AvuGUST 15, 1912] 
NATURE 
603 
of leaders of thought it is curiously old in form. ! in the terminology and in the pupil’s ignorance of 
They give rules for the treatment of signs on the 
removal of brackets, which we cannot imagine 
either of them using in actual teaching ; we imagine 
them constantly carrying the boys back to the 
meaning of the expression under consideration, 
until the boys have absorbed the rule without ever 
putting it into words. And the quantity of 
manipulation: there are tons and tons, enough to 
wear down the teeth of the most omnivorous boy. 
All this manipulation cannot be intended for the 
boy of mathematical ability; he will acquire all 
necessary manipulative skill on a tenth of it. It 
cannot be intended for the non-specialist; he does 
not need such manipulative skill, and if he does 
acquire it he has no time left for the more human 
mathematical studies to which he ought to push on. 
We are forced to conclude that the book is cast 
in this form to meet the demand of the market. 
We have no blame for suiting the book to the 
demand; on the contrary, we sympathise. Better 
to publish this book, which is the best on the 
market though weak in some ways, than an ideal 
book which no one would use. What we do 
suggest is that our leaders of thought should write 
books which meet the demand, and at the same 
time mark portions of the book for omission when- 
ever circumstances allow it, in order to wean the 
teacher and examiner from useless studies. 
In Mr. Hall’s “School Algebra” (3) we find the 
same excess of manipulative exercises as in God- 
frey and Siddons. On the other hand, we hail 
with delight his plan of using infinite series with- 
out proof of their validity. A clear consciousness 
of the concepts of mathematics is the first 
desideratum; abstruse proofs are for the few. A 
little more telescoping of the customary mathe- 
matical course and the non-specialist will be able in 
his school career to attain-to the ideas of the 
calculus. 
One desirable piece of telescoping is the omission 
from the compulsory course of permutations and 
combinations. They provide, of course, good 
mental gymnastic. As regards progress in know- 
ledge, they lead up to the binomial theorem; so 
that they cease to be necessary in a course which 
assumes the validity of that theorem. At the same 
time, their discussion gives rise to many elegant 
theorems, and it is therefore well to leave them 
available for the leisure hour of the boy who 
fancies them. 
Messrs. Hall and Stevens’ ‘Examples in Arith- 
metic” (4) includes the treatment of stocks and 
shares. No doubt examination requirements 
necessitate their inclusion, but we should be glad 
to see their omission recommended for schools the 
circumstances of which allow it. 
NO. 2233, VOL. 89| 
The difficulties lie 
the transactions involved; there are no arithmetical 
difficulties. Again, continued fractions, which at 
an earlier time provided the only means of obtain- 
ing approximations to complicated quantities such 
as surds, are now superseded by decimals, and 
might with advantage disappear from books on 
arithmetic. 
The pruning away of unnecessary excrescences 
from the school course makes possible the inclu- 
sion of the infinitesimal calculus, which is more 
and more coming to be recognised as a regular 
school subject, and we welcome Mr. Baker’s little 
book (5) as helping towards that desirable con- 
summation. Mr. Baker no doubt caters for the boy 
who will need the calculus as part of his technical 
equipment in later life, and for that boy he rightly 
provides logical proofs of all theorems. In course 
of time the non-specialist boy will study the calculus 
in place of stocks and shares, permutations and 
combinations, and such things; and this boy 
should have a book on the lines suggested by 
Mr. Newbold in his little paper on “ Higher Mathe- 
maties for the Classical Sixth Form,” in which 
the ideas of the subject are evolved from the 
discussion of interesting everyday problems. 
THEORETICAL AND APPLIED PHYSICS. 
(1) Heat and the Principles of Thermodynamics. 
By Dr. Charles H. Draper. New and revised 
edition. Pp. xv+428. (London: Blackie and 
Son, Ltd., 1911.) Price 5s. net. 
(2) Laboratory Problems in Physics. To accompany 
Crew and Jones’s “Elements of Physics.” By 
F. T. Jones and Prof. R. R. Tatnall. Pp. ix+ 
81. (New York: The Macmillan Company ; 
London: Macmillan and Co., Ltd., 1912.) Price 
2s. 6d. 
(3) Outlines of Applied Optics. By P. G. Nutting. 
(Blakiston’s Science Series.) Pp. ix+234. 
(Philadelphia: P. Blakiston’s Son and Co., 
1912.) Price 2 dollars net. 
(4) Elements of Hydrostatics. With numerous 
examples. For the use of schools and colleges. 
By George W. Parker. Pp. vili+ 150. (Lon- 
don: Longmans, Green and Co., 1912.) Price 
2s. 6d. 
(5) Junior Heat. By Dr. John Satterly. Pp. 
viii+ 184. (London: W. B. Clive, University 
Tutorial Press, Ltd., 1912.) Price 2s. 
(1) T is refreshing to find, occasionally, an 
elementary text-book in which the author 
has been bold enough to depart from the stereo- 
typed mode of treatment and introduce new 
features. Such is the case with the second edition 
of Dr. Draper’s book. The author’s intention, 
as expressed in the preface, of revising the book 
