During the French Revolution, Navier’s father was a lawyer to the Legislative Assembly at Paris and his mother’s uncle, the engineer Emiland Gauthey, worked in the head office of the Corps des Ponts et Chaussées at Paris. After her husband’s death in 1793, Navier’s mother moved back to Chalon-sur-Saône and left her son in Paris, under the tutelage of her uncle. In 1802, after receiving preparation from his granduncle, Navier entered the École Polytechnique near the bottom of the list; but he did so well during his first year that he was one of ten students sent to work in the field at Boulogne instead of spending their second year in Paris. Navier’s first year at the École Polytechnique had critical significance for the formation of his scientific style, which reflects that of Fourier because the latter was briefly his professor of analysis. He subsequently became Fourier’s protégé and friend.
In 1804 Navier entered the École des Ponts et Chaussées, from which he graduated in 1806 near the top of his class. After spending a few months in the field, he was brought to Paris to edit the works of his granduncle, who had just died and who had become France’s leading engineer. Navier, who seems to have been insecure financially, lived for the rest of his life in the St.-Germain-des-Prés quarter of Paris. His wife, Marie Charlot, whom he married around 1812, came from a family of small landowners in Burgundy.
Navier was a member of the Société Philomatique (1819) and of the Académie des Sciences (1824). In 1831 he became Chevalier of the Legion of Honor. From 1819 he taught and had complete charge of the courses in applied mechanics at the École des Ponts et Chaussées but did not become titular professor until 1830, when A.-J. Eisenmann died. In 1831 Navier replaced Cauchy at the École Polytechnique. Navier participated in Saint-Simonianism and the positivist movements. He had Auguste Comte appointed to be one of his assistants at the École Polytechnique and participated actively in Raucourt de Charleville’s Institut de la Morale Universelle.
Figures & Tables
Classics of Elastic Wave Theory
In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.
Table 1 is a quick outline of the key contributions of each paper reprinted in this book.
Robert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)
The article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.
Based on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,
which he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).
In his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement: