Hopkins, William

(1793-1866), mathematician and geologist

by Crosbie Smith

© Oxford University Press 2004 All rights reserved

Hopkins, William (1793-1866), mathematician and geologist, was born on 2 February 1793 at Kingston in Derbyshire, the only son of William Hopkins, gentleman farmer. The young Hopkins acquired agricultural skills in Norfolk prior to an unsuccessful attempt to farm a small property, purchased for him by his father, near Bury St Edmunds in Suffolk. Following the death of his first wife, a Miss Braithwaite, about 1821 Hopkins sold the farm, cleared his debts, and entered himself as an undergraduate at Peterhouse, Cambridge, in 1822. While an undergraduate he married Caroline Frances Boys (1799-1881). In 1827 he graduated seventh wrangler in the mathematical tripos, and three years later he received his MA. Since college fellowships were open only to unmarried men, Hopkins instead settled in Cambridge as a private tutor or mathematical coach whose task it was to 'drill' the most promising undergraduates for a high place in the mathematical tripos.

Hopkins quickly became one of Cambridge's most respected private tutors with the nickname 'senior wrangler maker'. He admitted that a successful private tutor could earn a comfortable £700-£800 per annum, each pupil paying upwards of £100. By 1849 he could claim nearly 200 wranglers among his pupils, of whom seventeen were senior wranglers and forty-four in one of the top three places. Among them were G. G. Stokes and William Thomson, and later pupils included James Clerk Maxwell and Isaac Todhunter. In an otherwise cold, unworldly, and monastic institution, Hopkins's humanity served to inspire his pupils. As Francis Galton later explained:

Hopkins to use a Cantab expression is a regular brick; tells funny stories connected with different problems and is no way Donnish; he rattles us on at a splendid pace and makes mathematics anything but a dry subject by entering thoroughly into its metaphysics. I never enjoyed anything so much before. (Pearson, 1.163)
Throughout a period of tripos reform during the 1840s and 1850s Hopkins sought to maintain 'the standard of acquirement in our higher class of students'. He thus opposed exclusion from the tripos of some of the more advanced branches of the mathematical sciences (including hydrodynamics). Such subjects contributed 'most to elevate and enoble the character of our mathematical studies' and were vital to that small but elite group of students who 'remain among us, and afterwards form the tutorial body of the University, occupy its important offices, and give to it its prevailing tone and character' (Hopkins, 10-12). Hopkins's primary commitment to the education of a mathematical and scientific elite differentiated him from Cambridge contemporaries such as William Whewell who sought to shape the university's ideals of a liberal education for the general body of undergraduates.

Adam Sedgwick, Cambridge professor of geology from 1819, fired Hopkins's enthusiasm for geological science from about 1833. An early paper (1834) focused on the stratification of Derbyshire and in the late 1830s Hopkins seemed a likely candidate to undertake an unpaid official survey of his native county at a time when the geological survey was in its infancy. In the event, Hopkins had more pressing commitments.

By 1835 he had read to the Cambridge Philosophical Society his first major scientific memoir which introduced a new subject, 'Researches in physical geology'. Physical geology would bring the power and prestige of mathematical analysis to bear on geological phenomena. Geological science would thereby be raised to the same high status as physical astronomy. As with the mythologized history of physical astronomy, the new geology would have three stages: first, a geometrical description of the relevant motions (analogous to Kepler's laws of planetary motion); second, postulation of a very general force that would cause the motions (analogous to gravity); and third, derivation of the actual motions from the general force according to dynamical principles. The formulation of geometrical laws of faults, fissures, mineral veins, and so on constituted the aim of his first memoir. Cautiously, Hopkins sought a very general cause, an 'elevatory force', responsible for all these phenomena wherever and whenever they occurred. He found that cause in the widely held doctrine of central heat whereby the earth, assumed to have been formed as a hot fluid mass that subsequently solidified, had undergone, and continued to experience, a progressive cooling. Like the doctrine of universal gravitation in its generality and simplicity, central heat became for Hopkins the fundamental agency of geological dynamics.

