342 
NATURE 
[ NOVEMBER 20, 1913 | 
practical use of logarithms, the meaning of the 
trigonometric functions, the mensuration of plane 
and solid figures, and variation. The concluding 
chapter introduces the reader to Cartesian 
geometry. 
(2) The lines on which this text-book is written 
show that the authors are convinced, and in our | 
opinion rightly, that a knowledge of the ideas 
and methods of the calculus can be obtained with- 
out any severe algebraic manipulation. They 
have wisely omitted all purely formal developments 
of the subject, and have introduced integration 
at an early stage. The explanations are given in 
a clear and simple style, and a variety of applica- 
tions are made which should secure the interest 
of the reader. In a work such as this a rigorous 
treatment is out of place, but it is well to warn 
the student of this, and we disagree with the 
authors in their suggestion that the proof given 
of Maclaurin’s theorem is complete, and secure 
against criticism. The subject-matter includes 
ordinary and partial differential equations and an 
excellent account of vector analysis. It is curious 
and regrettable that this is generally omitted by 
English writers. 
(3) The first half of this volume is occupied 
with the solution of rather a miscellaneous set of 
problems on the motion of plane and solid bodies 
and systems of bodies, with special reference to 
envelopes and roulettes. The remainder falls into 
three sections: (1) particle dynamics; (2) rigid 
dynamics; (3) a brief account of relative motion, 
and the composition of motions of translation and 
rotation. Each of these is taken in far less detail 
than would be the case in a similar English treat- 
ise, and no exercises are included. Many students, 
however, might profitably read a course of this 
kind to supplement their ordinary text-book. 
(4) This is a sequel to the author’s former work 
on structures, forming a supplementary volume 
dealing with recent developments of the subject. 
The first eighty pages give a clear and full account 
of the method of influence lines, which, although 
suggested in Germany forty years ago, has until 
quite recently received little attention in this 
country. The next sixty pages deal with the 
principle of work and its application to the deflec- 
tion of framed structures, redundant frames, and 
rigid or elastic arches; and the remainder to 
portals, wind bracings, and secondary stresses. 
The mathematical work is set out at full length, 
and so clearly that it should offer few difficulties. 
The diagrams are excellent; and the problems 
chosen for discussion are of real practical interest ; 
their selection and treatment is evidently the work 
of a tee experienced teacher. 
2299, VOL. 92| 
‘ 
- a SS a 
LABORATORY EXPERIMENTS IN 
AERONAUTICS. 
The Resistance of the Air and Aviation. Experi- * 
ments conducted at the Champ de Mars Labora- — 
tory. By G. Eiffel. Second edition, revised and 
enlarged. Translated by J. C. Hunsaker. Pp. — 
XVi+242+xxvii plates. (London: Constable 
and Co., Ltd.; Boston and New York: Hough-— 
ton Mifflin Co., 1913.) Price 42s. net. 
N English edition of this work will be wele) 
A comed by the large and increasing circle of © 
scientific and engineering men who are desirous of 
obtaining accurate experimental data in aero-— 
nautics from which to direct their work. It need — 
not be said that the experimental work of M. Eiffel 
repays study, for whether the reader seeks to gain 
information regarding the difficult and perplexing 
problems met with in this branch of physics, or 
practical “tips” for designing aerofoils, he will 
not be disappointed. Though the contents of this — 
book, based as they are upon experiments made — 
at the laboratory at the Champ de Mars, have 
passed into the category of established experi- 
mental facts, they are not so well known as they 
deserve to be. By 
The great new Auteuil laboratory 1 js described 
in the volume, from which in the future we may 
expect great things; nevertheless, the results ob- 
tained at the Champ de Mars with the smaller 
wind tunnel to which the volume before us is 
devoted, will pass the most critical examination 
for painstaking experimental work. From time to” 
time we are met with suggestions that capable 
mathematicians should be entrusted with problems 
of stability and like questions, but the mathe- 
matical investigator must be provided with care- 
fully ascertained facts if his conclusions are to 
be worth anything at all. 
From such experiments as these, and from those 
made at the National Physical Laboratory, the 
mathematician must derive the grain for his logi- 
cal mill. That good use will be made of them there 
cannot be any reason to doubt. As aeroplane wi 
sections are capable of indefinite variation, and no 
two experimenters have adopted similar sections, 
comparison of the work of different experimenters 
becomes difficult, hence the conflicting results 
which are quoted by those who have not taken into 
account the many independent variables entering 
into the experiments. 
Perhaps the most striking result in this series 
of experiments on aeroplane wings is the effect of 
the “negative” angle at the leading edge as in- 
creasing the efficiency. After considering the 
1 See Naturr, February 20, 1913, p. 677, e¢ seg. 
