The Structural Engineer, Vol. 85 No. 23, 4 December 2007
Thomas Young and the theory of structures 1807-
Alasdair N. Beal BSc, CEng, MICE, FlStructE Thomasons LLP
As the Institution of Civil Engineers celebrates the birth of Thomas Telford and the Institution of Structural Engineers celebrates its own centenary, engineers might be forgiven for overlooking another significant anniversary: 2007 is the bicentenary of a remarkable scientific publication which set out much of the structural theory modern engineers rely on today in their daily work: Thomas Young's A Course of Lectures on Natural Philosophy and Mechanical Arts.
The Age of Enlightenment
In 1807 the Industrial Revolution was in full flow: steam power and ironmaking were starting to transform industry and construction -
In this age of polymaths, perhaps the most outstanding of all was ‘Phenomenon Young’, of whom Sir Humphry Davy once said ‘he knew so much that it was difficult to say what he did not know’ . Born in 1773, Thomas Young was a child prodigy, learning to read at the age of two, and by his teens he had become a formidable linguist who also had a keen interest in science. When he was only 19 years old, his first major scientific paper was presented to the Royal Society: ‘Observations on Vision’ set out a new (and essentially correct) theory of the focusing mechanism of the human eye.
Young went on to become a medical doctor and one of the greatest scientists and linguists of his age, making breakthroughs in our understanding of subjects ranging from the theory of light to the hieroglyphs on the Rosetta Stone . The story of his life and achievements is outside the scope of the present paper but fortunately, after many decades of obscurity, there is now a revival of interest in his work: Andrew Robinson has written an excellent new biography  and, for those with deeper pockets (or access to library copies), Thoemmes Press has published beautiful new editions of Young's work  (available in the IStructE library).
Fig. 1. Portrait of Thomas Young
(reproduced by kind permission of
The British Museum and
Mr & Mrs S. Z. Young)
Royal Institution Lectures
In 1801, at the age of 28, Young was appointed Professor of Natural Philosophy at the Royal Institution in London and he immediately set about preparing a series of lectures which he presented between January and May 1802. When it was repeated in 1803, the course had grown to 60 lectures and covered everything from mechanics, drawing, architecture and carpentry to music, mathematics, the properties of liquids and gases, optics, heat, electricity, gravitation and light.
The work must have been immense: in March 1802 Young admitted that ‘an immediate repetition of the labour and anxiety that I have undergone for the last 12 months would at least make me an invalid for life’ . Sadly, as a public lecturer, Young was not a success. A tutor from Cambridge University commented:
‘I remember ... his taking me with him to the Royal Institution, to hear him lecture to a number of silly women and dilettanti philosophers but nothing could show less judgment than the method he adopted; for he presumed, like many other lecturers and preachers, on the knowledge and not on the ignorance of his hearers’ .
According to his friend, Hudson Gurney,
‘His style was compressed and laconic; he went into the depths of science, and indeed gave more matter than it would perhaps have been possible for persons really scientific to have followed at the moment without considerable difficulty’ 
After the second series of lectures in 1803, Young left the Royal Institution. He got married, he worked on his wave theory of light and he set about preparing his Lectures for publication, a task which took almost 4 years. The expanded and revised versions of the lectures finally appeared in 1807 in two volumes as A Course of Lectures on Natural Philosophy and the Mechanical Arts, which also included an annotated bibliography of 20,000 relevant publications. Gurney later described the published Lectures as:
‘a mine to which every one has since resorted, [which] contained the original hints of more things since claimed as discoveries, than can perhaps be found in a single production of any known author’ .
In a 1934 review of Young’s work, the physicist Sir Joseph Larmor described his Lectures as ‘the greatest and most original of all general lecture courses’ . In his Introduction to the 2002 edition of the Lectures, Professor Nicholas Wade observed that ‘Reprinting them renders Young’s insights accessible to modern scientists, who will marvel that one mind could encompass so much’ .
