JANUARY 25, 1917] 
To a certain extent Ibn Badr makes up formule 
of the type f(x, y)=o or f(x, y, s)=o to solve a 
whole set of problems; see, for instance, pp. 
88-90. He also discusses some problems which 
Jead to linear Diophantine equations; for instance 
{pp. 90-92), we have the problem :— 
“A man sold three kinds of grain, wheat, 
barley, and millet; the wheat at 4 dirhems per 
measure (gafiz), the barley at 2 dirhems per 
measure, the millet at half a dirhem per measure. 
Altogether he sold 100 measures for 100 dirhems; 
how many measures of each grain did he sell?” 
This leads, of course, to the equations 
X+y+s=4x+2y+4s=100, and hence to 7x+3y 
=100; but Ibn Badr’s analysis is quite different 
from this. The editor concludes (pp. xix—xx) 
from the occurrence of problems of this type that 
the author belongs to the twelfth or thirteenth 
century. 
_ An interesting feature of the text is the way 
in which different technical terms are used. Thus 
mal, which properly means “wealth,” is used by 
Ibn Badr not only in the sense of “capital,” but 
also (e.g. text p. 18, line 1) in the sense of x2, 
and this even when x is a quadratic surd. Does 
this arise from marshalling troops in squadrons, 
or possibly from reducing areas to equivalent 
squares? Other terms are noted by the editor. 
So far as we can judge, the editor’s work 
seems to be very well done. Besides the text 
and translation we have an introduction describ- 
ing the (unique) MS., now in the Escurial Library, 
photographic facsimiles of the first and last pages, 
a very useful summary of the contents (using 
modern notation), and a few notes on the history 
of mathematics in Spain. 
_ This and other recently published works indi- 
‘cate that Spain is becoming really alive to the 
value of scientific research; it may be added that 
it appears under the auspices of the Junta para 
ampliacién de estudios e investigaciones cientificas. 
G. BoM: 
OUR BOOKSHELF. 
Cours de Manipulations de Chimie Physique et 
d’Electrochimie. Par M. Centnerszwer. Pp. 
182. (Paris: Gauthier-Villars et Cie, 1914.) 
Price 6 francs. g 
WHEN a student actually measures the quantities 
involved in theory, a flood of light is frequently 
thrown on hitherto obscure points, and the object 
of the present practical course is to assist in the 
study of theory rather than to provide a training 
in manipulation. The book is orthodox according 
to the Ostwald school. It has been gradually 
evolved from teaching experience in the Riga Poly- 
technic, and meets with the approval of Walden. 
It thus has much to commend it. 
Following the well-known Leipzig lines, it 
presents mostly familiar features, except that it 
is almost unique among books on practical physical 
chemistry in giving exercises on the measurement 
of critical constants. No other practical book, 
except Ostwald-Luther, so far as we are aware, 
NO. 2465, VOL. 98] 
NATURE 
| ing restrictions came into operation. 
407 
deals with this subject, and in the short practical 
course at Leipzig the exercises on critical constants 
are marked as optional. The author’s special 
experience in this field no doubt accounts for this 
novelty, and what makes it the more welcome is 
that the methods described have been put to the 
test. 
Practical details are very fully given in the part 
on electrochemistry, which occupies 77 out of 
a total of 182 pages. We note, however, that a 
table of absolute potentials for elements is given 
instead of the more trustworthy and equally prac- 
ticable potentials relative to the hydrogen elec- 
trode. This is possibly due to the elementary 
nature of the work, just as in most elementary 
books on general chemistry it is not considered 
wise to confuse the beginner by giving arguments 
in favour of the oxygen basis for atomic weights. 
The same desire for simplicity also explains the 
absence of reference to the degree of uncertainty 
in experimental results. 
Francis W. Gray. 
The Nation of the Future: a Survey of Hygienic 
Conditions and Possibilities in School and Home 
Life. By L. Haden Guest. Pp. 115. (London: 
G. Bell and Sons, Ltd., 1916.) Price 2s. net. 
Tuis little book, clothed in an ambitious and 
somewhat misleading title, deals entirely with the 
welfare of the school child and with the medical 
inspection and treatment of school children. 
The first section deals with the disabilities to 
which school children are subject, their results, 
their treatment, and their prevention. 
In the second section the method of carrying 
out the medical inspection of school children is 
described, the system being that which has been 
adopted by the London County Council. Finally, 
the case for the school clinic is presented to the 
reader. 
The book is a. popular one suited to the require- 
ments of education committees, teachers, and 
health visitors, and as such may be useful. The 
text is illustrated with several plates. 
Stars at a Glance. Pp. 48. (London: G. Philip 
and Son, Ltd., n.d.) Price 1s. net. 
Tuis simple guide to the stars will admirably 
meet the requirements of those who are com- 
mencing the study of astronomy or who have 
become interested in the heavens since the light- 
It provides 
an “aspect chart” for each month, which will 
enable the observer to make a general acquaint- 
ance with the stars visible at a specified time 
and date, and four additional charts showing the 
constellations in greater detail. An important 
feature is a calendar-index, whereby the proper 
chart to be consulted at any time may easily be 
selected. In conjunction with a compass-card 
which is provided, the charts may be conveniently 
used for purposes of night-marching. The text 
includes a useful introduction to the study of the 
heavens and some brief notes on the constellations 
and principal stars. 
