William Thomson, Lord Kelvin

How to use this course

William Thomson is remembered in the name of a unit. Every temperature in science is quoted in kelvins, measured from an absolute zero he was the first to define independently of any thermometric substance. That is a small part of what he did. He gave one of the two classical statements of the second law of thermodynamics and drew from it the doctrine that useful energy is always being dissipated. He predicted a new thermoelectric effect. He worked out why signals crawl along submarine cables and then helped lay the cable that first joined Europe and America. He tried to date the Earth by its cooling, imagined atoms as knotted vortices in the ether, and designed instruments that ships used for decades.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The physics lessons follow the order of his work: thermodynamics (1848–1856), telegraphy (1854–1866), geophysics (1862 onward), fluid dynamics and vortex atoms (1867 onward), and the instruments of the 1870s.

Timeline

Belfast and Glasgow, 1824–1841

William Thomson was born in Belfast on 26 June 1824. His father, James Thomson, came from a farming family in County Down, had first been destined for the Presbyterian ministry, and taught mathematics at the Belfast Academical Institution, where he wrote widely used textbooks. His mother, Margaret Gardner, died in 1830, when William was six. The father raised the children himself and taught the two eldest boys, James and William, at home.

In 1832 the elder Thomson was appointed professor of mathematics at the University of Glasgow, and the family moved there in October 1833. Scottish universities then took boys young. In 1834, aged ten, William matriculated alongside his brother James, who was two years older. James later became a distinguished engineer and professor of engineering, and the two brothers argued about physics all their lives.

At Glasgow William studied natural philosophy and astronomy as well as mathematics. His essay on the figure of the Earth won a university gold medal in 1840. That winter he read Joseph Fourier’s Théorie analytique de la chaleur (1822) in a few weeks and was captivated. Fourier’s method of expanding a function into trigonometric series, and his treatment of heat flow by partial differential equations, run through nearly everything Thomson did afterwards: thermodynamics, electrostatics, cable signals, the cooling of the Earth and the tides.

Cambridge and Paris, 1841–1846

His father wanted him to have the prestige of a Cambridge degree. Thomson entered Peterhouse in April 1841 and came into residence that October. Before arriving he had already published a paper defending Fourier against a critic, signed P.Q.R. to hide his youth. In 1842 he published a paper showing that the equations of steady heat flow and of electrostatic attraction have the same mathematical form, so that results in one subject translate directly into the other. James Clerk Maxwell later described this analogy as one of the most valuable ideas for forming science.

He was also a keen oarsman, winning the Colquhoun silver sculls in 1843, and he played in the university musical society. His coach for the Mathematical Tripos was William Hopkins, the most successful tutor of the age. In January 1845 he was placed Second Wrangler, behind Stephen Parkinson, but he won the first Smith’s Prize, generally a better test of original ability. In June he was elected a fellow of Peterhouse and took over the editorship of the Cambridge Mathematical Journal, which he expanded as the Cambridge and Dublin Mathematical Journal.

Green and Faraday

Just before leaving Cambridge Thomson obtained copies of George Green’s privately printed Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (1828), which had been almost entirely ignored. He took them to Paris, showed them to Joseph Liouville and others, and arranged for the essay to be reprinted in Crelle’s journal. Green’s potential theory became one of Thomson’s main tools. In 1845 he gave the first mathematical treatment of Michael Faraday’s idea that electrical induction acts through the dielectric medium, and he invented the method of electrical images, which solves electrostatic problems for spheres and planes by placing fictitious charges behind the conductor.

Regnault’s laboratory

After graduating he spent several months of 1845 in Paris, working in the laboratory of Henri Victor Regnault at the Collège de France. Regnault was then making the most precise measurements of the thermal properties of steam and gases ever attempted. Thomson learned there the habits of exact measurement and absolute units that marked all his later work. In Paris he also encountered Émile Clapeyron’s 1834 account of Sadi Carnot’s theory of heat engines, though he could not yet find Carnot’s original book.

The young professor, 1846–1852

The Glasgow chair of natural philosophy fell vacant in May 1846. On 11 September 1846, after a campaign organized largely by his father, Thomson was elected unanimously. He was 22. He held the chair until 1899. He was not a clear lecturer for beginners, often wandering into his current research, but he transformed teaching by setting up one of the first physics teaching laboratories in Britain in rooms of the old college, staffed by student volunteers.

Joule

In June 1847, at the British Association meeting in Oxford, Thomson heard James Prescott Joule, a Manchester brewer, describe experiments showing that a fixed amount of mechanical work always produces the same amount of heat. Thomson was struck, and also troubled. Carnot’s theory, which he admired, assumed that heat is a conserved fluid that produces work by falling from high to low temperature. Joule claimed that heat is consumed when work is done. For four years Thomson tried to hold both views. His brother James contributed an important clue: since water expands on freezing, a Carnot engine could do work by freezing water, so the freezing point must fall under pressure. William’s laboratory confirmed the prediction in the 1849–50 session.

The resolution came in 1851, prompted in part by Rudolf Clausius’s paper of 1850 (Lesson 05). In the same period Thomson began a lifelong correspondence with George Gabriel Stokes; a letter of July 1850 to Stokes contains the integral theorem now called the Kelvin–Stokes theorem. In 1849 his father died. In September 1852 he married his second cousin Margaret Crum, daughter of the chemist and manufacturer Walter Crum. She became an invalid soon after the marriage and died in 1870. There were no children.

Absolute temperature

For the general reader. A mercury thermometer and an alcohol thermometer agree at freezing and boiling and disagree in between, because the two liquids expand differently. Which is right? Thomson’s answer, in 1848, was that temperature can be defined by the efficiency of an ideal heat engine, which by Carnot’s theorem does not depend on any substance. The scale built this way has a natural zero, and it is the kelvin scale.

Carnot’s theorem

A heat engine takes heat \(Q_1\) from a reservoir at a high temperature, rejects \(Q_2\) to a reservoir at a lower one, and does work \(W=Q_1-Q_2\). A reversible engine can be run backwards as a refrigerator with all flows reversed.

Proof sketch. Suppose engine \(X\) were more efficient than a reversible engine \(R\). Run \(X\) forwards and \(R\) backwards, adjusted so that \(X\) supplies exactly the work \(R\) needs. The net effect is heat drawn from the cold reservoir and delivered to the hot one with nothing else changing (or, adjusted the other way, work extracted from a single reservoir). The second law (Lesson 05) forbids this. Applying the argument with two reversible engines in both orders shows their efficiencies are equal.

The scale

Since \(Q_2/Q_1\) for a reversible engine is a universal function of the two temperatures, write \(Q_2/Q_1=f(\theta_1,\theta_2)\). Composing two engines in series, the first between \(\theta_1\) and \(\theta_3\), the second between \(\theta_3\) and \(\theta_2\), gives \(f(\theta_1,\theta_2)=f(\theta_1,\theta_3)f(\theta_3,\theta_2)\), which forces \(f(\theta_1,\theta_2)=\phi(\theta_2)/\phi(\theta_1)\) for a single function \(\phi\).

For an ideal gas, a Carnot cycle computed with \(pV=nR\Theta\), where \(\Theta\) is the gas-thermometer temperature, gives \(Q_2/Q_1=\Theta_2/\Theta_1\). So the thermodynamic scale coincides with the ideal-gas scale, and absolute zero sits near \(-273.15\ ^\circ\mathrm C\).

1848 and 1854

Thomson’s 1848 paper still used the caloric theory, in which the heat \(Q\) passes through the engine undiminished. He defined his degree so that a unit of heat falling through one degree yields the same work at every level of the scale. Once Joule’s equivalence was accepted, that definition no longer described the physics, and Thomson himself later called the 1848 scale unsatisfactory while defending its principles. In 1854 Joule and Thomson defined the scale above, chose its unit so that 100 degrees separate freezing and boiling water, and showed from their gas measurements that it agrees closely with the air thermometer. The 1848 paper also noted that the air thermometer points to an infinite cold about 273 degrees below the freezing point.

The Joule–Thomson effect

To check the ideal-gas assumption, Joule and Thomson forced gases through a porous plug from high to low pressure in experiments begun in 1852. The flow is at constant enthalpy \(H\). They found that most gases cool slightly, hydrogen warms at room temperature, and the effect measures the departure from ideal behaviour.

Derivation. From \(dH=T\,dS+V\,dp\) and \(dS=\frac{C_p}{T}dT-\big(\frac{\partial V}{\partial T}\big)_p dp\) (a Maxwell relation), \(dH=C_p\,dT+\big[V-T\big(\frac{\partial V}{\partial T}\big)_p\big]dp\). Setting \(dH=0\) gives the formula. The effect is the basis of the Linde process for liquefying air (1895).

The second law and the dissipation of energy

For the general reader. Energy is never destroyed, but it can become useless. Heat in the sea cannot drive a ship unless there is something colder to reject it into. Thomson stated this as a law of nature in 1851, and a year later drew the consequence: in the physical world, energy constantly runs down from forms that can do work into uniform warmth that cannot. He was the first to draw the cosmic implication, that the Earth and Sun have a finite past and a finite future as abodes of life.

Equivalence. If an engine violated Thomson’s form, its work could drive a refrigerator moving heat from cold to hot; the combination violates Clausius’s form. Conversely, if a device moved heat \(Q_2\) from cold to hot with no other effect, pair it with an ordinary engine that rejects exactly \(Q_2\) into the cold reservoir: the cold reservoir is unchanged and the combination turns heat from the hot reservoir alone into work, violating Thomson’s form.

Thomson’s 1851 paper On the Dynamical Theory of Heat accepted Joule’s principle that heat and work are interconvertible, kept Carnot’s principle as a second independent law, and derived Carnot’s function in terms of Joule’s mechanical equivalent. Clausius had reached a similar synthesis in 1850, and Thomson acknowledged his priority. It was Clausius who went on, in 1865, to define entropy; Thomson rarely used the word.

Available energy

Thomson’s formulation leads naturally to the idea of the work obtainable from a system in surroundings at temperature \(T_0\). For a body cooled from \(T_1\) to \(T_0\) by feeding a sequence of infinitesimal reversible engines, each slice of heat \(dQ=C\,dT\) yields work \(dQ\,(1-T_0/T)\).

The dissipation paper (1852)

In April 1852 Thomson published a two-page paper, On a Universal Tendency in Nature to the Dissipation of Mechanical Energy. It drew three conclusions, here paraphrased: there is at present a universal tendency to dissipation of mechanical energy; restoration of mechanical energy without more than an equivalent dissipation is impossible in inanimate processes; and within a finite past and future the Earth must have been, and must again be, unfit for human life as now constituted, unless operations take place that are impossible under known laws. The paper also did much to spread the word “energy” in its modern sense. With William Rankine he introduced the term potential energy.

The age of the Sun

If the Sun is not refuelled, its age is limited by its energy store. Chemical burning gives a few thousand years. In the 1850s and 1860s Thomson and Hermann von Helmholtz argued that gravitational contraction supplies the heat. Thomson’s 1862 essay On the Age of the Sun’s Heat concluded that the Sun had probably not illuminated the Earth for 100 million years, and almost certainly not for 500 million. The time scale \(t_{KH}\sim GM^2/(RL)\) is now called the Kelvin–Helmholtz time. Nuclear fusion, unknown until the twentieth century, removed the limit.

Thermoelectricity

For the general reader. Join two different metals in a loop and heat one junction: a current flows. Run a current through such a junction and it warms or cools. These two effects, found by Thomas Johann Seebeck in 1821 and Jean Peltier in 1834, looked unrelated. In 1851 Thomson applied the new thermodynamics to them, proved they are two faces of one property, and predicted a third effect in a single metal with a temperature gradient. Experiment confirmed it, and it bears his name.

The three effects

Use absolute coefficients for each conductor. The Seebeck coefficient \(S(T)\) is the thermoelectric emf per unit temperature difference: in a circuit of conductors \(A\) and \(B\) with junctions at \(T\) and \(T+\Delta T\), the open-circuit emf is \(\int_T^{T+\Delta T}(S_A-S_B)\,dT'\). The Peltier coefficient \(\Pi\) is the heat carried per unit charge by the current; at a junction where current \(I\) passes from \(A\) to \(B\), heat \((\Pi_B-\Pi_A)I\) is absorbed per unit time. The Thomson coefficient \(\mu\) describes heat exchange along one homogeneous conductor carrying current density \(\mathbf J\) in a temperature gradient: besides Joule heat, heat is generated at the rate

so for \(\mu>0\) the conductor absorbs heat where current flows towards hotter regions.

Derivation

Energy. Follow a unit charge moving along a conductor from \(T\) to \(T+dT\). The heat it carries rises from \(\Pi(T)\) to \(\Pi(T+dT)\). That increase is supplied by the Thomson heat absorbed, \(\mu\,dT\), and by the work done on the charge by the thermoelectric field, \(S\,dT\). Hence

Entropy. Thomson assumed that the reversible thermoelectric heats, considered alone, satisfy Carnot’s principle, producing no net entropy. The carriers then transport entropy \(\Pi/T\) per unit charge, and the entropy absorbed in moving up \(dT\) is \(\mu\,dT/T\). This gives \(d(\Pi/T)/dT=\mu/T\). Combining with the energy equation, \(\frac{d\Pi}{dT}-\frac{\Pi}{T}=\mu=\frac{d\Pi}{dT}-S\), so \(\Pi=TS\), and then \(\mu=\frac{d(TS)}{dT}-S=T\frac{dS}{dT}\).

The weak point is the separation of reversible from irreversible heat: Joule heating and heat conduction always accompany the thermoelectric effects. Thomson admitted the assumption was a hypothesis. It was justified only in 1931 by Lars Onsager’s reciprocal relations for irreversible processes, which reduce to the Kelvin relations here. In a magnetic field the Onsager relations relate coefficients at \(+\mathbf B\) and \(-\mathbf B\), and \(\Pi=TS\) must be modified.

Experiment

The energy equation alone forced a new effect: if \(S\) varies with temperature, \(\mu\) cannot vanish in every metal. Thomson searched for it with many experiments in the 1850s and reported the results in his 1856 Bakerian Lecture to the Royal Society, On the Electro-dynamic Qualities of Metals. He found that in copper heat is carried with the current, and in iron against it. The Thomson coefficient is the only one of the three that can be measured on a single material, so integrating \(\mu/T\) from low temperature gives absolute Seebeck coefficients.

The Atlantic cable and telegraph theory

For the general reader. On land, a telegraph pulse arrives almost at once. Under the sea, early cables blurred pulses into slow swells, and long cables were far worse than short ones. In 1854 Thomson showed that a submarine cable behaves like a rod conducting heat: the signal diffuses rather than travels, and its delay grows with the square of the length. The result shaped the design of the Atlantic cable and set him at the centre of the greatest engineering venture of the age.

The cable equation

A submarine cable is a copper core inside gutta-percha insulation, surrounded by sea water. The core and the sea form a long capacitor. Let \(R\) and \(C\) be the resistance and capacitance per unit length, and neglect inductance and leakage, as Thomson did. With voltage \(V(x,t)\) and current \(I(x,t)\),

This is Fourier’s heat equation with diffusivity \(D=1/(RC)\). Thomson, a Fourier enthusiast since boyhood, could write down its solutions at once.

