392 
NATURE 
[JUNE 10, 1915 

mination and on the growth of seedlings, includ- 
ing the methods of water culture. Then we have 
a section on ash-analysis and on carbon dioxide 
assimilation, which includes the qualitative and 
quantitative determination of the products of 
photosynthesis ; a section on fats, oils, and waxes, 
on nitrogen-assimilation, on enzymes, tannins, 
glucosides, caoutchouc, etc. 
tions on a “complete” analysis of a plant, and 
on respiration. Finally, we have a number of 
sections of a miscellaneous nature, such as the 
sterile culture of the higher plants, the determina- 
tion of the surface tension, permeability, and 
osmotic pressure of plant cells, the use of ether, 
hot water, and other means for producing preco- 
cious sprouting, the measurement of growth, 
“bleeding,” and transpiration. Finally, tables 
are given showing the colour changes of various 
indicators for the determination of the hydrogen- 
ion concentration of cell-saps by means of 
Friedenthal’s method. 
In a work of this size there are, of course, many 
points at which one might cavil, and in particular 
English and American work should have received 
fuller recognition. There is, however, no doubt 
that Prof. Grafe has laid all plant physiologists 
under a heavy debt of gratitude by the produc- 
tion of so useful a book of reference. 

Veen Bs 
MATHEMATICAL PRINCIPLES AND 
PRACTICE. 
(1) Longman’s Modern Mathematical Series. 
Exercises in Algebra (including Trigonometry). 
By Dr. T. P. Nunn. Parti. Pp. x+421. Price 
4s. Part ii Pp. xi+551. Price 6s. 6d. The 
Teaching of Algebra (including Trigonometry). 
By Dr. T. P. Nunn. Pp. xiv+616. Price 
7s. 6d. (London: Longmans, Green and Co., 
1914.) 
(2) Workshop Arithmetic. By F.. Castle. Pp. 
vili+173. (London: Macmillan and Co., Ltd., 
1915.) Price 1s. 6d. 
(3) Plane Trigonometry. By Prof. H. S. Cars- 
law. Pp. xviii+293. Price 4s. 6d. Solutions 
of the Questions in Plane Trigonometry. By 
Prof. H. S. Carslaw. Pp. 179. Price 6s. 6d. 
net. (London: Macmillan and Co., Ltd., 1915.) 
(4) Numericai Trigonometry. By N. J. Chignell. 
Pp. xii+126. (Oxford: Clarendon Press, 
1914.) Price 2s. 6d. 
(5) Longman’s Modern Mathematical Series. Ex- 
ercises in Arithmetic and Mensuration. By P. 
Abbott. Pp. ix+524. With Answers. (London: 
Longmans, Green and Co., 1913.) Price 4s. 6d. 
(1) ROF. NUNN’S three volumes form a 
unique treatise on the study of algebra. 
Beginning from the first notions in the subject 
NO. 2380, VOL. 95] 
There are also sec- | 


he separates the educational grain from the edu- 
cational chaff, and gives us the grain. So much 
is found fit for discarding as chaff that the author 
finds space for treating trigonometry, Cartesian 
geometry, and the calculus, in addition to a dis- 
cussion of such recent work as that on the com- 
plete number-scale. 
Throughout the book Prof. Nunn’s knowledge 
of psychology is brought to bear to improve the 
order of treatment. In the customary treatment 
negative quantities are introduced early, and 
form a serious stumbling block. Prof. Nunn re- 
stricts the subject to “‘non-directed quantities ” 
for a considerable time. In consequence the pupil 
first meets negative quantities at a more mature 
age and with a mind more developed algebraic- 
ally, and is better fitted to grasp the new idea. 
The complete number-scale is introduced with 
the view of clearing up the doctrine of limits. The 
treatment is lucid and simple, and the student of 
this book will gain clear views on a matter on 
which even the best writers of books on the cal- 
culus have hitherto gone wrong. The book is 
one in a thousand, and all students who go 
beyond the non-specialist school course will gain 
enormously by its study. 
(2) Castle’s “ Workshop Arithmetic” is a book 
on which a boy would be glad to be brought up 
even if he is not destined to be an engineer or 
builder (for whom the book is specially designed). 
The questions come straight from the workshop 
and other everyday sources, and the human in- 
terest never fails. While the author’s language 
sometimes jars upon us, as when he says, ‘“‘Com- 
pute the following operation, 471°99+2°363” (p. 
7), or “The objects are not the same dimension at 
different places” (p. 30), we yet fear that present- 
day usage justifies this use of operation, and the 
omission of a preposition before the same dimen- 
sion. The largeness of the square ruling of some 
diagrams deserves a special word of praise for its 
clearness. 
(3) Prof. Carslaw’s ‘Trigonometry’ passes 
over the early portions of the subject rapidly. It 
is suited to the strong digestion of the specialist 
schoolboy and to university students. It holds 
a midway position between the older style of book 
which includes all the attractive backwaters and 
exercises in manipulation, and the modern book 
which aims at putting a useful tool in the stu- 
dent’s hands and restricting proofs and explana- 
tions to bare necessities. The book includes all 
that has been customary, and improves on the 
older books by introducing numerical work at an 
early stage. It is well suited to the many teachers 
who desire the new but hesitate to break with the 
old. The solutions in the key show careful work, 