Hopkins's preferred model was of a largely solid earth containing cavities. Hot vapours or fluids forced into those cavities from below would produce elevatory pressures in local regions. This model clashed directly with the steady-state (non-progressionist) geological theory of Charles Lyell which denied the doctrine of primitive heat while upholding the notion of a largely liquid interior supporting a thin terrestrial crust less than 100 miles thick. Most of Hopkins's subsequent extensive investigations in physical geology were directed to justifying the adequacy of his model. Between 1838 and 1842 a series of papers for the Royal Society argued on mathematical grounds that the observed behaviour of the terrestrial planet around its axis (its precession and nutation) were consistent with a solid, but inconsistent with a liquid, interior. A long report to the British Association (1847) treated the phenomena of earthquakes and volcanoes within the same framework.

Guided by his one-time pupil William Thomson, Hopkins instituted a series of experiments with the assistance of James Prescott Joule and William Fairbairn in Manchester to determine the effects of enormous pressures on the melting point of substances, the results of which he interpreted as supporting the solidity of the earth. These experiments were supported by Royal Society grants. During the same period Hopkins argued that past climatic conditions, including those of an ice age, would be unaffected by the internal cooling of the earth, being due instead to changes on the surface of the earth.

Within the mid-nineteenth century British scientific establishment, Hopkins had few rivals in the field of physical geology. Only when he attempted to apply the same methods to explain the mechanism of glaciers did he find himself engaged in intense controversy with the doyen of glacial phenomena, J. D. Forbes, who regarded the subject as almost a personal possession and who resisted what he saw as an attempt at territorial annexation by a Cambridge analyst with no personal experience of his beloved alpine glaciers. Towards the end of Hopkins's life, however, William Thomson tactfully began to question his mathematical and astronomical arguments, though not his conclusions, regarding the solidity of the earth.

Hopkins received the Wollaston medal of the Royal Society in 1850 for his geological investigations, was elected president of the Geological Society in 1851 and became president of the British Association in 1853. His most enduring legacy, however, was his role in training the group of outstanding mathematical physicists (most notably Stokes, Thomson, and Maxwell) who dominated Victorian physics in the period 1850-80. Hopkins had one son and three daughters, including the social purity campaigner (Jane) Ellice Hopkins (1836-1904), from his second marriage. His other interests included music, poetry, and landscape painting. He died in Stoke Newington on 13 October 1866, survived by his wife.

CROSBIE SMITH

Sources  
C. Smith and M. N. Wise, Energy and empire: a biographical study of Lord Kelvin (1989)
C. Smith, 'William Hopkins and the shaping of dynamical geology, 1830-1860', British Journal for the History of Science, 22 (1989), 27-52
W. Hopkins, Remarks on certain proposed regulations respecting the studies of the university (1841)
K. Pearson, The life, letters and labours of Francis Galton, 3 vols. in 4 (1914-30)
S. Rothblatt, The revolution of the dons: Cambridge and society in Victorian England (1968)
DNB
J. A. Secord, 'The geological survey of Great Britain as a research school', History of Science, 24 (1986), 223-75
G. K. C. Clarke, 'A short history of scientific investigations on glaciers', Journal of Glaciology, Special Issue (1987), 4-24
B. Hevly, 'The heroic science of glacier motion', Osiris, 2nd ser., 11 (1996), 66-86

Archives  
CUL, letters to Sir George Stokes
CUL, letters to James Thomson and William Thomson
U. Edin. L., corresp. with Sir Charles Lyell
U. St Andr. L., corresp. with James Forbes

Likenesses  
oils, Peterhouse, Cambridge
woodcut, NPG

Wealth at death  
under £12,000: probate, 3 Jan 1867, CGPLA Eng. & Wales


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