Ferruary 18, 1904] 
NATURE 
363 
i i 
dustrial chemists, but that the education of the latter 
as physical chemists will open up new points of view, 
and gradually lessen the purely empirical methods by 
which the industrial chemist often tries to progress. 
The salt industry is next discussed; this is followed 
by an exposition of Cohen’s experiments on allotropic 
tin, a short and masterly exposition of the metal- 
lurgy of iron, and the relations between « and £ ferrite, 
pearlite, cementite, and carbon. 
In considering the bearing of physical cliemistry on 
physiology, the measurement of osmotic pressure by 
tradiscantia discolor, and by blood-corpuscles, and the 
curious experiments on the human eye by Dr. 
Massart are discussed, as well as Loeb’s discovery 
of the védle of osmotic pressure in fertilisation. |The 
influence of enzymes as accelerators or retarders of 
chemical action, and their effect in promoting synthesis 
as well as decomposition are particularly alluded to. 
The last chapters, dealing with geological pheno- 
mena, are suggestive; the type chosen is the very 
complicated relationships between the Stassfurt salts, 
in which no fewer than twenty-six components are 
present. A graphic representation of the conditions 
under which these salts are capable of existence is 
annexed. 
Prof. van ’t Hoff possesses in an almost unique 
degree the power of simple exposition and suggestive- 
ness. On reading this book one is tempted to exclaim, 
‘Why was all this not thought of ages ago?’’ But 
the fact is, all great discoveries can be simply stated, 
but it usually needs a great discoverer who can add 
to his discoveries simple methods of exposition. The 
magic consists in clearness of thought, and this is 
admirably illustrated in this interesting book. 
W. R. 
SCHOOL MATHEMATICS. 
A School Geometry. Parts i-v. By H. S. Hall, 
M.A., and F. H. Stevens, M.A. Pp. xii+340+ix. 
(London: Macmillan and Co., Ltd., 1903.) Price 
4s. 6d. 
Exercises in Theoretical and Practical Geometry. By 
R. B. Morgan. Pp. 96. (London: Blackie and 
Son, Ltd., 1903.) Price 1s. 
Graphs: or the Graphical Representation of Algebraic 
Functions. By C. H. French, M.A., and G. Osborn, 
M.A, Pp. viit64. (London: W. B. Clive.) 
Price 6d. 
P ART V. of the new geometry by Messrs. Hall and 
Stevens has been recently issued, and the whole 
work, so far as it is completed, is now conveniently 
published in one volume. The final part, dealing with 
solid geometry, is in preparation, and will be awaited 
with interest in many quarters. 
The authors follow the reform movement cautiously, 
on strictly orthodox lines, and adhere closely to the 
recommendations of the Mathematical Association and 
to the new Cambridge syllabus. The advantages of 
the newer methods of teaching geometry are very 
manifest in this excellently written text-book. A great 
change has been effected in the country in a compara- 
NO. 1790, VOL. 69] 
tively short time, but the subject is not yet sufficiently 
emancipated from the older influences. The field of 
elementary geometry is at present only partially 
covered. We are strongly of opinion that examiners, 
teachers and writers should take a more compre- 
hensive view of the scope of the subject. The scheme 
still generally followed in schools deals only with the 
shapes and sizes of figures, and takes no account of 
their relative positions. That is, attention is confined 
to scalar properties, and a vital portion of this 
essentially vector subject is ignored. It seems to us 
that boys at school should receive some account of the 
geometry of space, that is, they should be introduced to 
the conception and domain of vectors. This domain is 
far reaching and of supreme importance, and in subse- 
quent study is seldom fully comprehended because, in 
the supposed interests of logic, persons responsible for 
the teaching of geometry have neglected a part of their 
duties and have failed to treat the subject in a thorough 
manner. The foundation of a knowledge of vectors 
should be laid in the geometry and drawing classes, 
where it can be done appropriately and effectively, and 
able writers like the present authors could exert much 
influence for good by introducing the subject in their 
deservedly popular text-books. 
Mr. R. B. Morgan’s book consists of a collection 
of more than six hundred exercises in geometry, 
together with a few specimens of recent examination 
papers, the purpose of which seems to be to illustrate 
the course of geometry as outlined in the new Cam- 
bridge schedules. No answers are given to the ex- 
amples, or hints for solution or explanations of any 
kind, and the book is only adapted for use in conjunc- 
tion with an ordinary text-book. In the latter sufficient 
examples are usually provided, and generally of a 
superior merit to those under review, so that the sphere 
of usefulness of Mr. Morgan’s book seems likely to be 
very restricted. 
The text-book by Messrs. French and Osborn is one 
of the University Tutorial Series. It is a supplement 
to the ** New Matriculation Algebra’ of the series, 
and is intended primarily for students preparing for 
the London matriculation examination. The subject 
is introduced by some typical examples of statistical 
graphs, in which special attention is paid to the choice 
of scales and the kind of information to be obtained 
from graphs. The authors then at once proceed to 
the development of the properties of algebraical func- 
tions by means of graphs, the examples being con- 
fined mainly to equations of the first, second and third 
degrees. The problems dealt with relate to maxima 
and minima values, the solution of equations, limiting 
values and asymptotes, symmetrical properties, and 
the determination of algebraical 
through two, three, or four points. 
It will thus be seen that trigonometrical, exponential 
and logarithmic functions are outside the scope of the 
work, as are also considerations relating to slope, rate 
of increase, and the calculus. But the ground that is 
mapped out by the authors is well covered, and 
the book will be found very useful to the class of 
students for whom it is intended. 
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