448 
NATURE 
[JuLy 4, 1912 
deals with particle and rigid dynamics, theory of 
the potential, analysis of stress and strain, and 
the equations of hydrodynamics. This book, 
therefore, belongs to a class, of which we have 
seen previous examples, in which it is sought 
to condense into one volume the fundamental 
principles of several portions of applied mathe~ 
matics, the detailed study of each of which would 
occupy a volume to itself. As Dr. Timerding 
points out, this necessitated careful pruning down 
of the subject-matter, and he expresses the hope 
that the selection will suffice for the object in 
view. The kind of reader who will really profit 
by a book of this character is the student of 
modern physics who requires to acquire this par- 
ticular knowledge in his undergraduate days, and 
who subsequently proposes a course of training 
in research. For him the book should be very 
useful. 
(2) It would have been a great improvement if 
Col. Western had arranged for a few hours’ 
coaching with a modern graduate in mathematics 
or physics before attempting to enlighten the 
public on the practical science of billiards. His 
graphical constructions for the deviation of a 
billiard ball after impact are all right, but it 
would have been greatly conducive to lucidity if 
he had explained the dependence of the result on 
the coefficient of restitution. A more serious 
defect is that the author speaks of the “forces of 
a ball” when that ball may be moving with 
uniform velocity in a straight line. This is a mis- 
use of the term “force” which is quite unneces- 
sary, and calculated to prejudice the scientific 
reader against the book. The author’s explana- 
tion of the curved path of a ball on p. 75 is also 
on the face of it unsound. Nevertheless, he claims 
to have invented a “pointer,’’ which enables a 
beginner to find where to place his balls, and 
where to aim when attempting any particular 
stroke, and this appears to be correct in principle, 
and to enable allowances to be made for differ- 
ences in strength or mode of playing, as well as 
for other factors which may affect the result. 
(3) In “The Physical Significance of Entropy ’ 
Prof. J. F. Klein has attempted to present the 
general conclusions arising from the investigations 
of Boltzmann and Planck, the former dealing 
mainly with molecular systems, and the latter 
with radiation phenomena. Planck’s treatise was 
reviewed some time ago in Nature. The par- 
ticular aspect of the problem here dealt with is 
the connection of the second law with probability 
considerations. In separating the conclusions 
from their analytical proofs, Prof. Klein has given 
the unmathematical reader a statement of results 
which he must accept on the authority of Boltz- 
NO. VoL. 89| 
’ 
DOD, 
<--/;5 
mann and Planck unless he is prepared to study 
up the original difficult mathematical investiga- 
tions. The trouble is that these books fall into 
the hands of readers with whom a little knowledge 
is a dangerous thing, and who without troubling 
to study the matter thoroughly rush into print 
with theories of their own, in which the most 
conspicuous feature is the flagrant misuse of 
elementary physical terms. 
Although these statistical considerations have 
certainly been successfully applied to the interpre- 
tation of current physical events, it must not be 
forgotten that they possess one important diffi- 
culty. While the theory of probability shows that 
the entropy of a system tends to a maximum, the 
same arguments appear to indicate the extreme 
improbability that the entropy should ever deviate 
from this maximum, and we are thus required to 
postulate an initial state of the universe, the im- 
probability of which becomes increasingly difficult 
to understand as we go further and further back 
in the scale of time. 
It should be stated that Prof. Klein makes no 
claims to originality, and his book is well suited 
to specialists in other branches of science who 
want to know the gist of what has been done in 
this particular subject. 
In connection with this review, mention may 
be made of a recent paper by Planck in the 
Annalen der Physik, 37 (1912), on the foundation 
of the law of black-body radiation, in which the 
statistical method is again employed. 
(4) Prof. E. Mach’s “Popular Scientific Lec- 
tures’ is a miscellaneous collection of twenty-six 
articles averaging rather under twenty pages in 
length, dealing with varied questions in physics, 
philosophy, physiology, and psychology, and in- 
cluding music, photographs of flying bullets, 
binocular vision, space and time, relative value of 
different educational studies, elements of electro- 
statics, energy and entropy, and other subjects 
equally diverse in character. It is the kind of 
book to be read in leisure half-hours by a busi- 
ness man who is interested in science but has 
no time for extended study. Under ‘symmetry 
in music”? we notice an interesting experiment 
which may easily be reproduced by reversing a 
music-roll and playing it with the bass end towards 
the treble. 
(5) It would be unnecessary to refer in detail 
to the latest edition of Prof. Duhem’s ‘‘ Thermo- 
dynamics and Chemistry,” since this work has 
now become a recognised text-book, and the 
English translation, which appeared in 1903, is 
largely read both in this country and in America. 
Since the first edition science has lost Willard 
Gibbs, Van der Waals, and Bakhuis Roozeboom ; 
