JUNE 10, 1915 | 
NATURE 
393 

and the type is excellent in both books—the text 
and the key. 
(4) Mr. Chignell’s book is planned on the wise 
modern method of beginning trigonometry with 
a numerical treatment of the ratios, and postpon- 
ing the addition theorem and other formulas until 
the student has thoroughly grasped the meaning 
of the ratios. The solution of the oblique tri- 
angle is effected by dividing it into two right- 
angled triangles, a simple method which is in 
every way sufficient for non-specialists; the half- 
angle formulas were invented for astronomical 
use, and may very well be left to astronomers and 
other specialists. The quantity of exercises is 
ample for all purposes, and the wise schoolmaster 
will use only a minimum number of the introduc- 
tory tests and pass rapidly on to the “problems ”’ 
of human interest. 
(5) For the students who use Mr. Abbott’s book 
the bad old rule-of-thumb days are over. Vulgar 
fractions are introduced in most practical fashion, 
fractions of lengths and areas being shown in dia- 
grams. Then follow decimals in equally practical 
fashion by means of the paper abacus which 
served merchants up to the time of the invention 
of the zero; and so on in corresponding treatment 
throughout the range of mensuration. 
The relation (a+b)?=a?+b?+2ab we are 
pleased to see treated as the algebraic expression 
of a property which is fundamentally geometrical ; 
too often the relation is taken to be fundamentally 
algebraic, and the geometrical property reduced 
to the status of an illustration. The square-ruled 
diagrams are sometimes in tenths of an inch and 
sometimes in millimetres. The former are better, 
the latter being trying to the eye; and for many 
purposes quarter-inch or half-centimetre ruling 
would be better than either. The bulk of the 
exercises have the great merit of being drawn 
from human life. DB. ME 

OUR BOOKSHELF. 
Practical Irrigation and Pumping. By B. E. 
Fleming. Pp. xvi+226. (New York: J. 
Wiley and Sons, Inc.; London: Chapman and 
Hall, Ltd., 1915.) Price 8s. 6d. net. 
Ir is somewhat difficult for the inhabitants of a 
country intersected by numerous streams and 
characterised by an ample and fairly uniform 
rainfall, to realise the disabilities under which 
agriculturists labour in other lands less favoured 
with automatic supplies of natural moisture. The 
_great plains of India, the immense tract of Egypt 
and the Sudan, and the vast expanse of North 
America lying west of the tooth meridian, com- 
prising some dozen States and forming about one- 
third of the total area of the United States, are 

possible, without artificial aid, to render the soil 
productive in any effective degree. What this 
means may be gauged from a statement in the 
prefatory note of the volume before us, that up 
to July, 1910, it is estimated that a sum of more 
than 60,000,o00l. had been sunk in the reclama- 
tion, by irrigation, of 14,000,000 acres in the 
Western States of America. 
The purview of Mr. Fleming’s book is limited to 
a consideration of irrigation by means of pump- 
ing underground water, as practised in the United 
States, and in so far as this aspect of the subject 
is concerned, it is treated fairly comprehensively. 
The author enters succinctly, and at the same 
time with some degree of detail, into the various 
problems connected with the sinking of wells and 
the installation of a pumping plant. Consider- 
able space is devoted to a discussion of the merits 
and capabilities of the centrifugal pump, and a 
noticeable feature is the number of performance 
diagrams of various-sized pumps of this type. 
Reciprocating pumps are only lightly touched 
upon. Prime movers and windmills are described. 
There is a chapter on the cost of pumping opera- 
tions which contains some useful information; the 
governing conditions, as already stated, are those 
prevailing in the Western States, and, conse- 
quently, the facts are not generally intended for 
wider application. Within the limits set down 
by the author, this little volume is an interesting 
and practical handbook, based on his personal 
experience, some of which, he remarks, has been 
“rather bitter.” Bs GC: 
Brazil (1913). By J. C. Oakenfull. Fifth Edition. 
Pp. viii+604. (Frome: Butler and Tanner 
1914.) Price 7s. 6d. net. 
‘Tuts account of Brazil is the fifth revised edition 
of a handbook originally published in 1909, and 
distributed at the cost of the National Government. 
It discusses in detail the geography, history, 
natural productions, and economic resources of a 
country including an area of 8} million kilometres 
and an estimated population of 24 millions. The 
book is well arranged, the information is based 
on the most recent official reports, and it is pro- 
vided with good maps and illustrations. Brazil 
in its geographical features presents the most 
varied characteristics—the great river basins of 
the Amazon-Tocantins and La Plata, a shapeless 
mass of highlands, and a narrow coastal region. 
In its highland region suited for an agricultural 
and pastoral life, its vast forests providing 
unlimited supplies of valuable timber, its coffee, 
sugar, tobacco, and other useful products, it 
remains one of the few areas suitable for exten- 
sive development by settlers from Europe, a fact 
which has been fully grasped by the German 
Government, ever in search of new colonies and 
desirious of securing a footing on the continent 
of America. 
The book is admittedly intended to press the 
claims of Brazil on the colonist. Since 1820 
31 millions of emigrants, of whom the majority 
are Italians, have reached its shores, and progress 
instances of those arid regions in which it is im- | has recently been made in attracting Japanese 
NO. 2380, VOL. 95 | 
