Christoffel, Elwin Bruno
Christoffel studied at the University of Berlin, where he received his doctorate in 1856 with a dissertation on the motion of electricity in homogeneous bodies. He continued his studies in Montjoie. In 1859 he became lecturer at the University of Berlin, in 1862 professor at the Polytechnicum in Zurich, and in 1869 professor at the Gewerbsakademie in Berlin. In 1872 he accepted the position of professor at the University of Strasbourg, newly founded after its acquisition by the Germans. Here he lectured until 1892, when his health began to deteriorate.
Christoffel has been praised not only as a very conscientious mathematician but also as a conscientious teacher. Politically he represented the traditional Prussian academician loyal to emperor and army. This may have contributed to his choice of Strasbourg and his endeavor to create a great German university in that city.
Scientifically, Christoffel was primarily a follower of Dirichlet, his teacher, and of Riemann, especially of the latter. Their ideas inspired his early publications (1867, 1870) on the conformal mapping of a simply connected area bounded by polygons on the area of a circle, as well as the paper of 1880 in which he showed algebraically that the number of linearly independent integrals of the first kind on a Riemann surface is equal to the genus p. The posthumous “Vollständige Theorie der Riemannschen θ-Function” also shows how, rethinking Riemann’s work, Christoffel came to an independent approach characteristic of his own way of thinking. Also in the spirit of Riemann is Christoffel’s paper of 1877 on the propagation of plane waves in media with a surface of discontinuity, an early contribution to the theory of shock waves.
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: