Common experience reveals two basic aspects of wave propagation. First, while preserving their identity and travelling at definite speeds, sounds finally die out. Second, weak sounds may combine to form strong noises. Theories of acoustic propagation have succeeded in representing these aspects of experience separately, but never combined as in nature. The classical theories of sound in perfect fluids and elastic solids easily yield common speeds of propagation for plane infinitesimal disturbances, but no damping. Moreover, within EULER'S theory of the perfect fluid, or its generalization, the GREEN-KIRCHHOFF-KELVIN theory of finite elasticity, weak waves may grow stronger and become shock waves, which propagate according to more complicated but equally definite principles. Effects of internal damping are easily added for theories of infinitesimal deformation, but for finite motions a dead end was reached about sixty years ago. Indeed, in 1901 DUHEM proved that according to the NAVIER-STOKES theory of fluids acceleration waves and waves of higher order cannot exist, and for shock waves he claimed a similar result, which has since been shown to be valid subject to certain qualifications. So as to save the phenomena of sound and noise, as was necessary if the NAVIER-STOKES theory was to deserve the place proposed for it as a refinement upon EULER'S theory, DUHEM introduced the concept of "quasi-wave," a region of rapid but continuous transition.

The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con tinuous field of strain does not correspond, globally, to a continuous field of dis placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body."

This volume collects my shorter articles on the history of mechanics, some already published in various places, some revised from earlier papers, and some never published before. All of them began as lectures, and here they are printed as such, little changed from the last times I read them out to an audience. While the several articles concern different aspects of mechanics, overlap and even some repetition could not be avoided, since mechanics is one great science, and the same original oftentimes served more than one end in its growth. My three major historical treatises, which were published in Volumes (II) 11, 2 12, and 13 of L. Euleri Opera Omnia, are not included. To simplify the printing I have also mostly omitted detailed reference to sources discussed more fully in those treatises, but of course I have added to the texts of the lectures citations of other sources, some notes in answer to questions a reader might ask, and biblio graphical notes at the end of each. I am grateful to the U.S. National Science Foundation for its support of this work through a grant to The Johns Hopkins University."

German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr."

When, after the agreeable fatigues of solicitation, Mrs Millamant set out a long bill of conditions subject to which she might by degrees dwindle into a wife, Mirabell offered in return the condition that he might not thereby be beyond measure enlarged into a husband. With age and experience in research come the twin dangers of dwindling into a philosopher of science while being enlarged into a dotard. The philosophy of science, I believe, should not be the preserve of senile scientists and of teachers of philosophy who have themselves never so much as understood the contents of a textbook of theoretical physics, let alone done a bit of mathematical research or even enjoyed the confidence of a creating scientist. On the latter count I run no risk: Any reader will see that I am untrained (though not altogether unread) in classroom philosophy. Of no ignorance of mine do I boast, indeed I regret it, but neither do I find this one ignorance fatal here, for few indeed of the great philosophers to explicate whose works hodiernal professors of phil osophy destroy forests of pulp were themselves so broadly and specially trained as are their scholiasts. In attempt to palliate the former count I have chosen to collect works written over the past thirty years, some of them not published before, and I include only a few very recent essays."

