The Rational Mechanics of Flexible or Elastic Bodies 1638–1788

1 We search the concepts and methods ) of the theory of deformable sonds from GALILEO to LAGRANGE. Neither of them achieved much in our subject, but their works serve as 2 termini: With GALILEO's Discorsi in 1638 our matter begins ) (for this is the history of mathematical theory), while LAGRANGE's Mechanique Analitique closed the mechanics of 1) There are three major historical works that bear on our subject. The first is A history of the theory of elasticity and of the strength of materials by I. ToDHUNTER, "edited and completed" by K. PEARSON, Vol. I, Cambridge, 1886. Unfortunately it is necessary to give warning that this book fails to meet the standard set by the histories ToDHUNTER lived to finish. Much of what ToDHUNTER left seems to be rather the rough notes for a book than the book itself; the parts due to PEARSON are fortunately distinguished by square brackets. Researches prior to 1800 are disposed of in the first chapter, 79 pages long and almost entirely the work of PEARSON; as frontispiece to a work whose title restricts it to theory he saw fit to supply a possibly original pen drawing entitled "Rupture. Sur­ faces of Cast-Iron". Content: Front Matter....Pages 1-14 Remarks of the ancients on vibration and elasticity....Pages 15-18 Western researches before 1600....Pages 18-23 The vibrating string, the breaking of a beam, and the catenary in Galileo’s Discorsi (1638)....Pages 24-28 The unpublished work of Huygens on the suspension bridge (1646), the breaking of a beam (1662), the vibrating string (1673), and the vibrating rod (1688)....Pages 28-33 The contest to find the catenary (1690)....Pages 34-44 Researches on theoretical and experimental elasticity by James Riccati (1720–1723) and others....Pages 44-50 Experiments on the nodes of vibrating bodies by Noble and Pigot (1674), Sauveur (1696–1701), de la Hire (1709), and Zendrini (1715–1716)....Pages 50-53 Summary: Euler’s heritage....Pages 53-58 Further researches on the elastica; Euler’s general solution for linear vibration problems (1735–1739)....Pages 59-64 The first differential equations of motion: John Bernoulli’s and d’Alembert’s treatments of the hanging cord (1742–1743)....Pages 64-75 Summary to 1748....Pages 75-88 Miscellaneous polemics (1760–1767)....Pages 88-96 Miscellaneous polemics to 1788....Pages 96-109 Summary of the theory of the vibrating string to 1788....Pages 109-114 The earliest researches on non-uniform strings: Simple modes for special cases, and Euler’s general inverse method (1752–1765)....Pages 114-117 Polemics, errors, and further special cases (1770–1788)....Pages 118-129 Plane vibrations of a heavy cord hung from one end....Pages 129-132 Discrete models....Pages 132-136 The distinction of different kinds of buckling by Daniel & John III Bernoulli (1766)....Pages 136-141 Miscellaneous researches (1754–1768)....Pages 142-146 An evaluation from the eighteenth century: Lagrange’s Méchanique Analitique (1788)....Pages 146-150 Some later evaluations: Chladni (1802), T. Young (1807), Love (1892)....Pages 150-153 A modern evaluation....Pages 154-165 Back Matter....Pages 165-170 ....Pages 170-178