Although Green left school at an early age to work in his father’s bakery, he had probably already developed an interest in mathematics that was fostered by Robert Goodacre, the leading private schoolmaster of Nottingham and author of a popular arithmetic textbook. Virtually self-taught, Green acquired his knowledge of mathematics through extensive reading. Many of the works he studied were available in Nottingham at the Bromley House Subscription Library, which he joined in 1823. By that time the family had moved to Sneinton, a suburb, where his father had established a successful milling business; Green used the top story of the mill as a study.
Green’s most important work, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, was published by subscription in March 1828. Apparently, almost all of the fifty-two subscribers were patrons and friends of Green’s; a local baronet, Edward Ffrench Bromhead of Thurlby, assisted Green later but was not an early promoter. Until other evidence is available, one can only conjecture that Green’s supporters included some of the leading members of the Bromley House Library; the list of subscribers suggests only limited circulation outside Nottingham.
In the preface Green indicated that his “limited sources of information” preventing his giving a proper historical sketch of the mathematical theory of electricity, and indeed, he cites few sources. Among them are Cavendish’s single-fluid theoretical study of electricity of 1771, two memoirs by Poisson of 1812 on surface electricity and three on magnetism (1821–1823), and contributions by Arago, Laplace, Fourier, Cauchy, and T. Young. The preface concludes with a request that the work be read with indulgence, in view of the limitations of the author’s education.
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: