Eaton Hodgkinson (1789-1861), applied mathematician and structural engineer, was born on 26 February 1789 in the village of Anderton near to the market town of Northwich in Cheshire.
Largely self-taught Eaton Hodgkinson became widely known for the application of mathematics to the strength of materials, vital knowledge in the progress of the industrial revolution as it transitioned in the early nineteenth century from a world based on timber constructions to ones made from iron.
Eaton’s father, who rented and worked a farm in Anderton, died from a fever in 1794 leaving his wife Mary with a young family to support. Eaton’s uncle, the Rev. Henry Hodgkinson, rector of Aberfield in Berkshire, steered the boy towards the church profession, the path he had taken himself: grammar school, university and a church rectorship. He was sent to the grammar school at Witton (now Sir John Deane’s College) at eight years of age where he was to study Classics under the headmaster Rev. Robert Litler; this headmaster had been at Oxford’s Brasenose College just four years after Uncle Henry. For Eaton this move proved disastrous, Litler subscribing to a flogging regime as the way to inculcate the learning of Latin, Greek, and Hebrew, subjects for which Eaton showed little inclination. This experience undoubtedly caused mental scarring from which he never fully recovered, a cousin describing his condition as ‘the nervous tremor of his hands and speech which continued with him through life and was a serious impediment to his success.’
Fortunately, Eaton was soon transferred to a private school at Northwich run by a Mr Shaw who was alert to Eaton’s natural interest in mathematics in which he showed a distinct aptitude. Shaw was ‘a gentleman of superior mathematical attainments’ and under his tuition Eaton made great strides, setting the foundation for his later application of mathematics to practical engineering problems. He acquired the rudiments of the Calculus from student texts written by Thomas Simpson, William Emmerson and William Dealtry, these rooted in the mathematics of Newton and using his dot notation, a feature of English textbooks of the eighteenth century.
Mary Hodgkinson was a resourceful woman and after the death of her husband attempted to keep the farm viable with family help. This proved uncongenial to her son who was more attracted to academic pursuits and the farm became a burden. In 1811 the family left Anderton and moved to Salford where Mary bought a pawnbroker’s business. In moving from the country to the town they found new challenges; their premises in Chapel Street was the frequent target of thieves, and Eaton invariably slept with loaded pistols by him, and a large dog keeping guard.
In Salford, Eaton soon made contact with John Dalton then working as a private mathematics tutor. From 1804 Dalton had lodged with school master Rev. William Johns, the two being the driving force of the embryonic Manchester Literary and Philosophical Society (hereafter the Manchester Society). Dalton could count both Eaton and James Prescott Joule as his star pupils, these two becoming lifelong friends. In the Johns Academy setup daughter Catherine taught the younger children in the front parlour of their house. With Dalton, Eaton was introduced to the advanced mathematics of Euler, Lagrange, Laplace, and the Swiss Bernoulli family.
Eaton joined the Manchester Society in 1820, and his first paper was read 22 March 1822 entitled ‘On the Traverse Strain and Strength of Materials’ and subsequently was published in their Memoirs. This dealt with the optimal cross-sectional shape of metal and timber beams and columns being used in the building industry. One configuration came to be known as the ‘Hodgkinson beam’ and for its practicality was described as ‘the pole star for engineers and builders’. This work showed the depth of Eaton’s mathematical understanding. With the study of the European masters, he made use of the Leibnitzian notation in the Calculus leaving behind the antiquated dot notation of Newton.
In a paper of 1828, Hodgkinson investigated various shapes of suspension bridges involving the solutions differential equations. While mathematicians had long tackled this ‘catenary problem’, he approached the problem from a practical point of view. As he put it, the solutions were ‘an object of practical utility’. At a time when suspension bridges were being constructed, it was this utility which brought him scientific recognition. At this time, he met the enterprising Scottish engineer William Fairbairn of the same age as himself and so began their long association. They enjoyed a close social relationship and Hodgkinson frequently visited Fairbairn ‘s residence where he was called upon to teach mathematics to Fairbairn’s sons. Much of Hodgkinson’s experimental testing was carried out at engineering works operated by Fairbairn.
Hodgkinson became a stalwart of the Manchester Society and in time contributed six lengthy papers to its Memoirs. He served as its librarian, vice president (1845-1847) and (1852-1855), and president (1848-1850). On the latter election, Fairbairn playfully wrote: ‘I think the Members have exercised a sound discretion in the selection, and I am heartily glad, after all our squabbles, to find you in a position to which you are so justly entitled’.
Hodgkinson did not shy away from administrative duties. In 1832 he was invited to be Director of the Manchester Mechanics Institution, and he supervised its financial affairs for his three-year term. As well as the Manchester Society he served on the council of the British Association 1843, 1844, and 1848 and was vice president for the Mechanical Sciences Section on five occasions. He was a man who worked behind the scenes whether with administration or dealing with real engineering-based problems connected with cast and wrought iron and very detailed testing procedures. With the decease of his mother and a sister in 1835 and 1837, the pawnbroker’s business was sold and this enabled Eaton to be a ‘man of means’, albeit slender ones.
Introduced by mathematician Peter Barlow, who also studied the strength of materials, Eaton published his first paper in the Royal Society’s Transactions in 1840 entitled ‘Experimental Researches on the Strength of Pillars of Cast iron and other Materials’. This resulted in the publication of reliable formulae of practical use in designing pillars, and an investigation into their buckling characteristics. Following this, he was elected Fellow of the Royal Society in February 1841, among his backers being Marc Isambard Brunel, Peter Barlow (mathematician and engineer), George Peacock (mathematician), William Whewell (polymath), Robert Willis (mechanical engineer), and George Biddell Airy (Astronomer Royal). For this work he was awarded a Royal Society Gold Medal in November. In June he married Catherine Johns at a Unitarian Chapel in Manchester, and he went to live with her family at Eaglesfield House, Higher Broughton near Salford. After only a year his wife died (of consumption), and from that time he became totally absorbed by his scientific work.
In February 1847 Eaton Hodgkinson was appointed Professor of the Mechanical Principles of Engineering, a new chair created at University College London, a position he held until his death. In that year he was appointed to a Royal Commission to investigate the use of iron in railway structures and its potential for metal fatigue. This was set up following the collapse of a railway bridge over the River Dee at Chester when five travellers using the Chester and Holyhead Railway were killed in May 1847. When the Commission reported two years later, he was singled out for a special mention for his authorship of a section giving experimental results which occupied 180 pages of the Report.
The work on the Royal Commission had left Hodgkinson exhausted and this signalled a period of progressive ill-health. It overshadowed his duties as a professor in London. He had never been at ease giving lectures where his speech impediment was not suited to inspiring the next generation of engineers. A source of strength and support occurred when he married Eliza Holditch in Kensington Parish Church in October 1853. By 1857 his health and eyesight had significantly declined, interfering with the progress of his second paper intended for the Royal Society Transactions. This paper on the strength of iron columns had to be completed by his assistant.
He left London in 1859 and returned to Salford. Despite his mental and physical health problems he was elected vice-president for the British Association 1861 meeting to be held in Manchester in September with William Fairbairn as President for the meeting. He died at Eaglesfield House on 18 June 1861 before taking office.
Hodgkinson’s fellow mathematician Thomas P. Kirkman, also a vice president for the Manchester meeting, lamented his death and spoke for many. He was moved to insert a note in the Manchester Society’s Proceedings: ‘It is a great thing to outstrip one’s cotemporaries [sic] in commercial competition, and to accumulate fairly-gathered wealth; it is a great thing to win university distinctions, and to grow old in the plenitude of college dignities: it is a great thing to wear civic honour, and to enjoy, for any good reason, a social celebrity; but Hodgkinson aspired to more. He thirsted for enduring and worldwide fame, and he has won it … fame that will grow higher and speak louder, as the world grows happier and wiser.’
Tony Crilly, member of Manchester Lit & Phil