JuLy 17, 1902] 
NATURE 
269 
is less severe than these, but which is something more 
than a mere description of acoustic phenomena, is still a 
desideratum. Where attempts have been made to 
supply the want the result is not successful, owing chiefly 
to the clumsy methods employed in “ getting round” the 
calculus. We are not upholders of the doctrine that the 
calculus should be “got round”; it is much better, we 
think, to “get through” it. Experience in teaching 
others has taught us that pupils find no difficulty in 
grasping its elements, and this is the case whether they 
are taught analytically or geometrically. Why then 
should we seek to devise elaborate methods of eluding 
the calculus—methods which in most cases we would 
never think of employing ourselves, and which, moreover, 
are usually only adapted to the particular problem for 
which they are devised—when a straightforward intro- 
duction to the methods we use ourselves would clear the 
ground and render the student’s progress easy, and 
enable him the sooner to be his own path-finder instead 
of needing to rely on the guidance of others ? 
The book under review cannot supply this want in 
England, for it is a translation into German (from the 
Dutch) ; the substance of the book is in the above 
respect, however, entirely to our mind. 
No calculus is employed in name; but the notion of 
it is everywhere. Velocity is the limiting value of a ratio 
and so is acceleration, and their values are found by the 
usual direct methods employed in proving the initial 
theorems of the calculus. We would have gone a step 
further and given the process a name, in order to suggest 
to the student to what branch of mathematics these and 
similar theorems belong. But the notion is the main 
thing. There is nothing here which a man will discard 
at a future time, having learnt a better way ; though he 
will, of course, learn to abbreviate the logical statements 
of the process into the mere symbols d@x/d¢ and @2x/d7?. 
Without making a full analysis, the following subjects 
dealt with may be briefly stated :—In the mathematical 
treatment: simple harmonic motion—waves and their 
composition, with a proof of all the simple theorems. 
Fourier’s theorem is given, but not proved; it is 
illustrated, however. The dynamical equation to simple 
harmonic motion is given, and the motion deduced by 
showing that it satisfies the equation. Even the case of 
a restoring force involving second as well as first power 
of displacement is given, on account of its importance in 
connection with the Helmholtz theory of the production 
of combination tones. The equation to damped 
motion is treated as an article for faith ; its properties, 
however, are lucidly described. 
| 
Although the experimental phenomena are mainly 
is not | 
collected together, the mathematical portion 
wholly free from experimental illustration, For example, 
we specially note a device which should be found useful 
for illustrating the behaviour of forced oscillations with 
different degrees of damping. 
Perhaps the most interesting section is that dealing 
with the interference and diffraction of waves. This 
might be amplified by an account of recent experiments 
imitative of Lloyd’s mirror and diffraction from two 
apertures (Young’s experiment) ; and, in particular, an 
account of Rayleigh’s brilliant application of the principles 
of diffraction in restricting the spreading of sound to one | 
NO. 1707, VOL. 66] 
plane by suitably shaping the aperture of the fog horns 
employed in coast signals would form an _ excellent 
additional illustration. 
The last chapter is concerned with movements of air 
in pipes, concluding with an account of the secondary 
motions usually developed, such as the small striations 
in the cork figures in a Kundt’s tube, which were in- 
vestigated by Walther Konig and others (Konig is 
mentioned without being discriminated from R. Kénig). 
These are highly interesting, though many will no doubt 
consider them rather out of place in an elementary book. 
There is no mention of Riicker’s important experiments 
in connection with combination tones. 
OUR BOOK SHELF. 
Malarial Fever, its Cause, Prevention and Treatment. 
Containing full Details for the use of Travellers, 
Sportsmen, Soldiers, and Residents in Malarious 
Places. By Ronald Ross, F.R.S., Walter Myers 
Lecturer in the Liverpool School of Tropical Medicine. 
Ninth edition, revised and enlarged. Pp. 68. (London : 
Published for the University Press of Liverpool by 
Longmans, Green and Co., 1902.) Price 2s. 6d. 
THIS little book is an enlargement of a previous work 
by the same author, and should prove of the utmost use 
to those for whom it is written. The exact knowledge 
concerning the epidemiology of malaria which has been 
attained during the last six or seven years has made 
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locality. The wide dissemination of these principles and 
of the facts upon which they are based is the next obvious 
step in the campaign against malaria, and the Liverpool 
School of Tropical Medicine has done good service in 
the publication of this work. Within the short compass 
of some seventy pages we find a lucid and succinct 
account of the nature and life-history of the malarial 
parasite, of the habits and life-histories of the gnats 
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nothing is wanting that should enable an intelligent man, 
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aman may safely pass through countries where malaria 
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the book heartily to all who have occasion to sojourn in 
such lands. 
Velocity Diagrams. Their Construction and Uses. 
Intended for all who are interested in Mechanical 
Movements. By Prof. C. W. MacCond, A.M., Sc.D. 
Pp. iii + 116; 83 figures. (New York: John Wiley 
and Sons; London: Chapman and Hall, Ltd., 1902.) 
Price 1.50 dollars. 
IN this book some examples of plane motions of machines 
are worked out. The title well describes the scope and 
contents of the work and the very modest aims of the 
author. 
The main problem to which the discussion is directed 
is :—Given a skeleton drawing of a mechanism and the 
speed of the driving point, to find graphically the corre- 
sponding speed of the driven point, and to show the 
latter all throughout the cycle by means of a rectangular, 
