Faith and Thought

This chapter examines Stokes as an outspoken scientist of faith. It uses Stokes to examine the intellectual threats to conservative Christianity in the second half of the nineteenth century, and highlights his leading role among Victorian Britain’s religious scientists, through bodies such as the Royal Society and the Victoria Institute. It also explains how Stokes’s upbringing and education formed the basis for his own evangelical theology, and highlights his two most significant contributions to that field. First, it explores Stokes’s opposition to the doctrine of eternal punishment, and his promotion of conditional immortality as an alternative. Second, it highlights how Stokes continued to advocate the natural theology and teleological argument of William Paley a century after they were first proposed, as a method of harmonizing faith and scientific practice.

Stokes and Engineering

Railway safety in the nineteenth century relied heavily on the use of Commissions to analyse the causes of individual accidents and to decide on methods to avoid repetitions. Stokes played an important role in these. Following the collapse of the Dee bridge in 1847 he carried out the first mathematical study of the deflection and liability to break of a rail due to a moving railway engine. Following the Tay bridge disaster of 1879 he provided expert advice on the possible effects of the wind on railway bridges, and as an important member of the Commission on wind speeds he played a major role in the creation of a series of guidelines that have helped to keep railway bridges safer ever since.

Stokes’s Fundamental Contributions to Fluid Dynamics

George Gabriel Stokes made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter the primary focus is on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier–Stokes equations and the theory of finite amplitude oscillatory water waves.

Stokes and the Royal Society

This chapter examines George Gabriel Stokes’s almost four decades of service to the Royal Society. As Secretary from 1854 to 1885, Stokes devoted an enormous amount of time and effort to editing the Royal Society’s Philosophical Transactions and Proceedings. In this role, he acted as both gatekeeper and mentor to a generation of scientists. The same qualities that made Stokes, as Secretary, an excellent steward of the ‘internal scientific work’ of the Royal Society, were sometimes at odds with the political challenges he faced as Royal Society President, an office he held from 1885 to 1890.

Stokes’s Mathematical Work

This chapter gives an account of the seven purely mathematical papers written by Stokes. The first is an account of his famous memoir on Fourier series in which he discussed modes of convergence and introduced the idea of uniform convergence. A second paper dealing with moving loads over railway bridges represents Stokes’s only foray into industrial applied mathematics. The remaining five papers are concerned with asymptotic analysis in which he considered an approximation for the zeros of an integral measuring the intensity of light in the neighbourhood of a caustic applied to the familiar rainbow. This eventually led him to resolving a paradox in asymptotics that is now known as the Stokes phenomenon. A final paper gives an estimate of the asymptotic behaviour of the generalized hypergeometric function for large positive argument.

‘Stokes of Pembroke S.W. & a very good one’

George Gabriel Stokes won the coveted title of Senior Wrangler in 1841, a year in which the examination papers for the Cambridge Mathematical Tripos were notoriously difficult. It was a notable achievement but it was a prize hard won after several years of preparation, and not only years spent at Cambridge. When Stokes arrived at Pembroke College, he had spent the previous two years at Bristol College, a school which prided itself on its success in preparing students for Oxford and Cambridge. This chapter follows Stokes’s path to the senior wranglership, tracing his mathematical journey from its early beginnings in Ireland to its close at the end of his final year of undergraduate study.

The Stokes Family in Ireland and Cambridge

George Gabriel Stokes was a great-grandson of the well-known Dublin engineer, Gabriel Stokes, who became Deputy Surveyor General for Ireland. This chapter details the Irish Stokes family and identifies George Gabriel’s maternal ancestral lines. Then using the account by his daughter, Isabella, writing as Mrs Lawrence Humphry in her 1907 Notes and Reflections, we explore the family life and character of Stokes, concentrating on the correspondence leading to his marriage to Mary Robinson in 1857 and then their home life in Cambridge. An appendix contains biographical notes on a selection of the relatives of Stokes who were eminent, particularly in academic and medical fields, as church ministers or colonial administrators.

Stokes’s Optics 1

The purpose of this chapter and the following one is to explore and explain the rich diversity of Stokes’s contributions to physical optics in Cambridge and world contexts. He triggered debates and inspired friends through his semi-private speculations on the nature and motion of the ether in stellar aberration, double refraction, and optical rotation. He discussed deep-seated analogies between hydrodynamics and optics. He consolidated the fundamental laws of wave optics through mathematically sophisticated theories of interference, including Newton’s rings; diffraction, for which he provided a dynamical theory; and polarization. His theoretical achievements were backed up by carefully designed and extremely precise experiments.

Biographical Introduction

This chapter is an introductory biography of the life and works of Sir G. G. Stokes from his early life in Ireland, through his career in Cambridge as student and fellow of Pembroke, to his election as Lucasian Professor of Mathematics. It summarizes his lasting contributions to mathematics, optics, and continuum mechanics and his later role as Secretary and President of the Royal Society, particularly during the period of the Creation versus Evolution controversy. The Chapter touches on his family life and religious views, including his interest in the relation between science and religion, concluding with outline of his public life as a Member of Parliament for Cambridge University and mentioning the many honours which were accorded to him in later years.

The Scientific Legacy of George Gabriel Stokes

The scientific legacy of George Gabriel Stokes is considered. Certain aspects of Stokes’s research work are reviewed and related to more recent fields of research. These include the Navier–Stokes equations and other approaches to rational continuum mechanics, the issue of existence of solutions, the boundary no-slip condition; Stokes flow and the issue of pendulum drag; the Hele-Shaw cell, viscous fingering, wavelength selection in pattern formation; moving contact lines; the highest water wave, rogue waves, the NLS equation; Stokes lines, exponential asymptotics, dendrite growth, slow manifods, and diffraction.