Lamb’s father, John, was a foreman in a cotton mill who had a flair for inventing. Horace was quite young when his father died, and he was brought up by his mother’s sister in a kindly but severely puritan manner. At the age of seventeen he qualified for admission to Queen’s College, Cambridge, with a scholarship in classics but proceeded to a mathematical career. He gained major prizes in mathematics and astronomy and became second wrangler in 1872, when he was elected a fellow and lecturer of Trinity College. After three further years in Cambridge, he went to Australia as the first professor of mathematics at the University of Adelaide. He returned to England in 1885 as professor of pure mathematics (later pure and applied mathematics) at Owens College, Manchester, and held this post until his retirement in 1920. He married Elizabeth Foot; they had seven children.
Lamb was one of the world’s greatest applied mathematicians. He was distinguished not only as a contributor to knowledge but also as a teacher who inspired a generation of applied mathematicians, both through personal teaching and through superbly written books. As a young man he was noted as a hard worker, shy and reticent; in later life he played a prominent part in academic councils. He also possessed considerable literary and general ability and enjoyed reading in French, German, and Italian. He liked walking and climbing and was one of the early climbers of the Matterhorn.
Like his teachers, Sir George Stokes and James Clerk Maxwell, Lamb saw from the outset of his career that success in applied mathematics demands both thorough knowledge of the context of application and mathematical skill. The fields in which he made his mark cover a wide range—electricity and magnetism, fluid mechanics, elasticity, acoustics, vibrations and wave motion, statics and dynamics, seismology, theory of tides, and terrestrial magnetism. Sections of his investigations in different fields are, however, closely linked by a common underlying mathematics. It was part of Lamb’s genius that he could see how to apply the formal solution of a problem in one field to make profound contributions in another.
Figures & Tables
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: