Eaton A. Hodgkinson (1789-1861) was an English engineer, a pioneer of the application of mathematics to problems of structural design.
1789 February 26th. Born at Anderton, near Northwich, Cheshire, the son of James Hodgkinson (1756–1794), a farmer, and his wife, Mary (1767–1835). He had two sisters.
1795 His father died when Hodgkinson was six years old and he was raised with his two sisters by his mother who maintained the farming business. She sent her son to the Grammar School in Northwich where he studied the classics with the intention that he would fulfill the family's ambition that he prepares for a career in the Church of England. Unfortunately, the regime was unsuited to his tastes and talents which were already showing promise in mathematics. His mother moved him to a less prestigious private school in Northwich where his enthusiasm for mathematics was encouraged and fostered but, as the young Hodgkinson grew physically, he became indispensable on the family farm and soon left education to devote himself there.
1811 However, farming was no more to his taste than Greek and Latin and his mother yearned to satisfy her son's appetites. Family friends advised that Hodgkinson might find some more suitable outlet in nearby Manchester and so, in 1811, the family left for Salford to open a pawnbroking business. Hodgkinson used all his spare time in reading science and mathematics and soon introduced himself into Manchester's scientific community, meeting, among others, his future collaborator, William Fairbairn. He became a pupil of John Dalton, studying mathematics, and the two remained firm friends until Dalton's death in 1844. He retired early from the family business to devote a modest pension to his scientific work.
1830 Hodgkinson presented a Paper on his findings to date on experimental and theoretical work to determine the optimum design of cast iron beams. Hodgkinson's initial beam experiments were carried out at the Salford foundry of William and James Hatton. Subsequently they were carried out with generous supprt from Fairbairn and Lillie.
1841 On 2 June of that year, at Cross Street Chapel, Manchester, Hodgkinson married Catherine Sparke Johns, daughter of the Revd William Johns (with whom John Dalton had lodged). The witnesses included John Dalton and William Fairbairn. Catherine died a year later.
1841 Hodgkinson was elected a Fellow of the Royal Society
1847, he became professor of the mechanical principles of engineering at University College London.
1849 Joined the Institution of Mechanical Engineers.
In 1849, he was appointed by the UK Parliament to participate in a Royal Commission to investigate the application of iron in railroad structures, performing some early investigations of metal fatigue.
On 15 October 1853 he married Eliza Holditch (d. 1882), daughter of Captain Henry Holditch, at the parish church, Kensington. One of the witnesses was Robert Stephenson. There were no children of either marriage.
Hodgkinson worked with William Fairbairn in Manchester on the design of iron beams. His improved cross section was published by the Manchester Literary and Philosophical Society in 1830 and influenced much nineteenth century structural engineering. See 'Cast Iron Beams' below.
His expertise with beams led to his retention, along with Fairbairn, as consultant on the novel tubular design for the Britannia Bridge. Fairbairn built and tested several prototypes, and developed the final form adopted for the bridge. Both Hodgkinson and Robert Stephenson believed that extra chains would be needed to support the heavy spans, so the towers were built with spaces for the chains. Fairbairn, however, insisted that chains would not be necessary, and his opinion prevailed. He was right, and chains were never used, but the towers remain with their empty recesses.
1861 June 18th. Died at his home, Eaglesfield House, Higher Broughton, Manchester, and was buried in the family plot at Anderton. He was survived by his wife.
Read his obituary in The Engineer 1861/06/28.
1862 Obituary 
Eaton Hodgkinson was born on the 26th of February, 1789, at Anderton, in the parish of Great Budworth, near Northwich, Cheshire, at which place his father was engaged in farming pursuits.
On the death of his father, which occurred when the boy was only six years old, he was, at the instigation of his uncle, the Rev. Henry Hodgkinson, rector of Arberfield, Berkshire, placed at a classical school, with the view of his proceeding to the University, and of ultimately entering the Church.
In the study of the Classics he does not appear to have made any progress, and he was soon transferred to the care of Mr. Shaw, at that time the master of the grammar-school at Northwich, under whom he laid the foundation for his future mathematical acquirements, and to whose careful tuition Mr. Hodgkinson frequently alluded in after-years.
The pecuniary circumstances of Mrs. Hodgkinson induced her to remove, in the year 1811, to Salford, Manchester, where she entered into business, and, with the assistance of her son, eventually attained a comfortable position.
He was not, however, intended by nature to emulate the thrifty and active examples around him in that city of millionaires; his tastes led him rather to listen to the mathematical teaching of Dr. Dalton, one of whose most distinguished pupils he became, and with whom he formed a friendship which was only dissolved by the death of Dalton.
For nine years Hodgkinson's studies and researches led to no apparently useful result; but at length, on the erection of a fire-proof factory, he was engaged to make some experiments, which induced the proposition of a new form of cast-iron girder, differing materially from the form hitherto advocated by Tredgold and others. In the cross section of the girder recommended by Hodgkinson, the upper and lower flanges presented sectional areas proportioned to the power of resistance to compression and to extension respectively. This assumption was verified by careful experiments, conducted by Hodgkinson, at the works of Messrs. Fairbairn and Lillie, at Manchester; and for many years after he continued to conduct investigations of the same nature, either in conjunction with, or at the suggestion of William Fairbairn, who, in his various works, has communicated to the world the interesting and practically valuable results of these investigations.
The Manchester Philosophical Society, of which Dr. Dalton was the President, naturally attracted Hodgkinson’s attention; and in 1826 he became a Member, having as early as in 1822 contributed some Papers. There are published in the Memoirs of that Society seven Papers, chiefly on the mechanical principles of engineering. Eventually, in 1848, he was elected President, and Mr. William Fairbairn, with whom he had unfortunately had some differences, embraced the opportunity of gracefully writing:-
'June 28th, 1848.
'MY DEAR SIR,- I cannot resist the temptation to congratulate you on your election to the Presidency of the Manchester Philosophical Society. 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.
'I am yours faithfully,
'To Eaton Hodgkinson, Esq.'
Mr. Hodgkinson soon began to convey to other scientific societies the details of his labours; and in 1840 he communicated to the Royal Society a Memoir on 'Experimental Researches on the Strength of Pillars of Cast Iron and other Materials,' which was published in the Philosophical Transactions of 1840, and won for him the Royal Medal in 1841, and ended in securing his election a s F.R.S. in the same year. From that period his reputation increased rapidly, and his formu1ea were accepted with such confidence, that they have now a place in all engineering textbooks.
When Mr. Stephenson conceived the idea of constructing the Britannia Bridge in the form of a wrought-iron tube, he engaged the assistance of Mr. Fairbairn, whose experiments, commenced in April, 1845, were verified as to their mathematical value by Mr. Hodgkinson in the month of September of that year; and during the subsequent trials and investigations at Millwall and at Manchester, Mr. Hodgkinson gave his assistance. These experiments were important, as confirming the results previously obtained by Mr. Fairbairn, and although Mr. Hodgkinson entertained doubts of the self-supporting principle advocated by Mr. Fairbairn, his mathematical investigations, and his subsequent experiments, nevertheless, proved the correctness of the principle, and thus aided in establishing that which is perhaps the most remarkable event in the history of Engineering science of modern times. For his co-operation in this work, he, in conjunction with Mr. Fairbairn and Edwin Clark, received a Silver Medal at the Paris Exhibition in 1855, when the great Gold Medal and the Cross of the Legion of Honour were conferred upon Mr. Robert Stephenson.
Mr. Hodgkinson was an active and useful Member of the British Association for the Advancement of Science, and in the Reports of that Society many of his Memoirs are printed. He was also a Member of the Royal Commission issued to inquire into the application of iron to Railway Structures, and in the Report of that Commission he gave the results of some valuable investigations.
The records of his numerous investigations are to be chiefly found interspersed through the Transactions of the British Association for the Advancement of Science, and of the Literary and Philosophical Society of Manchester, as well as in other scientific collections; but the nature of his discoveries may also be gathered from the edition of 'Tredgold on the Strength of Cast-iron and other Metals,' which he edited, adding a supplementary volume. This edition bears date 1842-46; and subsequent to that period, the experiments for the Britannia and Conway Bridges demonstrated the remarkable fact of the opposite character of wrought to cast-iron, as to the capability to resist the relative forces of tension and compression, and showed the value of the cellular top in a tubular beam.
Amongst his earliest writings a paper on the 'Transverse Strain and Strength of Materials' will be found, in the fourth volume of the Memoirs of the Manchester Society (Second Series, 1822), in which he put forth his views in opposition to those which were general amongst scientific men, as to the situation of the neutral line in a bent body; and on that subject he was subsequently engaged by Mr. Robert Stephenson, to make a series of experiments, which have not yet been published.
In the fifth volume of the same Memoirs (1831), are five Papers by him, on the 'Forms of the Catenary in Suspension Bridges,' of which an abstract was given by the Rev. Dr. Whewell in his Analytical Statics (Cambridge 1833), and an amplification by the Rev. Canon Moseley in his Mechanical Principles of Engineering; two Papers 'On the Chain Bridge at Broughton, Manchester, with an Account of its Failure' and one on the subject of the strength and form of iron-beams. The Fourth Report of the British Association contains the results of an extensive series of experiments - 'On the Collision of Imperfectly- elastic Bodies;' and the Fifth Report, a Paper 'On Impact upon Beams.'
It would unduly extend the limits of this Memoir to endeavour to give even the titles of his numerous Papers, of which we may hope to see the most important published in a separate form; and for scientific men and engineers, such a collection would be very useful, as the volumes of the scientific societies in which they are now published are not always accessible. To foreign engineers, who highly appreciate the labours of Eaton Hodgkinson, and who have acknowledged their value in very flattering terms, such a publication would be a great boon.
In 1847 Mr. Hodgkinson was appointed Professor of the Mechanical Principles of Engineering in University College, London; and he subsequently removed from Manchester to the metropolis, to fulfil the duties of his post. He delivered several courses of lectures with success; but his health had already suffered, and during later years his labours were only intermittent.
It has been stated that his works were highly appreciated by foreign scientific men; to such an extent was this the case that, in 1851, his name was placed upon the list for nomination as a Corresponding Member of the Institute of France; and strenuous efforts were made by eminent men who recognised his merits, to secure his election.
He was unanimously elected an Honorary Member of the Institution of Civil Engineers in 1851, and nowhere could his practical merits be better appreciated. He was a constant attendant at the meetings, and not infrequently took a prominent part in the discussions.
He was personally held in high esteem by the Members, with a large number of whom he was on terms of intimacy. He was acknowledged to be perhaps the most laborious and careful experimenter who had ever devoted himself to the study of the laws which regulate the strength of materials, and his unselfish conduct in gratuitously giving to the world the result of his investigations was generally admired. He was attached to science for its own sake, and he was well versed in other branches than that to which he specially devoted himself.
In private life he was singularly simple and guileless; and his kindly disposition endeared him to all who had the good fortune to make his acquaintance.
His decease occurred on the 18th of June, 1861, at Eaglesfield House, near Manchester, in his seventy-second year, regretted not only by all who knew him, but by those who had professionally benefited by his labours.
1862 Obituary 
EATON HODGKINSON was born in February 1789 at Anderton near Northwich, Cheshire, where he received his first education at the grammar school.
He was originally intended for the church; but his father having died when he was only six years old, he commenced his career as a farmer, to aid his widowed mother in carrying on his father's business. Neither farming nor the church were however suited to his talents, and at the age of twenty-one he removed with his mother to Salford, Manchester, where they maintained themselves by keeping a shop, whilst he had the advantages of scientific instruction and society, and devoted his spare hours to the study of mathematics and mechanical science, as one of Dr. Dalton's private pupils.
At the age of thirty-three, he produced his first scientific work, an essay on the Transverse Strain and Strength of Materials, which was followed by a series of papers on the subject of Suspension Bridges read by him to the Manchester Philosophical Society in 1828 to 1830, his attention having been called to this subject by the erection and failure of a suspension bridge at Broughton near Manchester.
In 1833 he commenced that remarkable series of papers and researches on the strength and strains of materials, more especially of Iron, by which he became so eminently distinguished and made so important an addition to. the scientific knowledge at the disposal of engineers. In these researches he seems only to have resumed the subject of his earliest paper in 1822, which he may be considered to have completed when in 1857 he received the medal of the Royal Society and in 1861 became Vice-President of the British Association.
The great subject that Eaton Hodgkinson devoted himself to — the investigation of the nature and properties of iron — he followed up with an assiduity of research, a philosophical method, and a clear and strong sagacity, that enabled him to accomplish results which have been of the greatest practical importance in the various and extensive applications of iron, and have effected a complete revolution in practice with that metal, laying all branches of engineering under a great debt of gratitude to him.
Before his investigations the mechanical nature and the relative value of cast iron and wrought iron were little understood; and neither the practical value of their resistance to strains, nor the true form and distribution of material for obtaining the best application of their strength to mechanical use, were known: wrought iron was not trusted or used so much as it deserved, whilst cast iron was unduly relied on and inefficiently applied. The section of cast iron girders previously in universal use was an I shape, with nearly equal flanges at top and bottom; but Hodgkinson showed that the resistance of cast iron to fracture by compression being about five times its resistance to tension, the upper flange acting by compression should have only one fifth of the area of the bottom flange in tension, in order to be equal in strength and give the maximum strength of girder with the minimum weight of material, the section of the girder being therefore somewhat of a I shape a great saving in the weight of material required was thereby effected. He showed also the true action of the vertical web of the girder in preserving the top and bottom flanges in their relative positions, and ascertained the extent to which its thickness should be diminished, whereby the weight of material was still further reduced.
In the form and calculation of cast iron columns Eaton Hodgkinson also established some remarkable facts by a series of experiments on the force necessary to crush the column, which he found to be regular: he proved that the bearing strength was increased by enlarging the column in the middle, and also by making the ends flat instead of rounded; while it was diminished by adding to the height of the column beyond a certain point. His formula, for the calculation of solid and hollow columns, deduced from these experiments, have become the standards in general use.
In his investigation of the best form and proportions for wrought iron columns and beams, he showed how the inferior resistance to compression of wrought iron as compared with cast iron could be compensated for by correct distribution of the material, removing the previous practical objections to wrought iron for large structures, and leading to the gradual displacement of cast iron by the more safe and reliable material, wrought iron, thereby affording facilities for overcoming engineering difficulties previously almost insurmountable. He was also engaged in important investigations into the application of iron to railway structures, and the relative values of hot and cold-blast iron, in connexion with a Royal Commission and a committee of the British Association.
Eaton Hodgkinson was eminently a self-made and self-educated man. Deprived in early life of the benefits of a complete education, he devoted himself earnestly to business for the support of his family, and afterwards for the purchase of an honourable leisure, which he employed first in the completion of his own education, next in association with eminent men of science in Manchester, and finally in the advancement of mechanical science and public researches into various important branches of the subject. From his humble origin he raised himself by his exertions and talents to be successively Member of the Philosophical Society of Manchester, Fellow of the Royal Society, Vice-President of the British Association, and Professor in University College, London a bright example that the humblest occupation need not derogate from the dignity of personal character, nor interfere with the accomplishment of a brilliant career of public usefulness and high distinction. The secret of his success was undoubtedly his earnestness and singleness of purpose; whatever investigation he undertook he determined to get thoroughly to the bottom of the subject; and held that to understand part of a subject completely, it was requisite to master the whole.
He was elected an Honorary Life Member of this Institution in 1849, and died on 18 June 1861 at the age of seventy-two.
Cast Iron Beams
1830 Newspaper report
'CAST IRON BEAMS.
'We mentioned in our last the iron beams which were casting at Messrs. Fairbairn and Lillie, of this town, for the bridge viaduct by which the railway is to be carried over Water-street; and we shall now proceed give a short account of the important experiments of Mr. Hodgkinson, from which the form and proportions of those beams were deduced, and which, we believe, are the only experiments that have ever been made on a large scale, for the purpose of comparing the strengths of cast iron beams of different forms. Most our readers are. no doubt, well acquainted with the form the iron beams now in general use in this neighbourhood for the erection of fire-proof factories, though, perhaps, it may so generally known that they were first made, ( at all events in this neighbourhood) from design of the late Mr. Watt, of Birmingham, and used in the building the of the first fire-proof factory erected in the neighbourhood of Manchester, namely, that of Messrs. Philips and Lee, in Salford. We believe the original pattern, from which the beams were cast, and which was sent over from Messrs. Boulton and Watts’ works at Soho, is still in existence at the factory, and shews that, notwithstanding the extent to which iron beams have been used during the last twenty years, there has been very little deviation from the form prescribed by Mr. Watt, beyond that a slight increase in the flange or rib, which runs along the under-side of the beam.
'A few years ago, however, Mr. Tredgold, the author of a very valuable work on cast iron, suggested a different form of beam, which he recommended being better calculated than any other for bearing weight, for the following reasons:—lf a beam be placed with its ends resting on two supporters, and then loaded in the middle with heavy weight, it must be obvious that the tendency of that weight to break the beam is exerted in two different ways; in the first place by extending and tearing asunder the lower side of the beam; and in the second place, compressing or crushing in the upper side; both of which tendencies the beams should be calculated to resist. From the results of some experiments made by himself, as well as of others made by M. Duleau, an eminent French engineer, who has written a book on wrought iron, Mr. Tredgold assumed that the power of cast-iron (and we believe of all other materials), to resist extension was precisely equal to its power of resisting compression; or, in other words, that a cubic inch of cast-iron would have its elasticity destroyed by the same force, whether it tended to extend it or compress it. Mr. Tredgold therefore proposed, that, instead of having only one rib, on the under-side, beams should constructed with two ribs of equal sizes, one on the upper and the other on the under-side, in order that they might equally resist those tendencies to fracture by extension and compression, which he assumed to be equal. We believe that iron beams of this principle had not been generally used, though, from the high character of Mr. Tredgold’s book, it is probable they would have got into use, if the principle which they were constructed had not been shewn to be erroneous, by the experiments to which are now about to advert.
'Mr. Eaton Hodgkinson, of this town, the author of several papers on the strength of materials, which have appeared in the Memoirs the Manchester Literary and Philosophical Society, was led by some experiments which he had made on cast iron, to doubt the accuracy of the assumption on which the form of Mr. Tredgold’s beam was determined; and therefore resolved make a series of experiments on a tolerably extensive scale, with the view of ascertaining that form of beam, which, with the smallest quantity of metal, was calculated to support the greatest weight. With that view, an invitation was given to him by Messrs. Fairbairn and Lillie, of this town, who, feeling, as engineers, strong interest in the result of the experiments, which Mr. Hodgkinson proposed to make and having themselves made some valuable experiment upon the common form of beams, undertook to defray the whole expense of them. A number of beams, of pretty large size, and of considerable varieties of form, were therefore cast, and separately broken, by loading them in the centre; and the results were carefully observed, not only by Mr. Hodgkinson, but also by Mr. Ewart, of this town, whose extensive scientific attainments rendered his presence peculiarly valuable.
'The first experiments were made to determine the value of the form recommended by Mr. Tredgold, as compared with the form now in general use in this neighbourhood; and with this view, beams of about the same size, some on Mr. Tredgold’s principle, and others on the common principle (cast at the same time and from the same metal), were severally subjected to a pressure by which they were broken. These experiments shewed that Mr. Tredgold’s beams, instead of supporting a greater weight than those on the common principle, were broken by about one eleventh less than that required to break the others.
'Another beam formed with strong ribs at the top and bottom, and with vacuities between, was recommended in the same work by Mr. Tredgold, as a very economical one; this was found much weaker than the former, and by means fit to be adopted in practice. The inquiry was then pursued by a succession of experiments, in which the size of the rib on the upper side of the beam was progressively diminished, and that the one on the under-side progressively increased, until the lower rib was to the upper in the proportion of about six to one. It was found that each alteration of this nature, gradually and pretty regularly increased the strength of the beam, until, with something like the proportions we have mentioned, the beams supported three-tenths (or very nearly one third), more than beams of similar size on the common principle.
'A variety of experiments were subsequently made, to determine the best proportions as to the depth and thickness of beams, and their relative degrees of elasticity, as well as of strength,—the results of which were very satisfactory, but we have not space for any detailed notice of them. We may observe, however, that beams of the form proposed by Mr. Hodgkinson appear to possess much greater elasticity than those on the common principle, and are therefore much less liable to be broken by a sudden shock. They have also another advantage which is of considerable importance. Being of equal depth throughout their whole extent, they are very suitable for supporting boarded or planked floors which for which beams on the common principle are very ill adapted, because they are much deeper in the middle than at the ends. In order to remedy this defect, it has been the practice to turn them bottom upwards.—In which position (as would appear from some of Mr. Hodgkinson’s experiments) a very large proportion their strength is lost.
'The beams on Mr. Hodgkinson’s principle, which are intended for the bridge in Water-street, are very beautiful castings, 26 feet in length, and are calculated to support about 100 tons each. As there are to be five of them (not four, as stated in our last), the bridge will be capable of bearing a very much larger weight than is at all likely to ever likely to be placed upon it. In addition to the use of these beams for the railway bridge, we understand Messrs. Fairbairn and Lillie are about employ them in the erection of factories at Macclesfield, and in other places. In giving the preceding details, our object has been merely to call the attention those of our readers who are interested in such matters, experiments which, from the present extensive use of iron beams, and the number of lives entrusted their stability, are, in our opinion, of considerable importance. As to the precise form and proportions of Mr. Hodgkinson’s beams, we have declined to say anything, because, not being very minutely informed on the subject, we might only have misled our readers. Mr. Hodgkinson read, at a recent meeting the Literary and Philosophical Society, a paper containing a very full account of his experiments; which, we believe, will appear in the volume of the memoirs, and we hope he will also publish the results of his labours in some more generally accessible form.
• The beams were compared, not by weighing them, but by measuring the section of fracture in each.'
Sources of Information
-  Memoirs of the Literary and Philosophical Society of Manchester, Second Series Vol V, 1831: Theoretical and Experimental Researches to Ascertain the Strength and the Best Form of Iron Beams by Eaton Hodgkinson, read April 2nd, 1830
- 1849 Institution of Mechanical Engineers: New Members
- 1862 Institution of Civil Engineers: Obituaries
- 1862 Institution of Mechanical Engineers: Obituaries
- Manchester Mercury - Tuesday 25 May 1830