Thomas Young

How to use this course

Thomas Young is remembered for a handful of things that seem to belong to different people. Physicists know the double-slit experiment. Engineers know Young’s modulus. Chemists know Young’s equation for the contact angle of a drop. Vision scientists know the Young–Helmholtz theory of colour. Egyptologists know his work on the Rosetta Stone. All of these came from one London physician, mostly in his spare time, between 1793 and 1829.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Young wrote almost entirely in words and avoided equations, which partly explains why his contemporaries found him hard to follow. The lessons state his results in modern notation and mark where later workers, Augustin-Jean Fresnel above all, made his ideas quantitative.

Timeline

Milverton, Minehead, Compton, 1773–1787

Thomas Young was born on 13 June 1773 at Milverton in Somerset, the first of ten children of Thomas Young, a Quaker cloth merchant and banker, and Sarah Davis. He spent much of his early childhood with his maternal grandfather, Robert Davis, at Minehead, and learned to read very young. His first schoolmasters had little to teach him. At a boarding school near Bristol he worked through the set books in half the expected time.

From 1782 to 1786 he attended a school at Compton in Dorset that let pupils advance at their own pace. He left with Greek, Latin, French, Italian and Hebrew, a working knowledge of Newton’s physics and optics, and practice in building optical instruments. Afterwards he added Arabic, Persian, Syriac, Chaldee and Samaritan. Languages and natural philosophy stayed side by side in his life for the next forty years.

At about fourteen he became tutor and companion to Hudson Gurney, grandson of the Quaker banker David Barclay, living at a house near Ware in Hertfordshire and in London. Until 1792 he used the post to read Euclid, Newton’s Principia and Opticks.

Medicine in three countries, 1792–1799

His great-uncle, the physician Richard Brocklesby, encouraged him toward medicine. Young began study in London in 1792, at the hospitals and anatomy schools. In the course of dissecting an ox’s eye he formed a theory of how the eye focuses at different distances, by a change in the shape of the crystalline lens. The paper, Observations on vision, was read to the Royal Society on 30 May 1793. On 19 June 1794, still only twenty, he was elected a Fellow.

In 1794 he moved to Edinburgh, then the leading British medical school, and in October 1795 to Göttingen, where he passed his doctoral examination on 30 April 1796. His dissertation drew on anatomy, sound and language, and an appendix proposed a universal phonetic alphabet. He then toured German cities, including Berlin, Dresden and Weimar, and returned to England in February 1797.

A change in the rules for licensing physicians required study at an English university, so in 1797 Young entered Emmanuel College, Cambridge. He had to leave the Society of Friends to do so. The same year Brocklesby died and left him a fortune that made him independent. At Cambridge he studied physics on his own, especially sound, and thought about why the colours of soap films and the beats of two organ pipes might be the same phenomenon. In 1799 he set up as a physician at 48 Welbeck Street in London. His first papers on sound and light, published that year and the next, appeared under his name, but he later published some work anonymously to protect his medical practice.

The Royal Institution, 1799–1807

In 1800 Young read Outlines of experiments and inquiries respecting sound and light to the Royal Society, arguing that light might be a wave like sound. On 27 November 1800 he gave the Bakerian Lecture, On the mechanism of the eye, with careful measurements on his own eyes. They showed that accommodation comes from the lens, and described the astigmatism of his own eye. On 12 November 1801 he gave a second Bakerian Lecture, On the theory of light and colours, which stated the principle of interference and gave the first table of wavelengths of the colours (Lesson 04).

In 1801 Count Rumford’s new Royal Institution appointed him professor of natural philosophy. Beginning in January 1802 he gave a course of fifty lectures on mechanics, hydrodynamics, physics and mathematics. Listeners found them dense and allusive. He resigned in the summer of 1803, fearing that the post would hurt his medical practice. On 24 November 1803 he read Experiments and calculations relative to physical optics, describing the experiment with a narrow card in a sunbeam (Lesson 05).

Brougham’s attack

Between 1803 and 1804 the Edinburgh Review published anonymous reviews of Young’s optical papers, written by Henry Brougham, later Lord Chancellor. They ridiculed the wave theory as unworthy of the Royal Society. Young replied in a pamphlet that sold very few copies. A publisher withdrew from printing his lectures, and Young turned more fully to medicine. On 14 June 1804 he married Eliza Maxwell. In 1807 the lectures appeared at last, in two volumes, as A Course of Lectures on Natural Philosophy and the Mechanical Arts, with the modulus of elasticity and the famous figure of two-source interference.

The principle of interference

For the general reader. Two musical notes of nearly the same pitch produce beats: the loudness rises and falls as the waves fall into and out of step. Young saw that the coloured rings Newton had measured in thin films are the same effect for light. Light reflected from the top and bottom of a film travels slightly different distances, and the two waves add or cancel depending on that difference. From Newton’s own measurements Young extracted the wavelength of each colour.

