Nous avons tâché d'y rappeler, avec tous les détails que comportait l'étendue matérielle de texte dont nous pouvions disposer, l'existence si bien remplie et les travaux les plus marquants du profond ingénieurgéomètre, notre maître à tous deux, qui a été une des gloires de l'Académie à notre époque et un modèle pour les travailleurs de tous les temps. (Comptes rendus, T. civ., 1887, p. 215.) A more popular account of Saint-Venant's life based chiefly on the notices in the Annales and Nature will be found in the Tablettes biographiques; Dixième Année, 1888. [411.] Summary. In estimating the value of Saint-Venant's contributions to our subject, we have first of all to note that he is essentially the founder of practical, or better, technical elasticity. In his whole treatment of the flexure, torsion and impact of beams he kept steadily in view the needs of practical engineers, and by means of numerical calculations and graphical representations he presented his results in a form, wherein they could be grasped by minds less accustomed to mathematical analysis. At the same time he was no small master of analytical methods himself, and he undertook in addition purely numerical calculations before which the majority would stand aghast. His memoirs on the distributions of elasticity round a point and of homogeneity in a body opened up new directions for physical investigation, while his numerous discussions on the nature of molecular action have greatly assisted towards clearer conceptions of the points at issue. The hypotheses of modified molecular action and of polar molecular action may either or both be true, or false; but we see now clearly that it is to the investigation of these hypotheses and not to the experiments of Oersted etc. nor to the viscous fluid and ether jelly arguments of the first supporters of multi-constancy to which we must turn if we want to investigate the question of rari-constancy1. SaintVenant's foundation, on the basis of Tresca's investigations, of the new branch of theoretical science, which he has termed plasticodynamics, has not only direct value, but shews clearly the fallacy of those who would identify plastic solids and viscous fluids. The fundamental equations in the two cases differ in character; a difference which may be expressed in the words—the plastic solid 1 This is well brought out by the comparison of Voigt's recent memoir (Göttinger Abhandlungen, 1887) with those of the early supporters of multiconstancy. requires a certain magnitude of stress (shear), the viscous fluid a certain magnitude of time for any stress whatever, to permanently displace their parts. Not the least merit of Saint-Venant's work is the able band of disciples he collected around him. His influence we shall find strongly felt when investigating the work of Boussinesq, Lévy, Mathieu, Resal and Flamant. He formed the connecting link between the founders of elasticity and its modern school in France. The vigorous spirit, the striking mental freshness, the perfect fairness of his thought enabled him to penetrate to the basis of things; the depth of his affection, his kindly foresight and consideration, his rare personal devotion attached to him all who came in his way and stimulated them to renewed investigation (Flamant and Boussinesq: Notice sur la vie et les travaux de B. de St. V., p. 27). INDEX1. = The numbers refer to the articles of the book and not to the pages unless preceded by p. C. et A. Corrigenda and Addenda to Volume I. attached to this Part. ftn. =footnote. Amorphic Bodies, elastic coefficients for, 308: see also Ellipsoidal Distribution Amorphism, or confused crystallisation, 115, 192 (d) Angers, Church of, factor of safety for columns, 321 (b) Anticlastic Surfaces, Thomson and Tait's, 325 Arches, wooden, experiments on, C. et A. pp. 4-10 Ardant, his experiments on wooden arches, C. et A. p. 4; theory of circular ribs, C. et A. p. 10 Atomic Constitution of bodies, indivisi. bility of atoms, Berthelot and SaintVenant on, 269; Boscovich and Newton on atoms, 269; Saint-Venant's long memoir on, 275-280 Atoms: see also Intermolecular Action; Saint-Venant's arguments that they are without extension, 277-80 Axes, feathered, strength of, 177 (c) Axes of Elasticity: see Elasticity, Axes of Babinet, his proof of velocity of pressural or sound wave, 219 Bar: see Flexure of, Impact on, etc. Beam: see Rolling Load on, Torsion of, Flexure of, Impact on, etc.; of strongest cross-section, 176, 177 (b); formulae for stress-strain relation for, when stretch and squeeze moduli are unequal, 178; rupture of, deduced from empirical relation between stress and strain, Saint-Venant's and Hodgkinson's formulae, 178 Beam- Engine, stress in beam, 358; danger of certain speeds of fly-wheel, 359 Bending-moment, safe limit of, for nonsymmetrical loading, 14; in terms of shear, 319 Bernoulli-Eulerian formulae for flexure, 71, 80 Berthot, on law of intermolecular action, 408 Bertrand, reports on Saint-Venant's memoir on transverse impact, 104 Binet, on elastic rods of double curvature, 155 Blanchard, experiments on material under great pressure, 321 (b), 50 Boiler, Cylindrical, proper dimensions for spherical ends of, 125 Boltzmann, on longitudinal impact of bars, 203 Boscovich, his theory of atoms, p. 185, 280; deprived atom of extension, 269 Boussinesq, proves conditions of compatibility for given system of strains, 112; proves ellipsoidal distribution for amorphic bodies subject to permanent strain, 230; points out error in 1 This index will be incorporated in that for the entire second volume on its completion. Saint-Venant's memoir of 1863, 238; Bresse, on elastic curve of rods of double Brill, points out error in Saint-Venant's Briot, Saint-Venant's views on his theory Brix, on strength of railway-rails, C. et A. p. 11; on fail-points of uniformly Buckling Load of struts under dead load, Caoutchouc, Wertheim's and Clapeyron's Cerruti, on application of potential to Coriolis, on longitudinal impact of bars, Cornu, his experiments on elastic con- Cross-stretch Coefficients, how effected by Crystallisation, Confused, 115, 192 (d); Cylindrical Shell subjected to surface Desplaces, his experiments referred to, Double Refraction: see also Light; as to ditions for, 148-9, 154; Green's, Duleau, his experiments on torsion of Easton and Amos, their experiment, 164 Elastic Coefficients, terminology for, p. Elastic Equations, unique solution of, 6, Elastic Homogeneity, Distribution of, Elastic Line, when flexure is not small, 172; elementary proofs of equation to, Elastic Modulus: see Stretch-Modulus Elasticity, Axes of, 135, 137 (iii), 137 (vi); Elasticity, Distribution of, round any cular considerations, 228; involving Ellipsoidal Conditions, in terms of thlip- Ellipsoidal Distribution, 198 (e); adopted Ellipsoids of Cauchy, 226 Euler, on problem of plate, 167 Fail-Limit: see also Fail-Point, general 12 Fatigue, of a material, 169 (g) Flexure, some results for, given in |