Jury 24, 1902] 
NATURE 
291 
The chapter on the discharge of torpedoes is neces- 
sarily disappointing, as the author is unable to disclose 
information of a confidential nature. 
The most interesting chapter is that which deals with 
the different stabilities on which the successful navigation 
depends. There can be no stability of buoyancy when 
totally immersed ; the vessel either rises to the surface, 
or if it is ever so little heavier than the surrounding 
water it descends with ever-increasing velocity as the 
shell becomes compressed until the bottom is reached. 
When, however, the ship is moving longitudinally, the 
horizontal rudders determine the rise or fall. The 
author has no word of commendation for the method of 
rising or sinking by means of vertical screws. 
After discussing shortly the interesting question of 
lateral stability when floating and when immersed, the 
author proceeds to the explanation of the effect of the 
position of the horizontal rudder on the good behaviour 
of the ship when diving. It seems that the old contest 
between rear and front steering wheels in tricycles has 
its counterpart here, and that the front steering, as in the 
other case, leads to more steady and certain results. 
The stability of direction depends upon there being 
plenty of length with fine lines aft. We are told that 
the submarine of the French Navy, after a run under 
water of several miles, can come to the surface again on 
exactly the same course as that which was followed at 
first. 
A series of chapters on motors—steam, electric, 
petrol—and on tactics bring the author to his conclusion, 
which shows that he and the French Navy are in grim 
earnest, and that in his opinion so powerful and insidious 
a weapon will make naval warfare too terrible to be 
tolerated any longer. However confident the author 
may be, and whatever the truth may be, there is in this 
country much scepticism as to the power of the sub- 
marine, as will be gathered from an exce]lent article in 
the current number of Wztaker, p. 694. CaVAiB: 
THE DYNAMICAL FOUNDATIONS OF 
THERMODYNAMICS. 
Elementary Principles in Statistical Mechanics. 
J. Willard Gibbs, Ph.D., LL.D. 
(New York: Charles Scribner’s 
Arnold, 1902.) Price tos. 6d. net. 
V HERE a branch of science has been approached 
exclusively from the deductive side or exclusively 
from the experimental side, it is far easier to form a 
correct estimate of our state of knowledge in it than is 
the case where experimental and deductive methods 
have been continuously worked side by side. The study 
of rational dynamics has afforded excellent mental 
training for those who have made the greatest marks in 
the world as physicists, notwithstanding the fact that the 
conclusions arrived at in rational dynamics are in direct 
contradiction to ordinary experience. Thus it is impos- 
sible to verify experimentally that the times taken by 
particles to slide down ferfectly smooth chords of a 
vertical circle are equal, and the phenomena of Nature 
are far too complicated to allow of an experimental 
test of the velocity with which a boy would have to throw 
NO. 1708, VoL. 66] 
By 
Pp. xvili + 207. 
Sons; London: 
a cricket ball zz vacuo in order to give it a horizontal 
range of 200 yards. In the study of thermodynamics, 
on the other hand, where the experimental has preceded 
the deductive treatment, as has been the case ever 
since Joule discovered the so-called mechanical equiva- 
lent of heat, much confusion and failure to appreciate 
correctly our state of knowledge have necessarily re- 
sulted, and the only way of evolving order out of chaos 
is to formulate a theory on a purely deductive basis 
founded on certain hypotheses. The interest of the 
theory from a physical standpoint will then depend in the 
agreement or want of agreement between the conclusions 
of the theory and the results of observation. 
In his study of the equilibrium of heterogeneous sys- 
tems, Prof. Willard Gibbs, starting from the deductive side, 
gained a point of vantage which has proved of the greatest 
possible value to the experimental physical chemist. In his 
present work the same authoris to a large extent following 
in the footsteps of Boltzmann, Watson and other writers, 
but at the same time he is imparting a great amount of 
his own originality, both in form and in treatment, to 
their work. It is impossible to read this volume without 
feeling that Prof. Gibbs has been to a great extent imbued 
with the same spirit which led Dr. Watson to produce 
the second edition of his excellent treatise on the “ Kinetic 
Theory of Gases.” This is a valuable feature, for it 
would be difficult to produce in a small compass a better 
introduction to the purely deductive study of the kinetic 
theory than has been given us by Dr. Watson. But 
Prof. Gibbs has gone further, and has not only dis- 
cussed the subject at somewhat greater length, but by 
clothing the investigation in new language, under the 
title of “Statistical Dynamics,” has presented it in a 
form in which it can be studied quite independently of 
any molecular hypothesis as a purely mathematical 
deduction from the fundamental principles of dynamics. 
The study of statistical dynamics is based on the 
consideration, not of a single body or system, but of a 
very large number of such systems, and such a 
collection Prof. Gibbs calls an esemzb/e ; moreover, in the 
course of the work it is found necessary to distinguish be- 
tween grands ensembles and petits ensembles. The principle 
underlying the whole investigation is the well-known 
determinantal relation (corresponding to § 8 of Watson’s 
book) connecting the initial and final values of the 
multiple differentials of the coordinates and momenta of 
an ensemble. The precise meaning of this relation has 
always been exceedingly difficult to grasp. It surely 
adds considerably to our clear understanding of the 
property to have it now enunciated as the “principle of 
conservation of extension in phase.” A slightly modified 
form of enunciation gives the principles of conservation 
of density in phase, and of probability of phase. A 
further property is that extension in phase is an invariant 
in that it is independent of the choice of coordinates. 
The most interesting distribution of the coordinates 
and momenta of an ezsemdle is that determined by a 
probability coefficient of the form e~“" which is com- 
monly known as the Boltzmann-Maxwell distribution. 
Prof. Gibbs calls this the cavzontcal distribution, and the 
limiting case of =o where the coefficient of probability 
is unity is called the mmzcro-canonical distribution. The 