Derivation. Represent the waves by \(A\cos(\omega t)\) and \(A\cos(\omega t-k\Delta)\), \(k=2\pi/\lambda\). Their sum is \(2A\cos(k\Delta/2)\cos(\omega t-k\Delta/2)\). The intensity is proportional to the square of the amplitude: \(4A^2\cos^2(\pi\Delta/\lambda)\).

Thin films

A film of index \(n\) and thickness \(t\), viewed in reflection at near-normal incidence, produces two reflected waves whose optical path differs by \(2nt\). Young also saw that one of them suffers an extra half-period shift when the reflection is from a denser medium. He predicted that if the film were made of a substance intermediate in index between the two bounding glasses, the shift would disappear and the centre of Newton’s rings would turn bright. He confirmed it with oil of sassafras between a crown-glass lens and a flint-glass prism.

Derivation. The path difference is \(2t+\lambda/2\). Darkness requires \(2t+\lambda/2=(m+\tfrac12)\lambda\), i.e. \(2t=m\lambda\), and with \(t=r^2/(2R)\) this gives \(r^2=m\lambda R\). The central spot (\(m=0\)) is dark.

Two apertures and the edge of a shadow

For the general reader. Behind a thin object placed in a narrow beam of sunlight, the shadow is striped. Young found that the stripes inside the shadow vanish if he blocks the light passing one edge, even though the light passing the other edge is untouched. The stripes therefore need light from both sides together. The same reasoning applies to light passing two small openings, the arrangement now called Young’s double slit.

The card experiment (1803)

Young let sunlight through a small hole in a window shutter and held a slip of card about one-thirtieth of an inch wide in the beam. Fringes appeared inside the shadow. When he put a screen at one edge of the card, intercepting the light that passed that side, the internal fringes disappeared. He concluded that they came from the interference of light passing the two edges. He accounted for the external fringes by interference between the direct light and light “reflected” from the edge. Fresnel later showed that this edge account was not quite right and replaced it with the Huygens–Fresnel integral.

Two slits

Derivation. In the far field the amplitude is the Fourier transform of the aperture. A single slit gives \(\int_{-b/2}^{b/2}e^{-ikx\sin\theta}dx=b\,\frac{\sin\beta}{\beta}\). Two slits centred at \(\pm d/2\) multiply this by \(e^{ikd\sin\theta/2}+e^{-ikd\sin\theta/2}=2\cos(\pi d\sin\theta/\lambda)\). Squaring gives the result. Young had only the \(\cos^2\) factor; the envelope is Fresnel’s and Fraunhofer’s.

Polarization and transverse waves

For the general reader. In 1808 Étienne-Louis Malus found that light reflected from glass at certain angles is polarized: it behaves differently when turned about its own direction. Young at first saw this as the strongest objection to his wave theory, since waves in a fluid vibrate along their direction of travel and have no sidedness. In 1817 he found a way out. Light might vibrate across its path, like a wave running along a shaken rope.

In letters to Arago in 1817 and 1818 Young suggested that light might involve a transverse component of vibration, and compared it to the undulations of a cord agitated at one end. Arago showed the idea to Fresnel, who saw that it explained why beams polarized at right angles do not interfere, and in 1821 proposed that the vibration is wholly transverse. Fresnel credited Young with stating the idea first.

Derivation (transverse model). The vibration is a vector \(\mathbf A\) perpendicular to the ray. An analyser passes only the component along its axis, \(A\cos\varphi\). Intensity goes as amplitude squared. A longitudinal vibration has no component across the ray and cannot depend on \(\varphi\), which is why polarization forces transversality.

The elastic aether

In an elastic solid of shear modulus \(G\), bulk modulus \(K\) and density \(\rho\), there are transverse waves at speed \(c_T=\sqrt{G/\rho}\) and longitudinal waves at \(c_L=\sqrt{(K+\tfrac43G)/\rho}\). A fluid has \(G=0\) and cannot carry transverse waves. Young therefore concluded that the luminiferous medium must behave like a solid, and he was troubled that the planets move through it without resistance. The difficulty lasted until Maxwell’s electromagnetic theory replaced the elastic aether.

Elasticity and Young’s modulus

For the general reader. Hooke’s law says that a spring stretches in proportion to the load. But the constant depends on the size and shape of the spring as well as on what it is made of. Young separated the material from the geometry. His modulus of elasticity is a single number for steel, another for oak, from which the stretch of any rod can be computed.

Young expressed the modulus as a length. He defined it as the height of a column of the same substance whose weight, pressing on its base, would compress it by the full length of the column, if the linear law held that far. In modern terms this height \(M\) satisfies \(\rho gM=E\). The modulus is not Young’s alone: Leonhard Euler and Giordano Riccati had used similar quantities. Young’s formulation made it standard in engineering.

Derivation. The strain at \(x\) is \(u_x\), so the force across a section is \(EAu_x\). The net force on a slice \(dx\) is \(EA\,u_{xx}\,dx\), and its mass is \(\rho A\,dx\). Newton’s second law gives the wave equation. Young noted that the speed of sound in a substance equals the speed acquired by falling through half its modulus height: since \(c^2=E/\rho=gM\), and a fall through height \(h\) gives \(v^2=2gh\), the height is \(M/2\).

Capillarity and surface tension

For the general reader. Water climbs up a narrow glass tube; mercury sinks. A drop on a leaf beads up, on clean glass it spreads. In an essay published in 1805, Young explained these effects with two ideas: the surface of a liquid behaves as if under uniform tension, and where liquid meets solid it makes a definite angle set by the materials. He wrote it all in words. Pierre-Simon Laplace, working independently, gave the mathematical form of the first idea the same year.

Derivation. Balance the forces per unit length along the solid at the contact line: \(\gamma_{SV}\) pulls outward, \(\gamma_{SL}\) inward, and the liquid surface pulls with \(\gamma_{LV}\) at angle \(\theta\), contributing \(\gamma_{LV}\cos\theta\) inward. Equivalently, moving the contact line by \(dx\) changes the free energy per unit length by \((\gamma_{SL}-\gamma_{SV}+\gamma_{LV}\cos\theta)\,dx\), which must vanish at equilibrium. Athanase Dupré later combined it with the work of adhesion: \(W_{SL}=\gamma_{LV}(1+\cos\theta)\).

Derivation for a sphere. Cut a spherical drop of radius \(R\) in half. The pressure excess pushes the halves apart with force \(\Delta p\,\pi R^2\); the tension holds them together along the circumference with \(2\pi R\gamma\). Equating, \(\Delta p=2\gamma/R\), the case \(R_1=R_2=R\).

The meniscus is approximately a spherical cap of radius \(r/\cos\theta\), so the pressure just below it is lower than atmospheric by \(2\gamma\cos\theta/r\). Hydrostatic balance gives \(\rho gh\) equal to this.

The eye: accommodation and three colours

For the general reader. Young’s first and last scientific interests were in the eye. He settled a long debate over how the eye focuses on near and far objects: the lens changes shape. He found that his own eye focused vertical and horizontal lines at different distances, the first description of astigmatism. He also proposed that colour vision needs only three kinds of receptor in the retina, an idea confirmed a century and a half later.

Accommodation

In 1800 Young tested and excluded the alternatives. A change in the cornea was ruled out by viewing with the eye under water, which cancels the cornea’s power, and finding that accommodation persisted. A change in eye length was ruled out by pressing on the eye and finding no change. What remained was the lens.

Three colours

In modern terms, if the receptors have sensitivities \(s_j(\lambda)\), \(j=1,2,3\), a light with spectrum \(P(\lambda)\) produces responses \(r_j=\int s_j(\lambda)P(\lambda)\,d\lambda\). Two lights that give the same triple \((r_1,r_2,r_3)\) look identical though their spectra differ: they are metamers. Colour sensations form a three-dimensional cone in which mixing of lights is vector addition. Hermann von Helmholtz revived and extended Young’s idea in the 1850s, and James Clerk Maxwell confirmed it by colour-matching experiments. Three types of cone were identified by microspectrophotometry in the 1960s.

The pulse as a wave

For the general reader. When the heart beats, a pressure wave runs along the arteries faster than the blood itself moves. In his Croonian Lecture of 1808, Young treated the arteries as elastic tubes and the pulse as a wave in them, using the same reasoning as for sound in a rod. He also argued that the heart, not muscular action of the arteries, drives the circulation. The formula for the pulse speed is now a standard tool in cardiovascular medicine.

Derivation. With mean velocity \(u\), conservation of mass and momentum give, to linear order, \(A_t+A_0u_x=0\) and \(\rho u_t+p_x=0\). Write \(A_t=(dA/dp)\,p_t\). Eliminating \(u\): \(p_{tt}=\frac{A_0}{\rho\,dA/dp}\,p_{xx}\). For the thin wall, the hoop stress is \(pR/h\), the circumferential strain \(dR/R\), so \(dp=\frac{Eh}{R^2}dR\) and \(dA=2\pi R\,dR\). Then \(\frac{A}{dA/dp}=\frac{\pi R^2\,Eh}{2\pi R^3}=\frac{Eh}{2R}\). Young reached the equivalent result in 1808, in words and with his modulus height, seventy years before Moens and Korteweg.

Physician, secretary, decipherer, 1807–1829

After 1807 Young concentrated on medicine. He became physician to St George’s Hospital in 1811 and published An Introduction to Medical Literature (1813) and A Practical and Historical Treatise on Consumptive Diseases (1815). His rule for children’s doses, the adult dose times the age divided by the age plus twelve, was long in use. He was never a popular doctor; patients found his manner too scientific. He served the Royal Society as foreign secretary for the rest of his life, sat on a committee on the dangers of London’s gas lighting in 1814, and in 1816 was secretary of a commission on the length of the seconds pendulum. In 1818 he became secretary of the Board of Longitude and superintendent of the Nautical Almanac. In his last years he also took up the mathematics of life insurance.

For the supplement to the Encyclopædia Britannica he wrote dozens of articles, on subjects from tides to bridges, and a long article on languages that compared the grammar and vocabulary of about four hundred tongues. In 1813 he used the term “Indo-European” for the family that links Sanskrit with most European languages.

The Rosetta Stone

The Rosetta Stone, carrying one decree in Greek, demotic and hieroglyphic script, reached London in 1802. Young began work on it in 1814, building on the demotic alphabet of Johan David Åkerblad. By the end of that year he had a word-by-word translation of the demotic text. He recognised that demotic mixed phonetic and ideographic signs, and he correctly assigned sound values to several hieroglyphic signs in the royal names, starting from the name of Ptolemy. His article “Egypt” in the 1818 Britannica supplement set out his results. Jean-François Champollion announced the full phonetic decipherment of hieroglyphs in 1822. Young answered in 1823 with An Account of Some Recent Discoveries in Hieroglyphical Literature, claiming that his work was the foundation. Relations between the two were strained, though after 1826 Champollion, then a curator at the Louvre, gave Young access to demotic manuscripts.

Death and legacy

Recognition of Young’s optics came from France first. After Fresnel’s prize memoir of 1818–19 and his work on polarization, French physicists acknowledged Young’s priority on interference, and Young corresponded with Fresnel and Arago. In 1827 the Académie des sciences elected Young one of its eight foreign associates. His health declined from 1828. He continued to work on an Egyptian dictionary until shortly before his death in London on 10 May 1829, at the age of 55. An autopsy found severe disease of the aorta. He was buried in the churchyard of St Giles at Farnborough in Kent. A memorial tablet in Westminster Abbey, with an inscription by his old pupil Hudson Gurney, credits him with first establishing the undulatory theory of light.

Legacy

• Optics. The principle of interference, the first measured wavelengths, and the transverse-wave hypothesis. Combined with Fresnel’s mathematics they made the wave theory of light. The double-slit experiment became, in quantum mechanics, the standard illustration of wave–particle duality.
• Mechanics and materials. Young’s modulus, the energy stored in elastic bodies, and in 1807 the use of the word “energy” for the quantity proportional to \(mv^2\).
• Surfaces. Young’s equation and, with Laplace, the Young–Laplace equation: the basis of the science of wetting.
• Physiology. Accommodation, astigmatism, trichromatic colour vision (the Young–Helmholtz theory), and arterial wave mechanics.
• Languages. The term Indo-European, the comparative survey of languages, and the first real progress on demotic Egyptian.

John Herschel called him a truly original genius. Albert Einstein, in his 1931 foreword to Newton’s Opticks, named Young among those who carried optics forward. Andrew Robinson’s 2006 biography called him The Last Man Who Knew Everything.

Sources and further reading

Biography

1. Thomas Young, MacTutor History of Mathematics, University of St Andrews.
2. Thomas Young (scientist), Wikipedia.
3. Thomas Young, Royal Society, Science in the Making archive.
4. G. Peacock, Life of Thomas Young, M.D., F.R.S., John Murray, London, 1855.
5. A. Wood and F. Oldham, Thomas Young, Natural Philosopher, 1773–1829, Cambridge University Press, 1954.
6. A. Robinson, The Last Man Who Knew Everything, Pi Press, 2006.

Physics

1. T. Young, The Bakerian Lecture: On the mechanism of the eye, Phil. Trans. R. Soc. 91 (1801), 23–88. Project Gutenberg text.
2. T. Young, The Bakerian Lecture: On the theory of light and colours, Phil. Trans. R. Soc. 92 (1802), 12–48. Project Gutenberg text.
3. T. Young, The Bakerian Lecture: Experiments and calculations relative to physical optics, Phil. Trans. R. Soc. 94 (1804), 1–16.
4. T. Young, An essay on the cohesion of fluids, Phil. Trans. R. Soc. 95 (1805), 65–87.
5. T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, 2 vols, London, 1807.
6. T. Young, The Croonian Lecture: On the functions of the heart and arteries, Phil. Trans. R. Soc. 99 (1809), 1–31.
7. Young’s interference experiment, Wikipedia.
8. E. T. Whittaker, A History of the Theories of Aether and Electricity, vol. 1, 1910; revised 1951.
9. J. Z. Buchwald, The Rise of the Wave Theory of Light, University of Chicago Press, 1989.