Reading Young’s lectures today induces a sense of wonder at the extent of his knowledge and thinking. There are new ideas in all areas of physics, including the concept of kinetic energy, theories of light, colour and vision and even thoughts on the nature of matter and the first ever calculated estimate of the size of a molecule.
Amidst all these riches it would be easy to overlook Lecture XIII, modestly titled ‘On passive strength and friction’. However this was an ambitious lecture: Young’s Preface stated that:
‘The passive strength of materials of all kinds has been very fully investigated, and many new conclusions have been formed respecting it, which are of immediate importance to the architect and to the engineer, and which appear to contradict the results of some very elaborate calculations’.
What his Royal Institution audience made of it is anyone’s guess but the version which appeared in print in 1807 can fairly be described as a tour de force: not content with simply summarising the existing state of the art, Young introduced a large amount of new and original material, including solutions to problems which had taxed some of the best brains in Europe for decades.
The published text of the lecture was accompanied by carefully drawn diagrams and a supplement entitled ‘Mathematical Elements of Natural Philosophy’, which presented the detailed analysis and derivation of the ideas set out in the Lectures. Part II Section 9: ‘On the Equilibrium and Strength of Elastic Substances’ accompanied Lecture XIII.
Reading Young’s paper 200 years later is not always easy: his explanations sometimes use unfamiliar terminology and can be rather condensed. However it is worth the effort: this is the paper where Thomas Young presented to engineers not only the elastic modulus which bears his name but also much of the theory that they rely on for structural design.
In 1807 Young introduced the world to the concept of an elastic modulus which defines the stiffness of a material:
‘we may express the elasticity of any substance by the weight of a certain column of the same substance, which may be denominated the modulus of its elasticity, and of which the weight is such, that any addition to it would increase it in the same proportion as the weight added would shorten, by its pressure, a portion of the substance of equal diameter’.
Young’s definition is rather convoluted and, interestingly, slightly different from the modern one. His ‘weight of the modulus’ has units of force rather than stress and is equivalent to the modern elastic modulus (E) multiplied by the section area (A).
Confusing the matter a little further, Young also offered an alternative version: the ‘height of the modulus’, which is the height of his hypothetical column. This version has units of length and it is equivalent to the modern elastic modulus E divided by the material density (γ) and gravitational acceleration (g): ‘height of modulus’ = EAgγ). Young observed: ‘The height of the modulus is the same, for the same substance, whatever its breadth and thickness may be: for atmospheric air; it is about 5 miles, and for steel nearly 1500ft and the weight of the modulus of the elasticity of a square inch of steel ... is about 2 million pounds...’
Young refers to what we now call ‘shear’ as ‘detrusion’ and states that:
‘it may be inferred, however, from the properties of twisted substances, that the force varies in the simple ratio of the distance of the particles from their natural position, and it must also be simply proportional to the magnitude of the surface to which it is applied’.
Here Young correctly describes the shear deformation and the shear modulus and also concludes (correctly) that the shear strength of a member is proportional to its cross-
The position of the neutral axis
The position of the neutral axis of a beam in bending had troubled scientists since Leonardo da Vinci and Galileo and it was not until the 18th century that Parent and Coulomb derived the correct solution. Young extended the analysis to include the effects of axial force:
‘When a force acts on a straight column in the direction of its axis, it can only compress or extend it equally through its whole substance; but if the direction of the force be only parallel to the axis, and applied to some point more or less remote from it, the compression or extension will obviously be partial: it may be shown that in a rectangular column, when the compressing force is applied to a point more distant from the axis than one sixth of the depth, the remoter surface will no longer be compressed but extended, and it may be demonstrated that the distance of the neutral point from the axis is inversely as that of the point to which the force is applied.’
Here Young described how the position of the neutral axis varies with the load eccentricity and introduces the important engineering principle of the ‘middle third’ rule.
Fig. 2. Young’s Fig. 117: ‘An elastic column, compressed by a weight acting at the distance of one third of its depth from the concave surface; the compression being every where as the distance of the lines A B, A C.’
Fig. 3. Young's Fig 119: 'An elastic column, compressed by a weight acting immediately on the concave surface: the compression extends only to the line AB, the parts beyond this line being extended.'
In the supplement, Theorem 320 gives the detailed calculation of the stress variation across an eccentrically-
Theorem 321 shows that the radius of curvature of an eccentrically loaded rectangular column is b²m/12af, where b = section depth, m = ‘weight of modulus of elasticity’, a = load eccentricity and f= applied load. If we substitute the modern terms b = breadth, d = depth and ‘weight of modulus’ = EA = Ebd, Young’s equation becomes R = d³bE/12M, which is the familiar moment/curvature relationship M/EI = 1/R.
Deflexion of beams
‘When a rod, not very flexible, is fixed at one end in a horizontal position, the curvature produced by its own weight is every where as the square of the distance from the other end: and if a rod be simply supported at each end, its curvature at any point will be proportional to the product of the two parts into which that point divides it. But when the weights are supposed to be applied to any given points of the rod only, the curvature always decreases uniformly between these points and the points of support.'
This summarises what Euler and Bernoulli had already established about the bending deformation of beams but Young then goes on to correct an error by Euler, who had assumed that stiffness varies with the square of the section depth:
‘stiffness is directly as the breadth and the cube of the depth of the beam, and inversely as the cube of its length.’ and
‘It is evident that a tube, or hollow beam, of any kind, must be much stiffer than the same quantity of matter in a solid form: the stiffness is indeed increased nearly in proportion to the square of the diameter, since the cohesion and repulsion are equally exerted with a smaller curvature, and act also on a longer lever.’
Young draws attention to the importance of design for serviceability:
‘The property of stiffness is fully as useful in many works of art as the ultimate strength with which a body resists fracture: thus for a shelf, a lintel, or a chimney piece, a great degree of flexure would be almost as inconvenient as a rupture of the substance.’
Technical details follow:
‘When a beam is supported at both ends, its stiffness is twice as great as that of a beam of half the length firmly fixed at one end; and if both ends are firmly fixed, the stiffness is again quadrupled’
The detailed calculations to support these statements are given in Theorems in the supplement.
Theorem 326: ‘The weight of the modulus of the elasticity of a bar is to a weight acting at its extremity only, as four times the cube of the length to the product of the square of the depth and the depression’. The ‘weight of the modulus’ = EA, so this formula translates to EA /W = 4L³/d²δ; substituting I = bd³/12 then gives the familiar formula for deflexion of a cantilever under a point load: δ = WL³/3EI.
Theorem 328: ‘The height of the modulus of the elasticity of a bar, fixed at one end, and depressed by its own weight, is half as much more as the fourth power of the length divided by the product of the square of the depth and the depression’. The ‘height of the modulus’ = E/(gγ), so this formula translates to E/(gγ) = (3/2) L4/(d²δ); substituting w = gγbd and I = bd³/12 and rearranging the terms reveals that Young correctly worked out the deflexion of a cantilever under a uniformly distributed load: δ = wL4/8EI.
Theorem 330: ‘The height of the modulus of the elasticity of a bar, supported at both ends, is 5/32 of the fourth power of the length, divided by the product of the depression and the square of the depth’. This equates to: E/(gγ) = (5L4/32)/(δd²). Substituting w = gγbd and I = bd³/12 and rearranging the terms reveals it as the correct formula for the deflexion of a simply supported beam under a uniform distributed load: δ = 5wL4/384EI.
Strength of beams
‘The strength of beams of the same kind, and fixed in the same manner, in resisting a transverse force, is simply as their breadth, as the square of their depth, and inversely as their length’
‘The strength of a beam supported at both ends, like its stiffness, is twice as great as that of a single beam of half the length, which is fixed at one end; and the strength of the whole beam is again doubled if both the ends are firmly fixed’
Again Young’s conclusions are correct: the moment resistance of a beam is proportional to bd² and the moment under a point load is proportional to the span. The moment in a simply supported beam (WL/4) is a quarter of that in a cantilever (WL) and twice that in a fixed-
Having established these important analytical conclusions, Young makes some perceptive comments on material properties, highlighting the potential plastic behaviour of steel and also the dangers of brittleness:
‘Steel, whether perfectly hard, or of the softest temper; resists flexure with equal force, when the deviations from the natural state are small: but at a certain point the steel, if soft, begins to undergo an alteration of form; at another point it breaks if much hardened.’
‘... The effect of forging and of wire drawing tends to lessen the ductility of metals ... The corrosion of the surface of a metal by an acid is also said to render it brittle; but it is not impossible that this apparent brittleness may be occasioned by some irregularity in the action of the acid’
This is followed by a discussion of what Young called the ‘resilience’ of a beam -
Strength of slender columns
The buckling strength of a perfect axially-
Fig 4. Young's Fig. 120: 'A column bent, by a weight acting longitudinally, into the form of a harmonic curve: the line ABC D is the limit between the parts which are compressed, and those which are extended.'
Young’s paragraph about the position of the neutral axis continued with the following description of column buckling, which includes the fundamentals of stability and also the role of initial imperfections:
‘From the effect of this partial compression, the column must necessarily become curved; and the curvature of the axis at any point will always be proportional to its distance from the line of direction of the force, not only while the column remains nearly straight, but also when it is bent in any degree that the nature of the substance will allow. If the column was originally bent, any force, however small, applied to the extremities of the axis, will increase the curvature according to the same law, but if the column was originally straight, it cannot be kept in a state of flexure by any longitudinal force acting precisely on the axis, unless it be greater than a certain determinate force, which varies according to the dimensions of the column. It is not however true, as some authors have asserted, that every column pressed by such a force must necessarily be bent; its state when it is straight, and submitted to the operation of such a force, will resemble a tottering equilibrium, in which a body may remain at rest until some external cause disturbs it.’
This is followed by some words of caution about column load tests:
‘Considerable irregularities may be observed in all the experiments which have been made on the flexure of columns and rafters exposed to longitudinal forces; and there is no doubt but that some of them were occasioned by the difficulty of applying the force precisely at the extremities of the axis, and others by the accidental inequalities of the substances, of which the fibres must often have been in such directions as to constitute originally rather bent than straight columns.’
Theorem 322 analyses buckling of a slender column in more detail:
‘When the force is longitudinal, and the. curvature inconsiderable, the form coincides with the harmonic curve, the curvature being proportional to the distance from the axis and the distance of the point of indifference from the axis becomes the secant of an arc proportional to the distance from the middle of the column.’
Theorem 323 suggests an elegant method for determining column buckling load:
‘the strength of a bar of any other substance may be determined, either from direct experiments on its flexure, or from the sounds that it produces’.
The natural frequency of vibration of a pin-
where w is self weight/m and L is length.
If we substitute PE (Euler buckling load = π²EI/L²) and M (mass of column), we obtain PE= 4ML/fo².
Thus, just as Young suggested, if we know the mass and length of a column and the pitch of the sound it makes when struck (its natural frequency), we can calculate its Euler buckling load. To this day, the best way of determining the tension in a taut cable is by calculation from its measured natural frequency
Up to this point, Young’s detailed analysis (like Euler’s) only considered perfect straight columns. However in Theorem 323 he proceeds to consider an eccentrically loaded or bowed column:
‘If a beam is naturally of the form which a prismatic beam would acquire, if it were slightly bent by a longitudinal force, calling its depth, b, its length, e, the circumference of a circle of which the diameter is unity, c, the weight of the modulus of elasticity, m, the natural deviation from the rectilinear form, d, and a force applied at the extremities of the axis, f, the total deviation from the rectilinear form will be
a = (bbccdm)/(bbccm -
... It appears from this formula, that ... when bbccm = 12eef, a becomes infinite, whatever may be the magnitude of d, and the force will overpower the beam, or will at least cause it to bend so much as to derange the operation of the forces’.
If we replace a with δ, b with d, c with π, d with δo, m with Ebd, e with L and f with P and rearrange the formula, Young's equation becomes:
δ = (d²π²δoEbd)/(d²π²δoEbd -
Substituting I = bd³/12 and the Euler load PE = π²EI/L² gives the formula for the total deflexion of an imperfect slender column:
δ = δo/(1 -
If the column deflexion is known, its bending stress can be calculated and in his Scholium to Theorem 325 Young gives a (rather obscure) formula for this too.
Thus Young presented for the first time a complete and correct analysis of elastic stress and deflexion in an imperfect or eccentrically-
Young begins his discussion of torsion with consideration of stresses in a twisted cable:
‘Torsion, or twisting, consists in the lateral displacement, or detrusion, of the opposite parts of a solid, in opposite directions, the central particles only remaining in their natural state We might consider a wire as composed of a great number of minute threads, extending through its length, and closely connected together; if we twisted such a wire, the external threads would be extended, and, in order to preserve the equilibrium, the internal ones would be contracted; and ... the force would vary as the cube of the angle through which the wire is twisted.’
However he points out that for a solid section this is at odds with test results:
‘But the force of torsion, as it is determined by experiment, varies simply as the angle of torsion; it cannot, therefore, be explained by the action of longitudinal fibres only; but it appears rather to depend principally, if not intirely, on the rigidity, or lateral adhesion, which resists the detrusion of the particles. If a wire be twice as thick as another of the same length, it will require 16 times as much force to twist it once round; the stiffness varying as the fourth power of the diameter ... But if the length vary, it is obvious that the resistance to the force of torsion will be inversely as the length.’
Design of arches
The lecture ‘On Passive Strength and Friction’ was followed by Lecture XIV ‘On Architecture and Carpentry’, where ‘Architecture’ refers to the design of masonry and ‘Carpentry’ to the design of wooden structures. This lecture is full of interesting information on construction methods and structural details. It also includes a detailed consideration of the analysis of arches, again introducing new and original material.
Young starts with Hooke’s analysis, which used weights hung from a catenary chain as an inverted representation of loads on an arch. Based on this, he shows that the thrust line (the ‘line of pressure’) follows a parabolic curve under uniform loading and other curves for other types of load. However he says that near the supports the loads will not act vertically on the arch:
‘But the supposition of an arch resisting a weight, which acts only in a vertical direction, is by no means perfectly applicable to cases which generally occur in practice. The pressure of loose stones and earth, moistened as they frequently are by rain, is exerted very nearly in the same manner as the pressure of fluids, which act equally in all directions: and even if they were united into a mass, they would constitute a kind of wedge, and would thus produce a pressure of a similar nature, notwithstanding the precaution recommended by some authors, of making the surfaces of the arch stones vertical and horizontal only. This precaution is, however; in all respects unnecessary ... the effect of such a pressure only requires a greater curvature near the abutments, reducing the form nearly to that of an ellipsis, and allowing the arch to rise at first in a vertical direction.’
Young advises the designer to calculate the thrust lines for each loading and then to shape the arch so that it encloses the envelope of the possible thrust lines for the combined loads. He advises that:
‘in general, whether the road be horizontal, or a little inclined, we may infer that an ellipsis, not differing much from a circle, is the best calculated to comply as much as possible with all the conditions.’
He then sets out the principles of the structural behaviour of the arch itself
‘The equilibrium of a bridge, so far as it depends only on the form of the arch, is naturally tottering, and the smallest force which is capable of deranging it, may completely destroy the structure; but when the stones or blocks composing it have flat surfaces in contact with each other; it is necessary that the line expressing the direction of the pressure be so much disturbed, as to exceed at some part the limits of these surfaces, before the blocks can be displaced. When this curve, indicating the general pressure which results from the effect of a disturbing force, combined with the original thrust, becomes more remote from the centre of the blocks than one sixth of their depth, the joints will begin to open on the convex side, but the arch may still stand, while the curve remains within the limits of the blocks’.
Here Young explains clearly for the first time that to prevent its joints opening, the line of thrust in an arch ring should be kept within its middle third but that for failure to occur the thrust line must be outside the section.
Fig. 5. Young's Fig. 155. ‘A comparison of the curves which have various advantages for the construction of an arch supporting a horizontal road. The full line is an elliptic arc, somewhat less than half the ellipsis. The outside curve, which is also continued furthest down, is that which is calculated for resisting the pressure of materials acting like a fluid, or in the manner of wedges: the second dotted curve, for supporting the pressure of the materials above each part, supposed to act in a vertical direction only: the third is a circular arc, making one third of a whole circle: time fourth is part of a logarithmic curve, which is nearly of equal strength with respect to the tendency of the materials to give way for want of lateral adhesion, and the fifth is composed of parabolic curves, showing the outline which would be strongest for supporting any additional weight placed on the middle of the arch. If the height were greater in proportion to the span, as usually happens in practice, there would be less difference between the curves. The radius of curvature at the summit being A B, the horizontal thrust is equal to the weight of the portion A BCD of the materials.’
He then discusses the design of piers and abutments, drawing attention to the need to calculate the horizontal thrust correctly ‘... to avoid such accidents, as have too often happened to bridges for want of sufficient firmness in the abutments ...’ In an interesting passage he draws attention to the need for robustness, recommending that the piers of multispan bridges and viaducts should be designed to resist the horizontal thrusts which would be applied to them if an arch failed. He explains how to calculate the forces, showing that the pier will normally fail by overturning rather than sliding, and notes that resistance will be provided by the weights of the pier and the surviving arch acting together:
‘... in order that the pier may stand, the sum of these weights, acting on the end of a lever equal to half the thickness of the pier, must be more than equivalent to the horizontal thrust, acting on the whole height of the pier The pier may also be simply considered as forming a continuation of the arch, and the stability will be preserved as long as the curve, indicating the direction of the pressure, remains within its substance’
Once more Young’s judgment is hard to fault: he recommends designing the structure to resist progressive failure but as this is an extreme accidental loading the normal limits on forces in the structure do not apply -
In 1807 in the space of a single paper, Thomas Young introduced the concept of an elastic modulus to define material stiffness and presented the first full and correct analysis of many of the basic elements of structural elastic theory. In a second paper he followed this with a comprehensive treatment of arch design. However at the time most of this passed largely unnoticed by engineers.
This may have been partly because the material was buried amidst 58 other lectures on a vast range of other subjects. Also, although some of Young's explanations were admirably clear, others were obscure and difficult to follow. Todhunter and Pearson later commented:
‘The whole section seems to me very obscure like most of the writings of its distinguished author, among his vast attainments in sciences and languages that of expressing himself clearly in the ordinary dialect of mathematicians was unfortunately not included. The formulae of the section were probably mainly new at the time of their appearance, but they were little likely to gain attention in consequence of the unattractive form in which they were presented.’ .
Timoshenko’s assessment was rather more generous:
‘From this discussion we see that the chapter on mechanics of materials in the second volume of 'Natural Philosophy' contains valid solutions of several important problems of strength of materials, which were completely new in Young's time. This work did not gain much attention from engineers because the author's presentation was always brief and seldom clear’ .
However Young’s Lectures also faced another problem: there was interest in structural theory in France but British engineers tended to prefer the empirical approach, relying on load tests rather than calculations to determine the strength and stiffness of members. This caution was understandable when dealing with brittle, variable materials like cast iron and stone. It was not until later in the 19th century that interest in structural theory grew, first with increasing use of wrought iron and then as mass-
The story of the development of the theory of materials and structures from its early beginnings with Leonardo da Vinci and Galileo through to the 20th century is well told in Stephen Timoshenko’s History of Strength of Materials . Key developments included Hooke’s Law (1678) and then, in the 18th century, Bernoulli and Euler’s calculations of the deformed shapes of loaded beams and columns and Parent and Coulomb’s solution of the neutral axis and distribution of bending stress in beams. Later on, in the 19th century, Navier, Poisson, St Venant and others developed and formalised elastic theory and promoted its use.
The genius and significance of Young’s contribution was his realisation that defining the modulus of elasticity of a material would open the door to solutions of all aspects of member stress and deflexion under load. What is remarkable is how much of this he then proceeded to do. He solved:
* the position of the neutral axis and distribution of stress in a member subjected to bending and axial load,
* the relationship between the dimensions of a rectangular section and its bending strength,
* comparison of the bending properties of solid sections and thin-
* the deflexion of cantilever, simply supported and fixed-
* the calculation of deflexion and maximum stress in an imperfect or eccentrically loaded slender column,
* the effects of impact loads on beams and how these vary with different shapes of cross section.
He also offered major advances on shear and torsion and his following paper provided a comprehensive rational analysis for arch bridge design. Young’s analysis of eccentrically-
‘The equation was a drop in the ocean of Young's contributions to science, medicine, engineering and philology, but it was seminal to the design of compression members’ .
It is true that Young’s definition of the elastic modulus differs from the one that now bears his name, which was actually defined by Navier in 1826. Furthermore, Young’s formulae were sometimes obscure and presented differently from the way they are used today. However, it is also true that many of the fundamental theoretical elements of modern structural engineering appeared for the first time in this landmark paper.
The analysis and conclusions which Young presented in 1807 were almost all correct and they have stood the test of time. As structural engineers prepare to celebrate the 100th anniversary of the foundation of their Institution, it would be fitting if its members also raise glasses in a toast to Dr Thomas Young and the bicentenary of his outstanding contribution to the science of structural engineering.
The illustrations from Young’s original papers are reproduced by kind permission of Continuum International Publishing. The portrait of Thomas Young is reproduced by kind permission of the British Museum and Mr & Mrs S. Z. Young.
1. Sir Humphry Davy, quoted in Fleming, F, Barrow’s Boys, Granta, London, 1998, p.8
2. Beal, A. N., ‘Who Invented Young's Modulus?’, The Structural Engineer, 78/14, 18 July 2000
3. Robinson, A.: The Last Man Who Knew Everything, Oneworld, Oxford, 2006 (see also TSE Online 20 Nov 2007: A. Beal’s review of book)
4. Young, I.: A Course of Lectures on Natural Philosophy and the Mechanical Arts (4 vols.), reprint of 1807 edition, with foreword by N. J. Wade, Thoemmes, Bristol, 2002. Peacock G. & Leitch J. (eds.), Miscellaneous Works of the Late Thomas Young, reprint of 1855 edition, Thoemmes, Bristol, 2003. Peacock’s 1855 biography and the 1845 Kelland edition of Young's Lectures (which unfortunately omitted the 1807 edition’s mathematical supplements) are also available as free downloads from Google Books. There is a copy of the Thoemmes edition of Young’s Lectures in the Institution of Structural Engineers Library
5. Young, T.: letter to A. Dalzel, March 1802, quoted in Robinson op. cit. , p. 89
6. Robinson, op. cit. , p. 91
7. Gurney, H.: Memoir of the Life of Thomas Young, 1831, p. 21, quoted in Wade op. cit. , p. xiii
8. Gurney, H.: ‘Memoir’ in Thomas Young, Rudiments of an Egyptian Dictionary, pp. 24-
9. Larmor, J., ‘Thomas Young’, Nature, 133, 24th Feb. 1934, p. 276, quoted in Robinson op. cit ., p. 121
10. Wade, N. J. Introduction, op. cit. , vii
11. Todhunter l. & Pearson K.: History of the Theory of Elasticity, 1893, quoted in Timoshenko op. cit. , p. 94
12. Timoshenko, S.P.: op. cit. , p.97
13. Timoshenko, S.P.: History of Strength of Materials, McGraw Hill, New York, 1953, Dover reprint 1983
14. Chapman, J.C. & Buhagiar, D.: ‘Application of Young’s buckling equation to design against torsional buckling’, Proc. The Institution of Civil Engineers: Structures and Buildings, 99/3, Aug. 1993, ICE, London, pp. 359-