130 
American point of view, occasionally requires 
adaptation for English students, e.g., some of the 
test words in the chapter on apperception. This 
would be of little consequence were it not that 
the actual pages of the book are intended to be 
used in the experiments. In spite of this draw- 
back, however, it will be found extremely useful 
by anyone in charge of, or wishing to form, an 
experimental class of the kind indicated. 
AVIATION DYNAMICS. 
(1) La Théorie de l’Aviation, son application a 
l’Aéroplane. By Robert Gaston. Préface de 
Maurice Farman. Librairie des Sciences aéro- 
nautiques. (Paris: F. Louis Vivien.) Price 
1.50 francs. 
(2) Aéroplanes in Gusts. Soaring Flight and the 
Stability of Aéroplanes. By S. L. Walkden. 
Pp. xv+188. (London: E. and F. N. Spon, 
Ltd., 1912.) Price 7s. 6d. net. 
T is remarkable how many books have been 
written in connection with problems on 
aviation in which the principles of elementary 
dynamics have been ignored, misinterpreted, or 
otherwise misunderstood in a way that no candi- 
date for an intermediate B.Sc. examination would 
believe to be possible. These two books afford 
excellent examples of this disregard of elementary 
principles. 
(1) M. Robert Gaston, who has a highly flatter- 
ing preface from Mr. Maurice Farman, finds that 
if a body is allowed to fall and then stopped at 
intervals of one second, its average velocity will 
be 4°9 metres per second (with g=9'81 m/s”). If 
stopped more frequently its average velocity will 
be less, until we come to the case when it is being 
stopped at every instant—i.e. continually sup- 
ported—when its average velocity is nil. Having 
definitely proved this, he contradicts himself by 
saying that to maintain a body in the air an up- 
ward velocity of 4°9 metres per second must be 
imparted, so that if the weight is MW” kilograms, 
the rate of working must be 4'9MV kilogram 
metres per second. If he had adopted a minute, 
instead of a second, as unit of time, he would have 
found that the work required was 4'9IW x 60? 
kilogram metres per minute, or sixty times his 
estimate; similarly, by taking an hour as unit 
he would have found a result 3600 times as great 
as he has estimated. Can anything be more 
absurd? Yet Maurice Farman congratulates him 
on the clearness and simplicity of his book ! 
(2) Mr. Walkden’s main theme is based on a 
complete misunderstanding of the physical signi- 
ficance of the law of composition of accelerations. 
2292, VOL. 92| 
NATURE 
[OcToBER 2, 1913 
He measures the effect of a gust of wind by the 
accelerations of the air particles relative to the 
aéroplane, and by compounding this acceleration 
reversed with gravity he gets what he calls the 
resultant relative gravity. But the result means 
nothing at all. 
The only effect which a gust of wind can have 
on an aéroplane is due to the pressures of the 
air on the surfaces and other parts of the aéro- 
plane. These are in general functions of the rela- 
tive velocity components of the air rather than 
the accelerations. The best that Mr. Walkden’s 
method |can do is to determine their rates of 
increase, not their actual values. To solve the 
problem of the aéroplane in gusts it is necessary, 
in the first place, to determine the six force and 
couple components of the air pressures as functions 
of the six components of relative linear and angular 
velocity of the aéroplane, and, having done this, 
to investigate the six equations of motion of the 
aéroplane under the action of these forces’ and 
couples. This book does nothing towards solving 
this problem, and, on the other hand, the appear- 
ance of such books is calculated to deter competent 
mathematicians and physicists from attacking such 
problems. 
OUR BOOKSHELF. 
Himmelskunde und der AsStro- 
nomischer Geographie. Verfasst von Dr. Alois 
Héfler. Pp. xii+414. (Leipzig and Berlin: 
B. G. Teubner, 1913.) Price 12 marks. 
Tuis is the second volume of a useful series of 
handbooks which is appearing under the general 
title of ‘“‘ Didaktische Handbiicher fiir den Realis- 
tischen Unterricht an Héheren Schulen,” and 
arranged by Professor A. Héfler of Vienna and 
Professor F. Poske of Berlin. This volume fol- 
lows that from the pen of the first named, which 
dealt with mathematical instruction, and its object, 
like its predecessor, is to reform the teaching of 
astronomy and astronomical geography in the 
schools. The volume is essentially for teachers 
and displays a graduated series of courses of in- 
struction for students commencing when eleven 
years old and finishing at eighteen. The book 
is divided into four stages, each stage arranged 
to cover two years of the student’s training. The 
author strives at great length to impress on the 
teacher the importance of leading the students to 
observe for themselves as much as possible, and 
to show them simple experiments whenever the 
opportunity arises. 
No pains seem to have been spared to provide 
the teacher with numerous references to works 
that may be consulted by him, and to draw his 
attention to numerous points which are not often 
sufficiently clearly explained to the youthful 
student. 
While the full course here suggested would be 
Didaktik der 
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