Knott, Cargill Gilston
Cargill Gilston Knott was the son of Pelham Knott, author of a volume of poetry, who died young. Cargill was brought up by an uncle and aunt. He entered Edinburgh University in 1872, and after gaining his first degree became assistant to P. G. Tait in the Department of Natural Philosophy. In 1883 he left Edinburgh to become a professor of physics at the Imperial University of Japan. In Tokyo he married a Scottish lady, Mary Dixon, sister of the professor of English at the Imperial University. He returned to Edinburgh in 1891 as lecturer, later reader, in applied mathematics, and died in his office from a heart attack in 1922.
On arriving in Japan, Knott became a member of the famous group (J. Milne, M. Ewing, and T. Gray from Britain, and several Japanese) who inaugurated the modern era in earthquake study. Knott’s contributions were chiefly on the mathematical side. He utilized the observational results of his colleagues to pioneer the application of seismology to determine the internal mechanical properties of the earth. In the course of this work, he traced the connection between the times taken by earthquake waves in traveling from the center of the disturbance through the earth’s interior to seismic recording stations, and worked out many of the detailed physical characteristics of the waves. These and other pioneering results formed the basis of many later researches on the interior of the earth.
While in Japan, Knott also organized and supervised the first comprehensive magnetic survey of Japan. Many of his pupils and their pupils became Japan’s leading investigators of the earth’s magnetic field. In addition he investigated Japanese volcanic eruptions.
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: