THE RATIONAL SPIRIT IN MODERN CONTINUUM...

THE RATIONAL SPIRIT IN MODERN CONTINUUM MECHANICS

The Rational Spirit inModern ContinuumMechanics

Essays and Papers Dedicated to the Memory ofClifford Ambrose Truesdell III

Edited by

CHI-SING MANUniversity of Kentucky,Lexington, U.S.A.

and

ROGER L. FOSDICKUniversity of Minnesota,Minneapolis, U.S.A.

Reprinted from Journal of Elasticity: The Physical and Mathematical Scienceof Solids, Vols. 70, 71, 72 (2003)

KLUWER ACADEMIC PUBLISHERSNEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

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Portrait by Joseph Sheppard

Table of Contents

Portrait by Joseph Sheppard v

Foreword by Chi-Sing Man and Roger Fosdick xi

Published Works of Clifford Ambrose Truesdell III xiii

Serials Edited by Clifford Ambrose Truesdell III xli

Eulogium by Roger Fosdick xliii

Photograph: Bloomington, Indiana, 1959 xlv

BERNARD D. COLEMAN / Memories of Clifford Truesdell 1–13

ENRICO GIUSTI / Clifford Truesdell (1919–2000), Historian of Mathematics 15–22

WALTER NOLL / The Genesis of Truesdell’s Nonlinear Field Theories ofMechanics 23–30

JAMES SERRIN / An Appreciation of Clifford Truesdell 31–38

D. SPEISER / Clifford A. Truesdell’s Contributions to the Euler and theBernoulli Edition 39–53

STUART S. ANTMAN / Invariant Dissipative Mechanisms for the SpatialMotion of Rods Suggested by Artificial Viscosity 55–64

MILLARD F. BEATTY / An Average-Stretch Full-Network Model for RubberElasticity 65–86

MICHELE BUONSANTI and GIANNI ROYER-CARFAGNI / From 3-D Non-linear Elasticity Theory to 1-D Bars with Nonconvex Energy 87–100

GIOVANNI BURATTI, YONGZHONG HUO and INGO MÜLLER / EshelbyTensor as a Tensor of Free Enthalpy 101–112

SANDRO CAPARRINI and FRANCO PASTRONE / E. Frola (1906–1962):An Attempt Towards an Axiomatic Theory of Elasticity 113–125

GIANFRANCO CAPRIZ and PAOLO MARIA MARIANO / Symmetries andHamiltonian Formalism for Complex Materials 127–140

DONALD E. CARLSON, ELIOT FRIED and DANIEL A. TORTORELLI /Geometrically-based Consequences of Internal Constraints 141–149

vii

Photograph: Baltimore, Maryland, 1978

viii

YI-CHAO CHEN / Second Variation Condition and Quadratic Integral In-equalities with Higher Order Derivatives 151–167

ELENA CHERKAEV and ANDREJ CHERKAEV / Principal Compliance andRobust Optimal Design 169–196

JOHN . CRISCIONE / Rivlin’s Representation Formula is Ill-Conceived forthe Determination of Response Functions via Biaxial Testing 197–215

CESARE DAVINI and ROBERTO PARONI / Generalized Hessian and Ex-ternal Approximations in Variational Problems of Second Order 217–242

F. DELL’ISOLA, G. SCIARRA and R.C. BATRA / Static Deformations of aLinear Elastic Porous Body Filled with an Inviscid Fluid 243–264

GIANPIETRO DEL PIERO / A Class of Fit Regions and a Universe of Shapesfor Continuum Mechanics 265–285

LUCA DESERI and DAVID R. OWEN / Toward a Field Theory for ElasticBodies Undergoing Disarrangements 287–326

MARCELO EPSTEIN and IOAN BUCATARU / Continuous Distributions ofDislocations in Bodies with Microstructure 327–344

MARCELO EPSTEIN and MAREK ELZANOWSKI / A Model of the Evolu-tion of a Two-dimensional Defective Structure 345–355

J.L. ERICKSEN / On the Theory of Rotation Twins in Crystal Multilattices 357–373

MAURO FABRIZIO and MURROUGH GOLDEN / Minimum Free Energiesfor Materials with Finite Memory 375–397

ROGER FOSDICK and LEV TRUSKINOVSKY / About Clapeyron’s The-orem in Linear Elasticity 399–426

M. FOSS, W. HRUSA and V.J. MIZEL / The Lavrentiev Phenomenon in Non-linear Elasticity 427–435

GIOVANNI P. GALDI / Steady Flow of a Navier–Stokes Fluid around a Ro-tating Obstacle 437–467

TIMOTHY J. HEALEY and ERROL L. MONTES-PIZARRO / Global Bifurc-ation in Nonlinear Elasticity with an Application to Barrelling Statesof Cylindrical Columns 469–494

MOJIA HUANG and CHI-SING MAN / Constitutive Relation of Elastic Poly-crystal with Quadratic Texture Dependence 495–524

MASARU IKEHATA and GEN NAKAMURA / Reconstruction Formula forIdentifying Cracks 525–538

Body Impact 539–554

I-SHIH LIU / On the Transformation Property of the Deformation Gradientunder a Change of Frame 555–562

R.J. KNOPS and PIERO VILLAGGIO / An Approximate Treatment of Blunt

C

ix

KONSTANTIN A. LURIE / Some New Advances in the Theory of DynamicMaterials 563–573

GERARD A. MAUGIN / Pseudo-plasticity and Pseudo-inhomogeneity Effectsin Materials Mechanics 575–597

A. IAN MURDOCH / On the Microscopic Interpretation of Stress and CoupleStress 599–625

PABLO V. NEGRÓN-MARRERO / The Hanging Rope of Minimum Elonga-tion for a Nonlinear Stress–Strain Relation 627–649

MARIO PITTERI / On Certain Weak Phase Transformations in Multilattices 651–671

PAOLO PODIO-GUIDUGLI / A New Quasilinear Model for Plate Buckling 673–698

G. RODNAY and R. SEGEV / Cauchy’s Flux Theorem in Light of GeometricIntegration Theory 699–719

U. SARAVANAN and K.R. RAJAGOPAL / A Comparison of the Responseof Isotropic Inhomogeneous Elastic Cylindrical and Spherical Shellsand Their Homogenized Counterparts 721–749

M. ŠILHAVÝ / On SO(n)-Invariant Rank 1 Convex Functions 751–762

K. WILMANSKI / On Thermodynamics of Nonlinear Poroelastic Materials 763–777

WAN-LEE YIN / Anisotropic Elasticity and Multi-Material Singularities 779–808

Foreword

Through his voluminous and influential writings, editorial activities, organiza-tional leadership, intellectual acumen, and strong sense of history, Clifford Am-brose Truesdell III (1919–2000) was the main architect for the renaissance of ra-tional continuum mechanics since the middle of the twentieth century. The presentcollection of 42 essays and research papers pays tribute to this man of mathematics,science, and natural philosophy as well as to his legacy.

The first five essays by B.D. Coleman, E. Giusti, W. Noll, J. Serrin, andD. Speiser were texts of addresses given by their authors at the Meeting in memoryof Clifford Truesdell, which was held in Pisa in November 2000. In these essays thereader will find personal reminiscences of Clifford Truesdell the man and of someof his activities as scientist, author, editor, historian of exact sciences, and principalfounding member of the Society for Natural Philosophy.

The bulk of the collection comprises 37 research papers which bear witness tothe Truesdellian legacy. These papers cover a wide range of topics; what ties themtogether is the rational spirit. Clifford Truesdell, in his address upon receipt of aBirkhoff Prize in 1978, put the essence of modern continuum mechanics succinctlyas “conceptual analysis, analysis not in the sense of the technical term but in theroot meaning: logical criticism, dissection, and creative scrutiny.” It is in celebra-tion of this spirit and this essence that these research papers are dedicated to thememory of their bearer, driving force, and main promoter for half a century. Mostof these papers were presented at the Symposium on Recent Advances and NewDirections in Mechanics, Continuum Thermodynamics, and Kinetic Theory – InMemory of Clifford A. Truesdell III, held in Blacksburg, Virginia, in June 2002;parts of two papers were delivered at the meeting Remembering Clifford Truesdell,held in Turin in November 2002; and the rest was written especially for the presentcollection.

The portrait, a photo of which serves as the frontispiece of this collection,adorns the Clifford A. Truesdell III Room of History of Science in the library of

and permanently houses Clifford Truesdell’s previously private collection of books,papers, and correspondence. We are grateful to Mrs. Charlotte Truesdell for helpingus secure a digital file of this photo and for providing us with the list of publishedworks of Clifford Truesdell.

CHI-SING MAN ROGER FOSDICK

University of Kentucky University of MinnesotaLexington Minneapolis

xi

the Scuola Normale Superiore (Pisa, Italy), which was inaugurated in October 2003

Published Works ofClifford Ambrose Truesdell III �

The year of publication is omitted from the entry unless it differs from the yearunder which the entry is listed. Letters following a number indicate subsidiaryseparate publications, as follows:

P Preliminary report or preprint,

A Abstract, separately published or only published version,

C Condensed or extracted version,

L Lecture concerning part or all of the contents of main entry,

R Reprint, entire,

RE Reprint of an extract,

T Translation, entire,

TC Translation, condensed,

TE Translation of an extract.

The list excludes some 600 reviews published between 1949 and 1971 in Math-ematical Reviews, Applied Mechanics Reviews, Zentralblatt für Mathematik, In-dustrial Laboratories, and Mathematics of Computation but includes reviews pub-lished in other journals.

1943

1. (Co-author P. NEMÉNYI) A stress function for the membrane theory of shellsof revolution, Proceedings of the National Academy of Sciences (U.S.A.) 29,159–162.

Other publication in 1943: No. 3A1.

1944

2. ALONZO CHURCH, Introduction to Mathematical Logic, Part I, Notes byC.A. TRUESDELL, Annals of Mathematics Studies No. 13, Princeton, Uni-versity Press, vi + 118 pp.

� Note by the editors: This list and the list on p. 29 are slightly edited versions of those that wereceived from Mrs. C. Truesdell, to whom we are heartily grateful. In our editorial work we haveadded a few entries, updated several items, and made a small number of other minor corrections. ToG.P. Galdi, K. Hutter, R.G. Muncaster, F. Pastrone, and D. Speiser, we are beholden for their help intracking down article titles and numbers of journal volumes. In what follows, explanatory remarksset off by square brackets were made by Clifford Truesdell himself.

xiii

PUBLISHED WORKS OF C.A. TRUESDELL

1945

3. The membrane theory of shells of revolution, Transactions of the AmericanMathematical Society 58, 96–166.3A1. The differential equations of the membrane theory of shells of revolu-

tion, Bulletin of the American Mathematical Society 49 (1943), 863–864.

3A2. The membrane theory of shells of revolution, Bulletin of the AmericanMathematical Society 51, 225.

4. On a function which occurs in the theory of the structure of polymers, Annalsof Mathematics 46, 144–157.

5. Generalizations of Euler’s summations of the series∑∞n=1 n

−2m,∑∞n=0(−)n×

(2n+ 1)−2m−1, etc., Annals of Mathematics 46, 194–195.Other publication in 1945: No. 12A1.

1946

6. (Co-author R.C. PRIM) On Linearized Axially Symmetric Flow of a Com-pressible Fluid, U.S. Naval Ordnance Laboratory Memorandum 8885, 16 De-cember, 4 pp.

7. On Behrbohm and Pinl’s linearization of the equation of two-dimensionalsteady polytropic flow of a compressible fluid, Proceedings of the NationalAcademy of Sciences (U.S.A.) 32, 289–293 = U.S. Naval Ordnance Labora-tory Memorandum 8888, 18 December, 6 pp.

7A. On Behrbohm and Pinl’s linearization of the two dimensional steadyflow of a compressible adiabatic fluid, Bulletin of the American Mathe-matical Society 53 (1947), 59.

Other publications in 1946: Nos. 8A and 12A2.

1947

8. On Sokolovsky’s “Momentless shells”, Transactions of the American Mathe-matical Society 61, 128–133.

8A. Same title, Bulletin of the American Mathematical Society 52 (1946),240.

9. (Co-author R.N. SCHWARTZ) The Newtonian mechanics of continua, U.S.Naval Ordnance Laboratory Memorandum 9223, 18 July, 25 pp.

9A. (Co-author R. SCHWARTZ) On the Newtonian Mechanics of Continua,Bulletin of the American Mathematical Society 53, 1125.

10. A note on the Poisson–Charlier functions, Annals of Mathematical Statistics18, 450–454.

11. Review of L. Brand’s “Vector and Tensor Analysis”, Science 106, 623.Other publications in 1947: Nos. 7A, 12A3, 13P, 14P, 16P, 16A, 23P, 48P.

1948

12. An Essay toward a Unified Theory of Special Functions, based on the Func-tional Equation ∂F(z, α)/∂z = F(z, α + 1), Annals of Mathematics StudiesNo. 18, Princeton, Princeton University Press, iv + 182 pp.

xiv


12A1. On the functional equation ∂F(z, α)/∂z = F(z, α+1), Bulletin of theAmerican Mathematical Society 51 (1945), 883.

12A2. On a class of differential-difference equations, Bulletin of the Ameri-can Mathematical Society 52 (1946), 823.

12A3. On the Functional Equation (∂/∂z)F (z, a) = F(z, a+1), U.S. NavalOrdnance Laboratory Memorandum 8975, 17 February 1947, 13 pp. =Proceedings of the National Academy of Sciences (U.S.A.) 33 (1947),82–93.

12A4. A unified theory of special functions, American Mathematical Monthly56 (1949), 368.

12L. Une méthode nouvelle concernant les fonctions spéciales, pp. 53–72of Three Lectures on Mathematics and Mechanics, U.S. NavalResearch Laboratory Theoretical Mechanics Section MemorandumNo. 3836-1, August 1, 1949.

13. On the total vorticity of motion of a continuous medium, Physical Review (2)73, 510–512.

13P. The Transport of Vorticity, U.S. Naval Ordnance Laboratory Memo-randum 9260, 11 August 1947, 7 pp.

14. On the transfer of energy in continuous media, Physical Review (2) 73, 513–515.

14P. The Energy Theorem for Newtonian Continua, U.S. Naval OrdnanceLaboratory Memorandum 9224, 21 July 1947, 8 pp.

15. A New Definition of a Fluid, U.S. Naval Ordnance Laboratory Memorandum9487, 5 January, 31 pp.15A1. On the differential equations of slip flow, Proceedings of the National

Academy of Sciences (U.S.A.) 34, 342–347.15A2. On the differential equations for slip flow, Physical Review (2) 73,

1255.16. On the reliability of the membrane theory of shells of revolution, Bulletin of

the American Mathematical Society 54, 994–1008.16P. Same title, U.S. Naval Ordnance Laboratory Memorandum 9270, 14

August 1947, 15 pp.16A. Same title, Bulletin of the American Mathematical Society 53 (1947),

1125.17. Généralisation de la formule de Cauchy et des théorèmes de Helmholtz au

mouvement d’un milieu continu quelconque, Comptes Rendus Hebdomadairesdes Séances de l’Académie des Sciences (Paris) 227, 757–759.

17L. Sur la cinématique des mouvements tourbillonaires, pp. 3–20, 73–74of Three Lectures on Mathematics and Mechanics, U.S. NavalResearch Laboratory Theoretical Mechanics Section MemorandumNo. 3836-1, August 1, 1949.

xv


18. Une formule pour le vecteur tourbillon d’un fluide visqueux élastique, ComptesRendus Hebdomadaires des Séances de l’Académie des Sciences (Paris) 227,821–823.18L. Des théorèmes tourbillonaires de la mécanique des fluides, pp. 21–37,

75–76 of Three Lectures on Mathematics and Mechanics, U.S. NavalResearch Laboratory Theoretical Mechanics Section MemorandumNo. 3836-1, August 1, 1949.

Other publications in 1948: Nos. 19P, 32P, 64P.

1949

19. The effect of viscosity on circulation, Journal of Meteorology 6, 61–62.19P. Same title, U.S. Naval Ordnance Laboratory Memorandum 9516, 27

January 1948, 6 pp.19A. Same title, Physical Review (2) 76 (1949), 192–193.

20. Deux formes de la transformation de Green, Comptes Rendus Hebdomadairesdes Séances de l’Académie des Sciences (Paris) 229, 1199–1200.

Other publications in 1949: Nos. 12A4, 12L, 17L, 18L, 22P, 26P, 26L1, 26L2,26L3A, 29P, 35P, 64A.

1950

21A. On finite strain of an elastic body, Bulletin of the American MathematicalSociety 55, 1072.

22. Bernoulli’s theorem for viscous compressible fluids, Physical Review (2) 77,535–536.22P. Same title, U.S. Naval Research Laboratory Report 3558, October 12,

1949, iv + 3 pp.22A. Bernoulli’s theorem for viscous fluids, Bulletin of the American Math-

ematical Society 56, 253.23. (Co-author R. PRIM) A derivation of Zorawski’s criterion for permanent

vectorlines, Proceedings of the American Mathematical Society 1, 32–34.23P. (Co-author R.C. PRIM) Zorawski’s Kinematic Theorems, U.S. Naval

Ordnance Laboratory Memorandum No. 9354, 20 September 1947,4 pp.

24. On the effect of a current of ionized air upon the earth’s magnetic field,Journal of Geophysical Research 55, 247–260; 56 (1951), 134.

25. On the balance between deformation and rotation in the motion of a contin-uous medium, Journal of the Washington Academy of Sciences 40, 313–317.

26. A new definition of a fluid, I: The Stokesian fluid, Journal de MathématiquesPures et Appliquées (9) 29, 215–244; 30 (1951), 156–158.26P. Same title, pp. 351–364 of Proceedings of the 7th International

Congress of Applied Mechanics (1948), Volume 2, 1949 = [withminor alterations] U.S. Naval Research Laboratory Report P-3457,April 26, 1949, iv + 11 pp.

xvi


26L1. Deformation: Elastic, plastic, and fluid masses, Research Reviews(U.S. Office of Naval Research), 15 April 1949, pp. 10–14.

26L2. Une définition nouvelle des fluides, pp. 38–52, 76 of Three Lectureson Mathematics and Mechanics, U.S. Naval Research LaboratoryTheoretical Mechanics Section Memorandum No. 3836-1, August 1,1949.

26L3A. Recent continuum theories of fluid dynamics, Physical Review (2)75 (1949), 1293.

27. On the addition and multiplication theorems for special functions, Proceed-ings of the National Academy of Sciences (U.S.A.) 36, 752–755.

28. The effect of the compressibility of the earth on its magnetic field, PhysicalReview (2) 78, 823.

Other publications in 1950: Nos. 29A, 30A1, 30A2.

1951

29. A form of Green’s transformation, American Journal of Mathematics 73, 43–47.

29P. Same title, U.S. Naval Research Laboratory Report No. 3554, 11October 1949, iii + 4 pp.

29A. Same title, Bulletin of the American Mathematical Society 56 (1950),171.

30. Vorticity averages, Canadian Journal of Mathematics 3, 69–86.30A1. On Poincaré’s analogy between vorticity and mass density, Bulletin

of the American Mathematical Society 56 (1950), 347.30A2. Vorticity averages, Physical Review (2) 79 (1950), 229.

31. Verallgemeinerung und Vereinheitlichung der Wirbelsätze ebener und rota-tionssymmetrischer Flüssigkeitsbewegungen, Zeitschrift für AngewandteMathematik und Mechanik 31, 65–71.

31A. A new vorticity theorem, pp. 639–640 of Proceedings of the Inter-national Congress of Mathematicians, 1950, Volume 1, 1952.

32. On Ertel’s vorticity theorem, Zeitschrift für Angewandte Mathematik und Phys-ik 2, 109–114.

32P. On Ertel’s Theorem of the Diffusion of Vorticity, U.S. Naval Ord-nance Laboratory Memorandum No. 9528, 3 February 1948, 8 pp.

33. Caractérisation des champs vectoriels qui s’annulent sur une frontière fermée,Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences(Paris) 232, 1277–1279.

34. Analogue tri-dimensionnel au théorème de M. Synge concernant les champsvectoriels qui s’annulent sur une frontière fermée, Comptes Rendus Hebdo-madaires des Séances de l’Académie des Sciences (Paris) 232, 1396–1397.

35. A new definition of a fluid, II: The Maxwellian fluid, Journal de Mathéma-tiques Pures et Appliquées (9) 30, 111–155.

35P. Same title, U.S. Naval Research Laboratory Report No. 3553, Sep-tember 20, 1949, viii + 36 pp.

xvii


36. Proof that Ertel’s vorticity theorem holds in average for any medium suffer-ing no tangential acceleration on the boundary, Geofisica Pura e Applicata19, 1–3.

37. On the equation of the bounding surface, Bulletin of the Technical Universityof Istanbul 3, 71–78.

38. On the velocity of sound in fluids, Journal of the Aeronautical Sciences 18,501.

39. The analogy between irrotational gas flow and minimal surfaces, Journal ofthe Aeronautical Sciences 18, 502.

40A. Severe pure shear of an elastic body, Indiana Academy of Science Proceed-ings 61, 271.

41. Discussion of the paper by W.R. Osgood and J.A. Joseph, “On the generaltheory of thin shells”, Journal of Applied Mechanics 18, 231–232.

42. Review of J.L. Synge and R.A. Griffith’s “Principles of Mechanics”, 2ndedn, American Mathematical Monthly 57, 351–354.

Other publications in 1951: Nos. 24 (corrections), 26 (corrections), 54A1.

1952

43. The mechanical foundations of elasticity and fluid dynamics, Journal ofRational Mechanics and Analysis 1, 125–300; 2 (1953), 593–616; 3 (1954),801.43R. [corrected, with a preface, annotations, and appendices (1962)],

pp. i–vxi, 1–186, 204–214 of Continuum Mechanics I, New York,Gordon & Breach, 1966.

44. A program of physical research in classical mechanics, Zeitschrift für Ange-wandte Mathematik und Physik 3, 79–95.44R. [corrected and annotated] pp. 187–203, 215–218 of Continuum Me-

chanics I, New York, Gordon & Breach, 1966.45. On the viscosity of fluids according to the kinetic theory, Zeitschrift für

Physik 131, 273–289.46. On curved shocks in steady plane flow of an ideal fluid, Journal of the

Aeronautical Sciences 19, 826–828.47. Longueur critique pour la propagation des ondes libres dans un fluide visqu-

eux, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sci-ences (Paris) 235, 702–704.

48. Vorticity and the Thermodynamic State in a Gas Flow, Mémorial des Sci-ences Mathématiques No. 119, Paris, Gauthier-Villars, 56 pp.48P. (Co-author R.C. PRIM) Vorticity and the Thermodynamic State in the

Flow of an Inviscid Fluid, U.S. Naval Ordnance Laboratory Memo-randum 9416, 12 November 1947, 14 pp.

49. Review of “Advances in Applied Mechanics”, Volume 2, Bulletin of theAmerican Mathematical Society 58, 403–407.

xviii


50. Review of F.D. Murnaghan’s “Finite Deformation of an Elastic Solid”, Bul-letin of the American Mathematical Society 58, 577–579.50C. Same title, Science 115, 634.

51. Discussion of H.M. Trent’s paper, “An alternative formulation of the laws ofmechanics”, Journal of Applied Mechanics 19, 569–570.

52. Discussion of R.A. Toupin’s paper, “A variational principle for the mesh-typeanalysis of a mechanical system”, Journal of Applied Mechanics 19, 574.

53. Review of W. Prager and P.G. Hodge’s “Theory of Perfectly Plastic Solids”,Bulletin of the American Mathematical Society 58, 674–677.

Other publications in 1952: Nos. 31A, 57P, 59C1, 59C1T, 59C2.

1953

54. Two measures of vorticity, Journal of Rational Mechanics and Analysis 2,173–217.

54A1. A measure of vorticity, Bulletin of the American MathematicalSociety 57 (1951), 138.

54A2. La velocità massima nel moto di Gromeka–Beltrami, AccademiaNazionale del Lincei, Rendiconti della Classe di Scienze Fisiche,Matematiche e Naturali (8) 13, 378–379.

54A3. A measure of vorticity, pp. 245–246 of Proceedings of the 8th In-ternational Congress on Theoretical and Applied Mechanics 1953,1954.

55. Notes on the history of the general equations of fluid dynamics, AmericanMathematical Monthly 60, 445–458.

55R. Same title, Journal of the American Society of Naval Engineers 66(1954), 97–108.

56. Generalization of a geometrical theorem of Euler, Commentarii MathematiciHelvetici 27, 233–234.

57. Precise theory of the absorption and dispersion of forced plane infinitesi-mal waves according to the Navier–Stokes equations, Journal of RationalMechanics and Analysis 2, 643–742.

57P. Preliminary Report: Non-linear absorption and dispersion of planeultrasonic waves in pure fluids, Journal of the Washington Academyof Sciences 42 (1952), 33–36.

58. The physical components of vectors and tensors, Zeitschrift für AngewandteMathematik und Mechanik 33, 345–356; 34 (1954), 69–70.

59. Paul Felix Neményi, Journal of the Washington Academy of Sciences 43,62–63.

59C1. Same title, Science (2) 116 (1952), 215–216.59C1T. [inaccurate] Same title, Physikalische Blätter 7 (1952), 325–326.

59C2. Same title, Zeitschrift für Angewandte Mathematik und Physik 3(1952), 400–401.

59C3. Same title, Zeitschrift für Angewandte Mathematik und Mechanik 33,72.

xix


60. Review of H.M. Westergaard’s “Theory of Elasticity and Plasticity”, Bulletinof the American Mathematical Society 59, 412–413.

61. Review of V.V. Novozhilov’s “Foundations of the Nonlinear Theory of Elas-ticity”, Bulletin of the American Mathematical Society 59, 467–473.

62. Václav Hlavatý, International Mathematical News No. 29/30, 2–3.Other publications in 1953: Nos. 43 (corrections and additions), 65A.

1954

63. A new chapter in the theory of elastica, pp. 52–55 of Proceedings of the FirstMidwestern Conference on Solid Mechanics, 1953.

64. The Kinematics of Vorticity, Indiana University Science Series No. 19, xvii +232 pp.64P. Same title, U.S. Naval Ordnance Laboratory Memorandum 9591, 11

March 1948, 35 pp.64A. Same title, Bulletin of the American Mathematical Society 55 (1949),

296 and 699.65. Le pendule hydraulique, pp. 383–396 of Mémoires sur la Mécanique des Flu-

ides offerts à M.D. Riabouchinsky à l’occasion de son Jubilé scientifique, Pub-lications Scientifiques et Techniques du Ministère de l’Air, Paris.65A. The hydraulic pendulum, Indiana Academy of Science Proceedings 63

(1953), 263.66. Editor’s Introduction: Rational fluid mechanics, 1687–1765, pp. VII–CXXV

of Leonhardi Euleri Opera Omnia, Series II, Volume 12, Zürich, Füssli.67. The present status of the controversy regarding the bulk viscosity of fluids,

Proceedings of the Royal Society (London) A 226, 59–65.68. Mathematics, pp. 618–619 of The American Peoples Encyclopedia Yearbook

for 1953.69. Review of J. Pérès’ “Mécanique Générale”, Bulletin of the American Mathe-

matical Society 60, 286.70. Review of E.J. McShane, J.L. Kelley and F.J. Reno’s “Exterior Ballistics”,

Scripta Mathematica 20, 172–174.71. Review of A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi’s “Higher

Transcendental Functions”, Volumes I and II, American Mathematical Monthly61, 576–578.

Other publications in 1954: Nos. 43 (corrections), 55R, 54A3 and 84C.

1955

72. Hypo-elasticity, Journal of Rational Mechanics and Analysis 4, 83–133, 1019–1020.72L. L’ipoelasticità, Conferenze del Seminario di Matematica dell’Università

di Bari No. 29, Bologna, Zanichelli, 1957, 16 pp. [The text was some-what mangled by the editor.]

72R. [corrected] pp. 43–92 of Continuum Mechanics III: Foundations of Elas-ticity Theory, New York, Gordon & Breach, 1965.

xx


73. The simplest rate theory of pure elasticity, Communications on Pure and Ap-plied Mathematics 8, 123–132.

73R. [corrected] pp. 32–41 of Continuum Mechanics III: Foundations ofElasticity Theory, New York, Gordon & Breach, 1965.

74. Review of F.I. Frankl and E.A. Karpovich’s “Gas Dynamics of Thin Bodies”,Science 121, 163–164.

75. Some things you don’t know about mathematics and mechanics, IndianaAlumni Magazine 17, 2–5. [The title was supplied by the editor; C.T. wouldnot have accepted it, had he been informed.]

76. IU Prof says pupils can’t write, either, Indianapolis Times, June 16. [The titlewas supplied by the editor.]

77. I. Editor’s Introduction: The first three sections of Euler’s treatise on fluid me-chanics (1766). II. The theory of aerial sound, 1687–1788. III. Rational fluidmechanics, 1765–1788, pp. VII–CXVII of Leonhardi Euleri Opera Omnia,Series II, Volume 13, Zürich, Füssli.

Other publication in 1955: No. 80A.

1956

78. (Co-author E. IKENBERRY) On the pressures and the flux of energy in a gasaccording to Maxwell’s kinetic theory, I, Journal of Rational Mechanics andAnalysis 5, 1–54.

79. On the pressures and the flux of energy in a gas according to Maxwell’s kinetictheory, II, Journal of Rational Mechanics and Analysis 5, 55–128.

79L1. La crise actuelle dans la théorie cinétique des gaz (1955), Journal deMathématiques Pures et Appliquées (9) 37 (1958), 103–118.

79L1T. By B.H. Aleksanova i N.T. Pawenko, Sovremenny� kri-zis v kinetiqesko� teorii gazov, Mexanika No. 4/62 (1960),65–75.

79L2. Une solution exacte des équations de Maxwell (1955), Journal deMathématiques Pures et Appliquées (9) 37 (1958), 119–133.

79L3. Congetture intorno ad un nuovo metodo di approssimazione asintotica(1961), Rendiconti di Matematica 23 (1964), 185–192.

80. Das ungelöste Hauptproblem der endlichen Elastizitätstheorie, Zeitschrift fürAngewandte Mathematik und Mechanik 36, 97–103.

80A. Same title, Physikalische Verhandlungen 68 (1955), 129.80T1. By G.�. D�anelidze: Nerexenna� glavna� zadaqa ne-

line�no� teorii uprugosti, Mexanika No. 1/41 (1957), 67–74.

80T2. By C.T.: The main open problem in the finite theory of elasticity,pp. 102–108 of Continuum Mechanics III: Foundations of ElasticityTheory, New York, Gordon & Breach, 1965.

81. Hypo-elastic shear, Journal of Applied Physics 27, 441–447.81R. Pp. 93–100 of Continuum Mechanics III: Foundations of Elasticity

Theory, New York, Gordon & Breach, 1965.

xxi


82. Zur Geschichte des Begriffes “innerer Druck”, Physikalische Blätter 12, 315–326.

83. Experience, theory, and experiment, pp. l3–18 of Proceedings of the SixthHydraulics Conference, Bulletin 36, State University of Iowa Studies in Engi-neering.

84. Review of “Advances in Applied Mechanics”, Volume 3, Scripta Mathematica22, 65–68.84C. A comment on scientific writing, Science 120 (1954), 434.

85. Review of R. Dugas’ “La Mécanique au XVIIe Siècle”, Isis 47, 449–452.86. Query No. 150 [Bounded magic], Isis 47, 59.

1957

87. (Co-author B. BERNSTEIN) The solution of linear differential equations byquadratures, Journal für die Reine und Angewandte Mathematik 197, 104–111.

88. Sulle basi della termomeccanica, Accademia Nazionale del Lincei, Rendicontidella Classe di Scienze Fisiche, Matematiche e Naturali (8) 22, 33–38, 158–166.88T. By C.T.: On the foundations of mechanics and energetics, pp. 293–305

of Continuum Mechanics II: The Rational Mechanics of Materials, NewYork, Gordon & Breach, 1965.

89. Eulers Leistungen in der Mechanik, Enseignement Mathématique 3, 251–262.90. General solution for the stresses in a curved membrane, Proceedings of the

National Academy of Sciences (U.S.A.) 43, 1070–1072.91. Review of “The Principal Works of Simon Stevin”, Volume 1, edited by

E. Crone, E.J. Dijksterhuis, R.J. Forbes, M.G.J. Minnaert, A. Pannekoeg, Phys-ikalische Blätter 13, 578–579.

Other publications in 1957: Nos. 72L, 80T1, 95A.

1958

92. The new Bernoulli edition, Isis 49, 54–62.93. Geometric interpretation for the reciprocal deformation tensors, Quarterly of

Applied Mathematics 15, 434–435.94. Recent advances in rational mechanics, Science 127, 729–739.

94R. [corrected] Essay VIII in No. 165 below.95. Neuere Anschauungen über die Geschichte der allgemeinen Mechanik, Zeit-

schrift für angewandte Mathematik und Mechanik 38, 148–157.95A. Neuere Anschauungen über die Geschichte der Mechanik, Physikalische

Verhandlungen 83 (1957), 50.96. Neuere Entwicklungen in der klassischen statistischen Mechanik und in der

kinetischen Gastheorie, ausgearbeitet von D. MORGENSTERN, Ergebnisse derexakten Naturwissenschaften 30, 286–343.

97. (Co-author J.L. ERICKSEN) Exact theory of stress and strain in rods andshells, Archive for Rational Mechanics and Analysis 1 (1957/8), 295–323.

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97R. Pp. 307–323 of Continuum Mechanics II: The Rational Mechanics ofMaterials, New York, Gordon & Breach, 1965.

Other publications in 1958: Nos. 79L1, 79L2, 98P, 104P, 107P.

1959

98. The rational mechanics of materials – past, present, future, Applied Mechan-ics Reviews 12, 75–80.

98P. Same title, Mathematics Research Center, United States Army, TheUniversity of Wisconsin, Technical Summary Report No. 41, July1958, 28 pp.

98R. [corrected and modified] pp. 225–236 of Applied Mechanics Surveys,Washington, Spartan Books, 1966.

99. Invariant and complete stress functions for general continua, Archive forRational Mechanics and Analysis 4 (1959/60), 1–29.

100. 20 Lectures on the Elements of Fluid Mechanics, notes taken by R. Wells,Rheology Section, National Bureau of Standards, June 30–September 11,multiplied typescript, 131 pp.

101. Review of H. Rouse and S. Ince’s “History of Hydraulics”, Isis 50, 69–71.102. Review of “Rheology, theory and applications”, edited by F. Eirich, Quar-

terly of Applied Mathematics 17, 221–222.103. Query No. 158, “Physical Intuition”, Isis 50, 480.

Other publication in 1959: No. 110A.

1960

104. Intrinsic equations of spatial gas flow, Zeitschrift für Angewandte Mathe-matik und Mechanik 40, 9–14.104P. Same title, Mathematics Research Center, United States Army, The

University of Wisconsin, Technical Summary Report No. 33, July1958, 13 pp.

105. (Co-author R.P. KANWAL) Electric current and fluid spin created by the pas-sage of a magnetosonic wave, Archive for Rational Mechanics and Analysis5, 432–439.

106. (Co-author B.D. COLEMAN) On the reciprocal relations of Onsager, Journalof Chemical Physics 33, 28–31.

107. (Co-author R. TOUPIN) The classical field theories, pp. 226–793 of Flügge’sHandbuch der Physik, Volume 3, Part 1, Berlin/Göttingen/Heidelberg,Springer-Verlag.107P. [Chapter C only] Kinematics of singular surfaces and waves, Mathe-

matics Research Center, United States Army, The University of Wis-consin, Technical Summary Report No. 43, October 1958, 89 pp.

108. (translation by Mathäi) Zu den Grundlagen der Mechanik und Thermody-namik, Physikalische Blätter 16, 512–517.

108T. [English original] Text of the Chairman’s Introduction to the Col-loquium on the Foundations of Mechanics and Thermodynamics

xxiii


held at the U.S. National Bureau of Standards, Washington, October21–23, 1959, Appendix to No. 153, 1966.

109. A program toward rediscovering the rational mechanics of the age of reason,Archive for History of Exact Sciences 1, 3–36.109TE. By C.T.: La scienza del moto dai ‘Principia Mathematica Naturalis

Philosophiae’ di Newton alla ‘Méchanique Analitique’ di Lagrange,Atti e Memorie della Academia Nazionale di Scienze, Lettere edArti, Modena (6) 2, 3–32.

109R1. [corrected] Essay II in No. 165 below.109R2. [of the foregoing] No. HS-76 in The Bobbs-Merrill Reprint Series

in History of Science, 1972.110. Modern theories of materials, Transactions of the Society of Rheology 4, 9–

22.110A. Same title, Rheology Bulletin 28, No. 3 (1959), p. 5.

111. The Rational Mechanics of Elastic or Flexible Bodies, 1638–1788, L. EuleriOpera Omnia, Series II, Volume 11, Part 2, Zürich, Füssli, 435 pp.

111A. Outline of the history of flexible or elastic bodies to 1788, Journalof the Acoustical Society of America 32, 1647–1656.

111L1. Origin of the theory of vibrating systems, Res Mechanica 21 (1987),291–311. [This text was drawn by others from Truesdell’s notes fora lecture.]

112. [unsigned] Potentials (physics), pp. 539–542 of McGraw-Hill Encyclopediaof Science and Technology, Volume 10.

113. [unsigned] Unified field theories, pp. 200–201 of McGraw-Hill Encyclopediaof Science and Technology, Volume 14.

114. Review of “Die Deutsch–Russische Begegnung und Leonhard Euler”, editedby E. Winter, Isis 51, 115.

115. Review of Leonhard Euler’s “Vollständige Anleitung zur Algebra”, edited byJ.E. Hofmann, Isis 51, 434.

116. Query No. 161, Approximate theories in early research, Isis 51, 207. [An-swered by B.L. VAN DER WAERDEN on pp. 567–568.]

Other publication in 1960: No. 79L1T.

1961

117. Stages in the development of the concept of stress, pp. 556–564 of Problemsof Continuum Mechanics [Muskhelisvili Anniversary Volume], Philadelphia,Society for Industrial and Applied Mathematics.

117T. �tapy razviti� pon�ti� napr��eni�, pp. 439–447 of Prob-lemy mexaniki sploxno� sredy, Moscow, Izdatel�stvoAkademii Nauk SSSR.

118. Exact theory of self-expanding piston rings, Ingenieur-Archiv 30, 77–87.119. The Principles of Continuum Mechanics, Socony Mobil Oil Company Col-

loquium Lectures in Pure and Applied Science No. 5 (February, 1960), (x)+371 + XVIII pp. Reprinted in 1963 and 1965.

xxiv


120. General and exact theory of waves in finite elastic strain, Archive for RationalMechanics and Analysis 8, 263–296.

120L. Second-order theory of wave propagation in isotropic elastic mate-rials, pp. 187–199 of Proceedings of the International Conferenceon Second-order Effects, Haifa (1962), 1964.

120R1. [corrected] pp. 230–263 of Continuum Mechanics IV: Problems ofNonlinear Elasticity, New York, Gordon & Breach, 1965.

120R2. Ibid, [not repaginated] Memoir 1 in Wave Propagation in Dissi-pative Materials, a Reprint of Five Memoirs by B.D. COLEMAN,M.E. GURTIN, I. HERRERA R., and C. TRUESDELL, New York,Springer-Verlag, 1965.

121. Ergodic theory in classical statistical mechanics, pp. 21–56 of Rendicontidella Società Italiana di Fisica, XIV Corso = Ergodic Theory, ed. P. Caldirola,New York, Academic Press.

122. Review of M. Clagett’s “The Science of Mechanics in the Middle Ages”,Speculum 36, 119–121.

123. Review of “Critical Problems in the History of Science”, edited by M. Clagett,Manuscripta 5, 101–103.

124. Review of “Die Berliner und die Petersburger Akademie im BriefwechselLeonhard Eulers, Teil I, Der Briefwechsel L. Eulers mit G.F. Müller, 1735–1767”, edited by A.P. Juškevic, E. Winter, and P. Hoffmann, Isis 52, 113–114.

125. Review of M. Dyck’s “Novalis and Mathematics: A Study of Friedrich vonHardenberg’s Fragments on Mathematics and its Relation to Magic, Music,Religion, Philosophy, Language and Literature”, Isis 52, 606–607.

1962

126. Mechanical basis of diffusion, Journal of Chemical Physics 37, 2336–2344.126L. Una teoria meccanica della diffusione, pp. 161–168 of Celebrazioni

Archimedee del Secolo XX (Siracusa, 1961), Volume 3.127. Reactions of the history of mechanics upon modern research, pp. 35–47 of

Proceedings of the Fourth U.S. National Congress of Applied Mechanics.127A. Same title, Journal of Applied Mechanics 29, 225.127R. [corrected] Essay VII in No. 165, below.127T. [of the foregoing] by P. Zimmermann: Rückwirkungen der Ge-

schichte der Mechanik auf die moderne Forschung, Humanismusund Technik 13 (1969), 1–25.

128. Solutio generalis et accurata problematum quamplurimorum de motu corpo-rum elasticorum incomprimibilium in deformationibus valde magnis, Archivefor Rational Mechanics and Analysis 11, 106–113; 12 (1963), 427–428; 28(1968), 397–398.

129. (Co-author R.P. KANWAL) Fluid and magnetic distortion carried by magne-tosonic waves, The Physics of Fluids 5, 368–369.

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130. Review of “Die Berliner und die Petersburger Akademie im BriefwechselLeonhard Eulers, Teil II, der Briefwechsel L. Eulers mit Nartov, Razumovskij,Schumacher, Teplov und der Petersburger Akademie, 1730–1763”, editedby A.P. Juškevic, E. Winter, P. Hoffmann, and Ju.Ch. Kopelevic, Isis 53,411–413.

Other publication in 1962: No. 144P1.

1963

131. (Co-author R.A. TOUPIN) Static grounds for inequalities in finite strain ofelastic materials, Archive for Rational Mechanics and Analysis 12, 1–33; 19(1965), 407.

132. The meaning of Betti’s reciprocal theorem, Journal of Research of the Na-tional Bureau of Standards 67B, 85–86.

133. Remarks on hypo-elasticity, Journal of Research of the National Bureau ofStandards 67B, 141–143.

134. Review of M. Jammer’s “Concepts of Mass in Classical and Modern Physics”,Isis 54, 290–291.

135. Review of D. Morgenstern and I. Szabò’s “Vorlesungen über theoretischeMechanik”, Bulletin of the American Mathematical Society 69, 330–332.

136. Query 170 – Portrait of George Green, Isis 54, 277.

Other publication in 1963: No. 128 (corrections).

1964

137. Second-order effects in the mechanics of materials, pp. 1–47 of Proceedingsof the International Conference on Second-order Effects, Haifa (1962).

138. The natural time of a visco-elastic fluid: its significance and measurement,The Physics of Fluids 7, 1134–1142.

139. A theorem on the isotropy groups of a hyperelastic material, Proceedings ofthe National Academy of Sciences (U.S.A.) 52, 1081–1083.

140. Whence the law of moment of momentum?, pp. 588–612 of Mélanges Alexan-dre Koyré, Volume 1, Paris, Hermann.

140R. [corrected] Essay V of No. 165, below.140TE. By C.T., with a different appendix: “Die Entwicklung des Drall-

satzes”, Zeitschrift für Angewandte Mathematik und Mechanik 44,149–158.

141. The modern spirit in applied mathematics, I.C.S.U. Review of World Science6, 195–205.

142. Fluid mechanics before the Society for Natural Philosophy, Science 143, 382.143. [Gratiae ob lauream honoris causa ab Academia Polytechnica Mediolanensi

collatam], p. 40 of Cerimonie Celebrative del Centenario del Politicnico, 2–4Aprile 1964, Milano.

Other publications in 1964: Nos. 79L3, 120L, 144P2.

xxvi


1965

144. Rational mechanics of deformation and flow [Bingham Medal Address],pp. 3–30 of Proceedings of the 4th International Congress on Rheology(1963), Volume 2.

144P1. Il punto di vista invariantivo nella meccanica dei corpi continui,Rendiconti del Seminario Matematico e Fisico di Milano 32 (1962),91–104.

144P2. Die Rationale Mechanik der Kontinua, Zeitschrift für AngewandteMathematik und Mechanik 44 (1964), 341–347.

144P2T. By A.I. Va�ndiner: Racional�na� mexanika sploxno�sredy, Mexanika No. 4/92 (1965), 103–111.

144RE. [with editorial changes in incorrect English] Buletinul InstitutuluiPolitehnic din Iasi (n.s.) 13 (17) (1967), 415–418; 14 (18) (1968),131–136.

145. (Co-author W. NOLL) The Non-Linear Field Theories of Mechanics, Flügge’sHandbuch der Physik, Volume 3, Part 3, Berlin-Heidelberg-New York,Springer-Verlag, viii + 602 pp.

146. (Co-author B.D. COLEMAN) Homogeneous motions of incompressible ma-terials, Zeitschrift für Angewandte Mathematik und Mechanik 45, 547–551.

147. Fluids of the second grade regarded as fluids of convected elasticity [with anappendix by C.-C. WANG], The Physics of Fluids 8, 1936–1938.

148. Twenty prefaces in Continuum Mechanics II: The Rational Mechanics ofMaterials, New York, Gordon & Breach.

149. Sixteen prefaces in Continuum Mechanics III: Foundations of Elasticity The-ory, New York, Gordon & Breach.

150. Seventeen prefaces in Continuum Mechanics IV: Problems of Non-LinearElasticity, New York, Gordon & Breach.

151. Preface to Wave Propagation in Dissipative Materials, a Reprint of FiveMemoirs by B.D. COLEMAN, M.E. GURTIN, I. HERRERA R., and C. TRUES-DELL, New York, Springer-Verlag, 1965.

Other publications in 1965: Nos. 72R, 73R, 80T2, 81R, 88T, 97R, 120R1, 120R2,135 (corrections).

1966

152. Instabilities of isotropic perfectly elastic materials in simple shear, pp. 139–142 of Proceedings of the Eleventh International Congress of Applied Me-chanics, Munich (1964).

153. Six Lectures on Modern Natural Philosophy, New York, Springer-Verlag,(viii) + 117 pp.

153T1. By Magdalena Staszel and Wojciech Zakrewski: Szesc WykładówNowoczesnej Filozofii Przyrody, Warsaw, Panstwowe WydawnictwoNaukowe, 1969, 143 pp.

xxvii


153TE. [first three lectures] by I.T. Rabotnova: Glavy iz knigi«Xest� lekci� po sovremenno� naturfilosofii»,Mexanika No. 4/122 (1970), 99–136.

153RE. [Lecture 5], pp. 55–73 of A Taste of Science, ed. R.J. Tykodi, West-port, Connecticut, Technomic Publishing Co., 1975.

154. The Elements of Continuum Mechanics, New York, Springer-Verlag, [iv] +279 pp. Corrected second printing, 1985.154L1. Foundations of continuum mechanics, pp. 35–48 of Delaware Sem-

inar in the Philosophy of Physics (1965), edited by M. Bunge, NewYork, Springer-Verlag, 1967.

154L2. Thermodynamics of deformation, pp. 101–112 of Non-EquilibriumThermodynamics, Variational Techniques and Stability, Chicago,University of Chicago Press.

154L3. Thermodynamics of deformation, pp. 1–12 of Modern Develop-ments in the Mechanics of Continua, New York, Academic Press.

154L4. The nonlinear field theories in mechanics (1966), pp. 19–215 ofTopics in Nonlinear Physics, Berlin-Heidelberg-New York, Springer-Verlag, 1968.

154L5. La thermodynamique de la déformation, pp. 207–231 of CanadianCongress of Applied Mechanics (1967), Proceedings, Volume 3,1968.

154L6. Classical and modern continuum theories, pp. 79–92 of Polymersin the Engineering Curriculum, Proceedings of the Third Buhl In-ternational Conference on Materials, Pittsburgh, October 28–29,1968, 1971.

155. Existence of longitudinal waves, Journal of the Acoustical Society of Amer-ica 40, 729–730.

156. Preface, pp. IVA–IVL, to the second edition of G.G. Stokes’s Mathematicaland Physical Papers, New York, Johnson Reprint Co., Volume 1.

Other publications in 1966: Nos. 43R, 44R, 98R, 163L1.

1967

157. Reactions of late baroque mechanics to success, conjecture, error, and failurein Newton’s Principia, The Texas Quarterly, Autumn, 238–258.157R1. [corrected] Essay III in No. 165, below.157R2. [of the preceding], pp. 2–47 of Mechanics 1970, American Acad-

emy of Mechanics, 1970.157R3. [of No. 157R1], pp. 192–232 of The Annus Mirabilis of Sir Isaac

Newton, 1666–1966, edited by R. Palter, Cambridge, Massachusetts,M.I.T. Press, 1971.

157R4. [of No. 157R1] No. HS77 in The Bobbs-Merrill Reprint Series inHistory of Science, 1972.

158. Reply to the paper “Zum Begriff des Elastischen Körpers” by H. Ziegler andD. McVean, Zeitschrift für Angewandte Mathematik und Physik 18, 293.

xxviii


159. Review of C.W. Kilmister and J.E. Reeve’s “Rational Mechanics”, AmericanMathematical Monthly 74, 748–749.

160. Review of “Manuscripta Euleriana Archivi Academiae Scientiarum URSS,Tomus 1, Descriptio Scientifica”, Isis 58, 271–273.

160C. Same title, Scripta Mathematica 28 (1968), 210–211.161. Review of “Manuscripta Euleriana Archivi Academiae Scientiarum URSS,

Tomus 2, Opera Mechanica”, Isis 58, 273–274 = Scripta Mathematica 28(1968), 211–212.

162. Review of I.E. Farquhar’s “Ergodic Theory in Statistical Mechanics”, Quar-terly of Applied Mathematics 24, 386.

Other publications in 1967: Nos. 144RE, 154L1, 165P.

1968

163. Thermodynamics for beginners, pp. 373–387 of Irreversible Aspects of Con-tinuum Mechanics, Proceedings of the IUTAM Symposia Vienna, June 22–28,1966, Wien/New York, Springer-Verlag.163L1. Termodinamica per principianti, Atti e Memorie della Accademia

Nazionale di Scienze, Lettere ed Arti, Modena (6) 8 (1966), 136–144.

163L2. Termodinamica elementare, Rendiconti del Seminario Matematicodell’Università e del Politecnico di Torino 27 (1967/68), 19–33.

163T. By I.T. Rabotnova: Termodinamika dl� naqina�wix,Mexanika No. 3/121 (1970), 116–128.

164. Sulle basi della termodinamica delle miscele, Accademia Nazionale del Lin-cei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali (8)44, 381–383.

164T. By C.T.: On the foundations of the thermodynamics of mixtures,pp. 273–297 of Mechanics 1971, American Academy of Mechanics,1973.

165. Essays in the History of Mechanics, New York, Springer-Verlag, (x)+384 pp.165P. [Essay I only] Leonardo da Vinci, The Myths and the Reality, Johns

Hopkins Magazine, Spring, 1967, 29–42. [The title was supplied bythe editor without informing C.T., who would not have accepted it.]

165A. “Essays in the History of Mechanics”, Archives Internationalesd’Histoire des Sciences 23 (1970), 177–178.

165T. By J.C. Navascues Howard and E.T. Perez-Relaño: Ensayos de His-toria de la Mecánica, Madrid, Editorial Tecnos, 1975, 343 pp.

165TE. [Essay VI] by P. Zimmermann: Frühe kinetische Gastheorien, Hu-manismus und Technik 14 (1970), 1–29.

See also Nos. 94, 109, 127, 140, 157.166. Comment on longitudinal waves, Journal of the Acoustical Society of Amer-

ica 43, 170.

xxix


167. Parole [di ringraziamento per il V Premio internazionale con medaglia d’oro“Prof. Modesto Panetti”], Atti della Accademia di Scienze di Torino 102,21–24.

168. Preface, pp. III–V of Continuum Theory of Inhomogeneities in Simple Bod-ies, Berlin-Heidelberg-New York, Springer-Verlag.

Other publications in 1968: Nos. 128 (corrections) 144RE, 154L4, 154L5, 161(second publication).

1969

169. Rational Thermodynamics. A Course of Lectures on Selected Topics, NewYork, McGraw-Hill, (x) + 208 pp.169T1. By D.J. Fernandez Ferrer: Termodinámica Racional, Barcelona, Ed-

itorial Reverte 1973, X + 221 pp.169T2. By M. Fichera Colautti: Termodinamica Razionale, with an appen-

dix, Contributi del Centro Linceo di Scienze Matematiche e Appli-cazioni No. 20, Roma, Accademia dei Lincei, 1976, 235 pp.

170. A precise upper limit for the correctness of the Navier–Stokes theory withrespect to the kinetic theory, Journal of Statistical Physics 1, 313–318.

170T. By E.G. Berner: Toqny� verhni� predel korrektnostiteorii Nav�e–Stoksa s uqetom kinetiqesko� teorii,Mehanika No. 4/122 (1970), 137–142.

171. A teaching assistant remembers, Wall Street Journal, January 27, p. 14. [Thetitle was supplied by the editor.]

Other publications in 1969: Nos. 127T, 153T1, 157T.

1970

172. De pressionibus negativis in sinu et in pariete regionis fluido viscoso moventiimpletae schedula, Annali di Matematica Pura ed Applicata (4) 84, 213–224.

172A. Same title, Zentralblatt für Mathematik 207 (1971), 252–253.173. Review of L. Suklje’s “Rheological Aspects of Soil Mechanics”, American

Scientist 58, 210–211.Other publications in 1970: Nos. 153TE, 163T, 165A, 165TE, 170T, 181C.

1971

174. Letter to the Editor, The Johns Hopkins Magazine, Spring, 3–4.175. Review of O. Penrose’s “Foundations of Statistical Mechanics”, American

Scientist 59, 638.176. Review of R.M. Christensen’s “Theory of Viscoelasticity: An Introduction”,

American Scientist 59, 615.177. Review of T.L. Hankins’ “Jean d’Alembert: Science and the Enlightenment”,

Centaurus 16, 56–59.Other publications in 1971: Nos. 154L6, 157R3, 172A.

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1972

178. Leonard Euler, supreme geometer (1707–1783), pp. 51–95 of Studies in Eigh-teenth Century Culture, Volume II, Irrationalism in the Eighteenth Century,Case Western Reserve University Press.

179. Review of G.A. Tokaty’s “A History and Philosophy of Fluidmechanics”,Nature 236, 84–85.

180. Review of C. Naux’s “Histoire des logarithmes de Neper à Euler, Tome II, Lapromotion des logarithmes au rang de valeur analytique”, Isis 63, 443–444.

Other publications in 1972: Nos. 109R2 and 157R4.

1973

181. Is there a philosophy of science? An essay review of “Induction and Intuitionin Scientific Thought” by Peter Brian Medawar, Centaurus 17, 142–172.181C. Review of Medawar’s “Induction and Intuition in Scientific Thought”,

Die Naturwissenschaften 57 (1970), 314.182. (Co-author C.-C. WANG) Introduction to Rational Elasticity, Leyden,

Wolters–Noordhoff, xii + 566 pp.183. Introduction à la Mécanique Rationnelle des Milieux Continus [translation

by D. Euvrard of an unpublished English text], vii + 367 pp., Paris, Masson[published as of 1974].

184. Theoria de effectibus mechanicis caloris pridem ab illmo Sadi Carnoto verbisphysicis promulgata nunc primum mathematice enucleata, Atti della Accad-emia di Scienze dell’Istituto di Bologna Classe die Scienze Fisiche (12) 10,29–41.184T. By B. Cimbleris, annotated: Carnot finalmente matematizado, Revista

da Escola da Engenharia da Universidade Federal do Minas Gerais2 (1974), 3–21.

185. The efficiency of a homogeneous heat engine, Journal of Mathematical andPhysical Sciences (Madras) 7 [Milne-Thomson anniversary volume], 349–371; 9 (1975), 193–194.185A. Sul rendimento delle macchine termiche omogenee, Accademia

Nazionale dei Lincei, Rendiconti della Classe die Scienze Fisiche,Matematiche e Naturali (8) 53, 549–553.

185T. By S. Benenti: Sul rendimento di una macchina termica omogenea,Rendiconti del Seminario Matematico dell’ Università e del Politec-nico di Torino 31 (1971/3), 47–68 (1974).

186. Mathematical Aspects of the Kinetic Theory of Gases, Notas de MatemáticaFísica, Volume III, Instituto de Matemática, Universidade Federal do Rio deJaneiro, (viii) + 246 pp.

187. The scholar’s workshop and tools, Centaurus 17, 1–10.188. Review of I. Bernard Cohen’s “Introduction to Newton’s Principia”, Physics

Today, April, p. 59.189. Review of “Die Werke von Jakob Bernoulli, Band I”, Isis 64, 112–114.

xxxi


190. Review of W. Flügge’s “Tensor Analysis and Continuum Mechanics”, Amer-ican Scientist 61, 100.

191. Review of G.S. Gilmor’s “Coulomb and the Evolution of Physics and Engi-neering in Eighteenth-Century France”, Eighteenth-Century Studies 7(1973/4), 213–225.

Other publications in 1973: Nos. 164T, 169T1, 203PT, 224P.

1974

192. The meaning of viscometry in fluid dynamics, Annual Review of Fluid Me-chanics 6, 111–146.

193. (Co-author H. MOON) Interpretation of adscititious inequalities through theeffects pure shear stress produces upon an isotropic elastic solid, Archive forRational Mechanics and Analysis 55, 1–17.

194. Preface, pp. V–VI, The Foundations of Mechanics and Thermodynamics,Selected Papers by W. Noll, Berlin-Heidelberg-New York, Springer-Verlag.

195. A simple example of an initial-value problem with more than one solution,Istituto Lombardo, Accademia di Scienze e Lettere. Rendiconti, Classe diScienze Matematiche e Naturali (A) 108, 301–304.

Other publications in 1974: Nos. 184T and 185T.

1975

196. Pervonaqal�ny� kurs racional�no� mehaniki sploxnyh sred ,translation by R.V. Gol�dxte�n and V.M. Entov of an unpublishedEnglish text, edited by P.A. �ilin and A.I. Lur�e, Moscow, Mir,592 pp.

197. (Co-author H. MOON) Inequalities sufficient to ensure semi-invertibility ofisotropic functions, Journal of Elasticity 5, 183–189.197A. Same title, Zentralblatt für Mathematik 324 (1976), 513–514.

198. Early kinetic theories of gases, Archive for History of Exact Sciences 15,1–66.

199. Les bases axiomatiques de la thermodynamique, Entropie 11, No. 63, 6–11;No. 64, 4–10; No. 65, 4–8. [The title is an unauthorized editorial replace-ment for the author’s “Trois conférences sur la structure conceptuelle de lathermodynamique, 1973”.]

200. Review of P. Costabel’s “Leibniz and Dynamics”, Historia Mathematica 2,360–361.

201. Review of A.C. Eringen and E.S. Suhubi’s “Elastodynamics, Volume I,Finite Motions”, Journal of the Acoustical Society of America 58, 539–540.

Other publications in 1975: Nos. 153RE, 185 (corrections), 213A.

1976

202. History of classical mechanics, Die Naturwissenschaften 63, 53–62, 119–130.202T. História da Mecânica clássica, Revista Brazileira de Ciências

Mecânicas 4 (1982), No. 2, 3–17, and No. 3, 3–21.

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203. The scholar, a species threatened by professions, Critical Inquiry 2, 631–648.203A. Same title, Sociological Abstracts 26 (1978), 807.

203PT. By C. Wintzer and C.J. Scriba: Der Gelehrte: Eine durch die Profes-sionen bedrohte Spezies, Humanismus und Technik 17 (1973), 113–127. [An entire page of text is accidentally omitted.]

203R. [corrected] Speculations in Science and Technology 3 (1980), 517–532.

204. Improved estimates for the efficiencies of irreversible heat engines, Annali diMatematica Pura ed Applicata (4) 108, 305–323.

205. Review of “The Mathematical Papers of Isaac Newton, Volume VI”, editedby D.T. Whiteside, American Scientist 64, 230.

206. Questioni vecchie e nuove di termodinamica razionale (Corso Linceo di1973), published as an appendix (pp. 209–235) to No. 169T2.

207. Irreversible heat engines and the second law of thermodynamics, Letters inHeat and Mass Transfer 3, 267–289.207L. Macchine termiche irreversibili e la seconda legge della termodinam-

ica, pp. 297–307 of Problemi attuali di meccanica teorica e appli-cata, Atti del Convegno Internazionale a ricordo di Modesot Panetti,Torino.

208. Review of “L. Euleri Opera Omnia Series IVA, Volume 1”, edited by A. Juške-vic, V. Smirnov, and W. Habicht, Eighteenth-Century Studies 9, 627–634 =[corrected] Archives Internationales d’Histoire des Sciences 27 (1977),292–296.

209. (Co-authors G. ASTARITA and G.G. SARTI) Insegnamento della termodi-namica nella Facoltà di Ingegneria con i metodi della termodinamica razio-nale, La Chimica e l’Industria 58, 204–206.

210. Review of K. Walters’ “Rheometry”: “Theoretical Rheology”, edited byJ.F. Hutton, J.R.A. Pearson, and K. Walters; R.R. Huilgol’s “ContinuumMechanics of Viscoelastic Liquids”; and P. Chadwick’s “Continuum Me-chanics”, American Scientist 64, 705–706.

1977

211. A First Course in Rational Continuum Mechanics, Part I: Fundamental Con-cepts, New York, Academic Press, xxiii + 280 pp.

212. (Co-author R. FOSDICK) Universal flows in the simplest theories of fluids,Annali della Scuola Normale Superiore di Pisa (IV) 2, 323–341.212R. Pp. 330–348 of Volume 1 of Raccolta degli Scritti dedicati a Jean

Leray, Scuola Normale Superiore, Pisa, 1978.213. (Co-author S. BHARATHA) The Concepts and Logic of Classical Thermo-

dynamics as a Theory of Heat Engines, Rigorously Constructed Upon theFoundation Laid by S. Carnot and F. Reech, New York, Springer-Verlag,xxii + 154 pp.

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213A. How to understand and teach the logical structure and the history ofclassical thermodynamics, pp. 577–586 of Volume 2 of Proceedingsof the International Congress of Mathematicians, Vancouver, 1974,1975.

214. Correction of two errors in the kinetic theory of gases which have been usedto cast unfounded doubt upon the principle of material frame-indifference,Meccanica 11 (1976), 196–199.

215. Review of “Commentationes Mechanicae et Astronomicae, Commentationesad Scientiam Navalem Pertinentes, Volumen Prius, Leonhardi Euleri OperaOmnia Series II, Volumen 20”, edited by W. Habicht, Centaurus 21, 76–77.

216. Review of “Lodovico Ferrari e Niccolò Tartaglia, Cartelli di Sfida Matemat-ica”, edited by A. Masotti, Isis 68, 643–644.

1978

217. [Address upon receipt of a Birkhoff Prize, 1978], The Mathematical Intelli-gencer 1, 99–101, 193.

218. Review of “Die Berliner und die Petersburger Akademie der Wissenschaftenim Briefwechsel Leonhard Eulers, Teil 3, Wissenschaftliche und Wissen-schaftsorganisatorische Korrespondenzen 1726–1744”, edited by A.P. Juške-vic, E. Winter, P. Hoffmann, I.N. Klado, and Ju.Ch. Kopelevic, Isis 69, 301–303.

219. Some challenges offered to analysis by rational thermomechanics, pp. 495–603 of Contemporary Developments in Continuum Mechanics and PartialDifferential Equations (Proceedings of the International Conference on Con-tinuum Mechanics and Partial Differential Equations, Rio de Janeiro, Au-gust 1977), edited by G.M. de LaPenha and L.A. Medeiros, Amsterdam,North-Holland.

1979

220. Absolute temperatures as a consequence of Carnot’s General Axiom, Archivefor History of Exact Sciences 20, 357–380.

221. Schizzo concettuale della termodinamica per gli studiosi di meccanica, Bol-lettino della Unione Matematica Italiana (5) 16-A, 1–20.

222. Essay review of I. Szabò’s “Die Geschichte der Mechanischen Prinzipien”,Centaurus 23, 163–175.

223. [translation of an unpublished English text] Meccanica e Termomeccanicarazionale (1974), pp. 33–52 of Volume IV of Enciclopedia del Secolo XX,Rome.

1980

224. (Co-author R.G. MUNCASTER) Fundamentals of Maxwell’s Kinetic Theoryof a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics,New York, Academic Press, xxvii + 593 pp.

225. The Tragicomical History of Thermodynamics, 1822–1854, New York,Springer-Verlag, XII + 372 pp.

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