BOOK
REVIEWS
Progress in Solid Mechanics, Vol. 1. Edited by I. N. SNEDDON and R. Holland Publishing Company, Amsterdam, 1960, 448 pp., 100s.
HILL.
North-
THIS is the first volume of a new addition to the publishers’ ‘ Progress ’ series. Three of the eight articles deal with elastic boundary-value problems. MARGUERRE’S ‘ iUatrioesof transmission in beam problems ’ is concerned with the use of matrices which relate conditions at one end of a beam to those at the other. The title of W. A. GREEN’S article, ‘ Dispersion relations for elastic waves in bars,’ refers to the various approximate wavelength-velocity relations which have been derived, and not to dispersion relations as commonly understood in modern physics. Using the language of dislocation theory, we might describe the latter as Peierls-Nabarro equations in frequency-space ; there is an example on p. 14 of HUNTER’S article in the volume under review. MUKI’S article on ‘ Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plate ’ presents a generalization of methods already worked out for the axisymmetric case. One may question the usefulness of presenting detailed solutions of highly specific problems, but it is certainly convenient to have recorded solutions of fair generality which can be applied to special problems as they arise. For instance, from Mum’s equations (21) and (22) one could quickly find the stress-field of an edge dislocation in a semi-infinite solid. Some aspects of CHADWICK’S subject ’ Thermoelasticity. The dynamic problem ’ received the attention of physicists before the war. Zener and PLsler, for example, found the rate of thermoelastic damping in vibrating solids of various shapes. CHADWICK is concerned with more recent work by applied mathematicians, mostly on thermoelastic waves. It is perhaps worth noting that the characteristic length Z* which he introduces, being equal to the thermal diffusivity divided by the velocity of sound is, in a non-metal, practically the mean free path of the carriers fphonons) responsible for heat conduction. In metals also, as it happens, I* is about the mean free path of the appropriate carriers (electrons). Thus the results presented for waves of length less than I* should not be taken too seriously. In ‘ Viscoelastic waves ’ HUNTER applies Laplace and Fourier transforms to the propagation of waves in rods, compares theory and experiment, andindicates what progress has been made with the three-dimensional problem. H. G. HOPKINS’ ‘ Dynamical expansion of spherical cavities in metals ’ successfully combines physical considerations with the theories of elasticity and plasticity. The remaining two articles are more philosophical. In KOITFX’S ‘ General theorems for elastic-plastic solids ’ it is fascinating to see such a wealth of results derived from very modest premisses. BILBY’S ‘ Continuous distributions of dislocations ’ is a thorough treatment by one of the founders of the theory. For the reviewer, at least, the continuum theory of dislocations has thrown much light on higher differential geometry. No doubt when the subject is further advanced the converse will also be true. J. D. ESHELBY
N. FEATHER : An Introduction to the Physics University Press, 1959, pp. x + 358, 18s.
of Mass,
Length
and Time.
Edinburgh
THE SCOPE of this book is essentially the Mechanics and Properties of Matter which is covered by a good sixth form course in England. The treatment, however, is unusual, in that it is explicitly aimed at providing an understanding of the concepts and principles of the subject matter, and gives no account of techniques. Such a book might expect a wide potential audience in view of what must be a common experience among teachers and students, namely that the ability to reproduce a set of techniques in an examination by no means implies a thorough grasp of the principles involved. 67
68
&OK The
author’s approach commends
REVIEWS
itself in two aspects.
One is the attempt
to convey
an
‘ historical awareness ’ of the evolution of the ideas. Each topic is presented against a mush stronger background of the historical facts than is commonly found in formal textbooks with the same scope. For example, much space is devoted to the problem of defining arbitrary and natural standards of length and time, The other aspect is the way in which the concepts themselves, and their derived notions, are discussed. This is done by implicit insistence on the impotiance of being able to interpret an equation in words, in terms of the physical ooncepts involved. The significant equations are quoted where they cannot be deduced simply (the calculus is eschewed), and they are used to illustrate rather than to express the physieal rehtionships. This important viewpoint is not new - what is unusual is the present attempt to apply it systemmatically in one volume to each topic in turn. It is on the whole successful, if occasionally lacking in conviction in respect of unproved generalization and quotation. The mathematical limitation is presumably imposed for the benefit of the ‘ humanist ’ to whom the book is rather boldly addressed on the fiyleaf. lClore informed readers may disagree on points of emphasis ; the reviewer cannot accept the argument on 1,. 130 that Newton’s Second Law is ‘ certainly not a law of nature.’ The author regards a law of nature as a general statement which tells us that ‘ the universe Iras this particular character - not that possible one.” Thus he appears to regard it as obvious tl priori that 1nomentuIn should be the particular quantity whose rate of change provides a quantit~~t~~~emeasure of the intuitive concept of force. However, the book should make interesting, and at times illuminating, rending for anyone coneerned
with the subject
at this level. M. J.
K. R.
SYMON : Mechanics
(2nd Ed.).
Addison-Weslcy,
Reading,
SEWELL
Mass., 1930, 557 pp., $10.50.
THIS TEXTBOOK has been written mainly for physicists, and forms a basis for an undergraduate course of study. Interest is centred on the ~ntroductio1~ and llnde~tanding of the basic principles of mechanics, and not in the detailed methods of solving individual problems. The examples used to emphasize the theory are of an essentially physical nature, nnd these are supplemented by problems included at the end of each chapter. The first nine chapters are substantially the same as in the first edition, and introduce the fundamental laws and definitions, particle motion in one, two and t,hree dimensions, statics and dynamics of rigid bodies, gravitation theory, moving axiai systems, mechanics of wave propogation and kinematics of fluid motion, and the Lagrange and Hamilton equations of motion. Vector algebra has been used consistently in developing the theory, and a summary of the main results appears in Chapter 3. The remaining three chapters contain more advanced material which does not appear in the first edition. Chapter 10 gives a detailed account of the algebra of second order tensor quantities, and the inertia tensor and tensors associated with the state of stress in fluid and elastic media are defined. The motion of a rigid body about a fixed point is considered in Chapter IX based on Euler’s equ&ions of motion, with particular rcferencc to the mot,ion of a symmetrical top under gravity. Tensor algebra is utilized in Chapter 12 to give an elegant method of investigating the stabiiit,y of an equilibriunk ~on~gur~~tion of a dynamical system. The stability of the Lagrange three-body
configuration
is discussed
iu detail. E. E.
.,ONES