Marcu 14, 1907 | 
NATURE 
459 
determined and a result in sight the correctness of 
which is only limited by the imperfections of the 
method. Instead, the methods are often conventional, 
depending upon such factors as the method of pre- 
paring the sample or the solvent employed, 
or they may be determinations like the absorptive 
power of the soil for water, which have no 
absolute meaning at ail, but are merely at- 
tempts in the laboratory to get a number which 
shall represent the behaviour of the soil in the field. 
With regard to so many of these determinations of a 
physical nature the difficulty lies, not in carrying out 
the process, but in interpreting it afterwards, and 
correlating it with some practical aspect of the soil. 
The present volume of Dr. Wiley’s book becomes, in 
consequence, something more than a collection of 
analytical methods; it is in many respects a treatise 
on soil chemistry and soil physics, so full the 
introductory discussions dealing with each the 
various means of investigating the soil, and as such 
it is indispensable to all serious students of agricul- 
tural chemistry. 
Dr. Wiley has cut out some of the matter of the 
earlier edition, though retaining processes which have 
a historical interest or are necessary in tracing the 
development of the more modern method; he has 
further incorporated methods and _ investigations 
which have been published in the twelve years that 
have elapsed since the appearance of the first edition. 
The present volume is dated October, 1906; we miss, 
however, one or two methods which appeared before 
that date, e.g. Mitscherlich’s interesting determina- 
tion of the heat evolved when a soil is moistened 
(benetzungwarme), which is correlated with the active 
surface of the soil particles. In one or two other 
respects als> we think later work might have modi- 
fied some of the conclusions expressed, but of course 
the subject is in a constant state of progress, and the 
time occupied in writing a book of this magnitude is 
sufficient to bring about a revision of some of the 
points of view. We notice, indeed, but scant re- 
ference to the more recent developments in soil investi- 
gation which have issued from the Division of Soils 
in the United States Department of Agriculture; 
perhaps we may take this negative attitude of Dr. 
Wiley’s as a critical one. 
In conclusion, we can only express our thanks for 
what must always be one of the most useful books 
in the library of any agricultural laboratory. 
A. Di HE 
are 
of 
OUR BOOK SHELF. 
Introduction to the Theory of Fourier’s Series and 
Integrals and the Mathematical Theory of the Con- 
duction of Heat. By H. S. Carslaw. Pp. xvii+ 
434. (London: Macmillan and Co., Ltd.) Price 
14s. net. 
Tuts book is an interesting sign of the times. 
The gulf between pure and applied mathe- 
matics, in this country at any rate, has of recent 
years become more and more complete. Indeed 
there is no one who so heartily detests and despises 
NO. 1950, VOL. 75] 
mathematics proper as the ordinary physicist. He is 
often compelled to use elaborate mathematical 
analysis, but he does not feel or profess any interest 
in anything but the result, and questions as to the 
mathematical basis of his arguments seem to him 
merely trifling and vexatious. 
Prof. Carslaw has therefore shown a good deal of 
courage in offering to English readers a book on the 
theory of conduction of heat which includes a 
serious account of the mathematical difficulties of 
| the theory and may expose him to unsympathetic 
criticism from different points of view which have 
little in common. However, the experiment is a dis- 
tinct success, and it is to be hoped that it will lead 
| to similar and equally successful experiments with 
other and more difficult branches of mathematical 
physics. 
The book is divided into two parts. Part i. is 
entirely mathematical, and it is this part which con- 
tains most that is novel in an English book and is, 
therefore, most interesting to the critic. A short but 
well-written historical introduction is an attractive 
feature. In the first two chapters, which deal with 
irrational numbers and infinite sequences in general, 
the author mostly follows Dedekind and Tannery, 
and he could not have chosen better guides. The 
chapters on uniform convergence are also good, 
though here the arrangement and method of present- 
ation do not seem to us in every respect the best. 
The author, we are glad to see, speaks of ‘‘ infinite 
definite integrals,’’ and discards the barbarous 
‘‘improper.’’ He might perhaps have brought out 
more clearly the fact that the infinite integral is 
essentially a repeated limit—as it is, he rather ex- 
agegerates the analogy between the integral and the 
infinite series; and it is a pity that he should have 
omitted to prove the fundamental inversion theorems 
for finite integrals. But the chapters dealing 
especially with Fourier’s series seem to us the best; 
we are particularly glad to see Fejér’s theorem in- 
cluded. Part ii. contains a clear account of the prin- 
cipal problems of conduction, and requires no special 
comment here. 
This book shows very clearly how much of the 
Continental spirit of rigour English mathematics has 
absorbed in recent years. It also shows how much 
the heaviness of the Continental 5 and ¢€ can be 
lightened by a bright and attractive style, interest- 
ing illustrations, numerous examples, and other 
touches of the Cambridge tradition. 
Ga HEEL. 
Museu Paraense de Historia e Ethnographia: Arbore- 
tum Amazonicum. By Dr. J. Huber. Pp. 40; with 
4o plates. Decades i. to iv. (Para, 1900 and 1906.) 
Tor a development of moist equatorial vegetation no 
region surpasses that bordering the Amazon and its 
tributaries, which Dr. Huber, in the course of his 
long association with Para, has had unique oppor- 
tunities of visiting. The form in which Dr. Huber 
presents his information is similar to the *t Vegeta- 
tionsbilder,’’ where the illustrations are the chief 
feature and the notes are explanatory thereto, but 
it should be stated that the first two parts of the 
“ Arboretum Amazonicum ’’ were issued in rIgoo, pre- 
vious to the frst numbers of the ‘* Vegetationsbilder.’’ 
Two additional parts appeared last year, and it is 
proposed to complete the work in ten numbers. The 
publication of the work has been undertaken by the 
Polygraphisches Institut of Ziirich, and the photo- 
Seivnnce afford a criterion of the excellence of their 
work. 