I. Containing the Analysis of Determinate Quantities.- Section I. Of the Different Methods of calculating Simple Quantities.- Chap. I. Of Mathematics in general.- II. Explanation of the signs + plus and - minus.- III. Of the Multiplication of Simple Quantities.- IV. Of the Nature of whole Numbers, or Integers, with respect to their Factors.- V. Of the Division of Simple Quantities.- VI. Of the Properties of Integers, with respect to their Divisors.- VII. Of Fractions in general.- VIII. Of the Properties of Fractions.- IX. Of the Addition and Subtraction of Fractions.- X. Of the Multiplication and Division of Fractions.- XI. Of Square Numbers.- XII. Of Square Roots, and of Irrational Numbers resulting from them.- XIII. Of Impossible, or Imaginary Quantities, which arise from the same source.- XIV. Of Cubic Numbers.- XV. Of Cube Roots, and of Irrational Numbers resulting from them.- XVI. Of Powers in general.- XVII. Of the Calculation of Powers.- XVIII. Of Roots, with relation to Powers in general.- XIX. Of the Method of representing Irrational Numbers by Fractional Exponents.- XX. Of the different Methods of Calculation, and of their Mutual Connexion.- XXI. Of Logarithms in general.- XXII. Of the Logarithmic Tables now in use.- XXIII. Of the Method of expressing Logarithms.- Section II. Of the different Methods of calculating Compound Quantities.- Chap. 1. Of the Addition of Compound Quantities.- II. Of the Subtraction of Compound Quantities.- III. Of the Multiplication of Compound Quantities.- IV. Of the Division of Compound Quantities.- V. Of the Resolution of Fractions into Infinite Series.- VI. Of the Squares of Compound Quantities.- Chap. VII. Of the Extraction of Roots applied to Compound Quantities.- VIII. Of the Calculation of Irrational Quantities.- IX. Of Cubes, and of the Extraction of Cube Roots.- X. Of the higher Powers of Compound Quantities.- XI. Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded.- XII. Of the Expression of Irrational Powers by Infinite Series.- XIII. Of the Resolution of Negative Powers.- Section III. Of Ratios and Proportions.- Chap. I. Of Arithmetical Ratio, or of the Difference between two Numbers.- II. Of Arithmetical Proportion.- III. Of Arithmetical Progressions.- IV. Of the Summation of Arithmetical Progressions.- V. Of Figurate, or Polygonal Numbers.- VI. Of Geometrical Ratio.- VII. Of the greatest Common Divisor of two given Numbers.- VIII. Of Geometrical Proportions.- IX. Observations on the Rules of Proportion and their Utility.- X. Of Compound Relations.- XI. Of Geometrical Progressions.- XII. Of Infinite Decimal Fractions.- XIII. Of the Calculation of Interest.- Section IV. Of Algebraic Equations, and of the Resolution of those Equations.- Chap. I Of the Solution of Problems in General.- II. Of the Resolution of Simple Equations, or Equations of the First Degree.- III. Of the Solution of Questions relating to the preceding Chapter.- IV. Of the Resolution of two or more Equations of the First Degree.- V. Of the Resolution of Pure Quadratic Equations.- VI. Of the Resolution of Mixed Equations of the Second Degree.- VII. Of the Extraction of the Roots of Polygonal Numbers.- VIII. Of the Extraction of Square Roots of Binomials.- Chap. IX. Of the Nature of Equations of the Second Degree.- X. Of Pure Equations of the Third Degree.- XI. Of the Resolution of Complete Equations of the Third Degree.- XII. Of the Rule of Cardan, or of Scipio Ferreo.- XIII. Of the Resolution of Equations of the Fourth Degree.- XIV. Of the Rule of Bombelli for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree.- XV. Of a new Method of resolving Equations of the Fourth Degree.- XVI. Of the Resolution of Equations by Approximation.- II. Containing the Analysis of Indeterminate Quantities.- Chap. I. Of the Resolution of Equations of the first Degree, which contain more than one unknown Quantity.- II. Of the Rule which is c

B. Coleman, M.E. Gurtin: Thermodynamics and wave propagation in Elastic and Viscoelastic media.- L. De Vito: Sui fondamenti della meccanica di sistemi continui (II).- G. Fichera: Problemi elastostatici con ambigue condizioni al contorno.- G. Grioli: Sistemi a trasformazioni reversibili.- W. Noll: the foundations of mechanics.- R.A. Toupin: Elasticity and electromagnetic.- C.C. Wang: Subfluids.

A compact, moderately general book which encompasses many fluid models of current interest The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments..

