of 
mathematical scholarship candidates. Such work 
as this enables a student to coordinate his know- 
ledge, and so consolidates the material that is 
floating vaguely about his mind, when he has 
completed the various courses of reading pre- 
scribed for him. It is indeed mainly by essay 
work that he begins to see the bearing of one 
subject on another and to appreciate the help 
which can be derived from the interfusion of 
subjects. We do not therefore recommend the 
use of this book merely because it will stand the 
candidate in good stead for examination purposes, 
but because we believe that the greater breadth 
of outlook essay work produces is of real educa- 
tional value to him, and because it plays a part 
in his mental development which no other form 
of exercise can achieve. 
(2) This course takes the reader as far as 
quadratic equations, and the two final chapters 
deal with indices and logarithms. In addition to 
illustrative examples, there is a considerable 
amount of explanatory matter. The former is 
NO. 2386, VOL. 95] 
NATURE 

[JULY 22, 1915 
essential, but it is open to question whether junior 
students can profitably read the discussions which 
text-books often contain: for example, on page 70 
we find “Related Unknowns.—One of the chief 
uses of algebra is that of solving problems where 
it would be either difficult or impossible to solve 
them by arithmetic. The method is to represent 
the unknown quantities by letters, then to express 
the problem as an equation and to solve this 
equation.” In our view, such passages as these 
merely overload the book and assist neither the 
pupil nor the teacher. There are no particularly 
original features, but the examples are well 
arranged and provide a sensible elementary course. 
(3) The reprint in a cheap and compact form of 
papers set in the Mathematical and Engineering 
Triposes at Cambridge is of real service to a 
large circle of students. The general character 
of the papers is evidence of the recent changes in 
mathematical teaching. Those engaged in the 
higher work in secondary schools will find here 
much that will enrich their weekly problem papers. 
The questions are both practical and stimulating. 
(4) This small volume includes all the arith- 
metic that in our view ordinary students require 
and some things, such as true discount or inverse 
compound interest, they should omit. If the 
general education is to include, as we believe it 
ought, trigonometry, practical mechanics and, if 
possible, the ideas of the calculus, it is essential 
that arithmetic should be merely a means to an 
end, a preparation for other work rather than a 
subject in itself. It is the comparatively slight 
dimensions of this text-book that constitute its 
chief claim to favourable consideration. 
(5) The author has already published a course 
of practical mathematics for first year technical 
students: this volume contains the subject 
matter of the second year course. In this volume, 
as in the first, there is a first-rate set of examples, 
and we have no hesitation in recommending’ it 
for extensive use. 
(6) This discussion of the meaning and validity 
of the fundamental laws of algebra is intended for 
senior divisions of secondary schools. It includes 
rational and irrational numbers, and rational 
indices, but excludes imaginaries, infinities, limits, 
and irrational indices. The language is through- 
out simple and the argument is set out clearly, 
but we are doubtful whether the author’s partition 
is satisfactory. The theory of limits has now 
assumed so prominent a place in modern analysis 
that it is hard to refuse to admit it into the school 
curriculum, and it seems wise therefore to take 
it in conjunction with any substantial discussion 
of irrational numbers. 