Mathematical Reviews

The book should be useful for graduates and researchers not only in applied mathematics and mechanical engineering but also in advanced materials science and technology Each public scientific library as well as hydrodynamics hand libraries should own this timeless book Everyone who decides to buy this book can be sure to have bought a classic of science and the heritage of an outstanding scientist.

Silik ty

All applied mathematicians, mechanical engineers, aerospace engineers, and engineering mechanics graduates and researchers will find the book an essential reading resource for fluids.

Simulation News Europe

Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject. Its main parts are: - The General Theory of Material Behavior - Elasticity - Fluidity This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph’s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

The authors have backgrounds which are ideally suited for writing this book. The late C. Truesdell is well known for his monumental treatises on continuum thermomechanics. K.R. Rajagopal has made many important contributions to the mechanics of continua in general, and to nonlinear fluids in particular. They have produced a compact, moderately general book which encompasses many fluid models of current interest The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments. This is an excellent book which is highly recommended to students and researchers in fluid mechanics.

Mathematical Reviews

The writing style is quintessential Truesdellania: purely mathematical, breathtaking, irrepressible, irreverent, uncompromising, taking no prisoners...The book is filled with historical nuggets Its pure, exact mathematics will baptize, enlighten and exhilarate.

Applied Mechanics Review

The most positive aspect of this book is its brevity; a large number of topics are covered within the space of a little more than 250 pages.

Current Science

This advanced monograph presents one of the best new views on the subject for those who like relative simplicity and certain abstractness combined with mathematical rigor and elegance All the details are carefully worked out and to a large degree based on original work and lifelong experience. The topics range from Euler fluids to memory fluids, and the framework is general enough to treat other nonlinear fluids than those explicitly mentioned The book should be useful for graduates and researchers not only in applied mathematics and mechanical engineering but also in advanced materials science and technology Each public scientific library as well as hydrodynamics hand libraries should own this timeless book Doubtlessly everyone who decides to buy this book can be sure to have bought a classic of science and the heritage of an outstanding scientist.

Silik ty

All applied mathematicians, mechanical engineers, aerospace engineers, and engineering mechanics graduates and researchers will find the book an essential reading resource for fluids.

Simulation News Europe

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of N AVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[s] '" or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary l of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER ticular kinds NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of loVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

The lectures here reported were first delivered in August and September, 1965, for the Department of Mechanical and Aerospace Engi neering at syracuse University, New York under the sponsorship of the New York State Science and Technology Foundation. Lectures 1-6 and 22-23 are revised from a version prepared by Professor Kin N. Tong on the basis of a transcription of the lectures, kindly provided by Professor S. Eskinazi. The remainder of th text has been written out afresh from my own notes. Much of the same ground was covered in my lectures to the Austra lian Mathematical Society's Summer Research Institute at Melbourne in January and February, 1966, and for the parts affected the text conforms to this latter presentation. I am grateful to Professors C.-C. Wang and K. N. Tong for criticism of the manuscript. These lectures constitute a course, not a treatise. Names are attached to theorems justly, to the best of my knowledge, but are not intended to replace a history of the subject or references to the sources."

This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monographs genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

Additional Contributors Are D. Gilbarg, V. Hlavaty, And E. Hopf. Indiana University Mathematics Journal.

In the first edition of this book I tried to survey in brief compass the main ideas, methods, and discoveries of rational thermodynamics as it then stood, only five years after Messrs. COLEMAN & NOLL, while in Baltimore, had written the fundamental memoir that provided for the new science the one root theretofore wanting. A survey in the same style today would require an almost wholly new book, three or four times as long. As it was in 1968, again in 1983 a consecutive treatise restricted to the foundations would be premature, for at this moment they are under earnest discussion, probing analysis, and powerful attack by several students and from several directions. Because, although in the first edition I expressed some opinions I no longer hold and made some statements I should now recast or even re tract, it seems even yet to offer a simple introduction to some aspects of the field that remain current, I have chosen to reprint it unaltered except for emendation of slips and bettering of the English here and there."