Derivation. Try \(V=V_0F(\xi)\) with the similarity variable \(\xi=\frac{x}{2}\sqrt{RC/t}\). The equation becomes \(F''+2\xi F'=0\), so \(F'\propto e^{-\xi^2}\), and the conditions \(F(0)=1\), \(F(\infty)=0\) give \(F=\operatorname{erfc}\xi\). The current follows from \(I=-\frac1R\partial_xV\). A finite cable earthed at the far end needs a Fourier series, which Thomson also gave, but the scaling is the same.

The cable in practice

The Atlantic Telegraph Company, promoted by the American financier Cyrus Field, was formed in 1856 with Thomson as a director. Its chief electrician, Wildman Whitehouse, disputed the law of squares at the British Association in 1855 and relied on high-voltage induction coils. The 1857 expedition failed when the cable broke. In 1858 the cable was completed on 5 August, and Queen Victoria’s message to President James Buchanan was sent on 16 August. Signalling was painfully slow. Thomson’s mirror galvanometer (Lesson 10) could read the faint currents; Whitehouse’s heavy voltages damaged the insulation, and the cable failed in September after about three weeks. An inquiry blamed Whitehouse, who was dismissed.

Thomson’s programme of a thick, well-insulated copper core of tested conductivity, low voltages and sensitive receivers was adopted for the next attempt. In 1865 the Great Eastern lost the cable in mid-ocean. In 1866 it landed a cable at Heart’s Content, Newfoundland, on 27 July, then recovered and completed the 1865 cable. Thomson, on board both times, was knighted that November.

After Thomson

Including inductance \(L\) and leakage conductance \(G\) per unit length gives the telegrapher’s equations of Oliver Heaviside (1876–1887). Heaviside showed that a line is distortionless when \(R/L=G/C\), and that adding inductance improves long lines. Thomson’s diffusion model is the limit in which \(R\) dominates \(\omega L\), which was the case for the slow signals of 1858–66.

The age of the Earth

For the general reader. Mines get hotter as they go deeper, so heat flows out of the Earth. If the Earth began molten and has been cooling ever since, the steepness of that gradient is a clock. Thomson read the clock in 1862 and found tens of millions of years, far less than the geologists and Charles Darwin assumed. The calculation was elegant and the conclusion wrong, for reasons that teach as much as the mathematics.

The model

Thomson treated the outer Earth as a uniform half-space \(z>0\) (depth \(z\)), initially at uniform temperature \(T_0\) and with its surface held at \(T_s\) from \(t=0\). Heat moves by conduction with diffusivity \(\kappa\): \(\partial_tT=\kappa\,\partial_z^2T\). The curvature of the Earth is negligible over the depths involved.

This is the same similarity solution as the cable of Lesson 07, read from the other side: there the potential rises from zero, here the temperature falls. The derivative of \(\operatorname{erf}u\) at \(u=0\) is \(2/\sqrt\pi\), which gives \(G\).

Thomson’s numbers

In On the Secular Cooling of the Earth, read to the Royal Society of Edinburgh in 1862, Thomson took an initial temperature of about 7,000 °F (roughly 3,900 °C), a surface gradient of about 1 °F per 50 feet, and conductivities measured on Edinburgh rocks. His central estimate was near 100 million years, and allowing for the uncertainties he gave limits of 20 and 400 million years. Over the following decades he narrowed the range. In 1897 he settled on between 20 and 40 million years, probably nearer 20.

What went wrong

• Convection. In 1895 John Perry, Thomson’s former assistant, pointed out that if the interior conducts heat better than the crust, for instance because it is partly fluid and convects, the surface gradient is maintained far longer, and the age could be billions of years. Thomson did not accept the objection. Mantle convection is now known to be the decisive flaw.
• Radioactivity. Radioactive decay, discovered in 1896, releases heat inside the Earth. In 1903 George Darwin and John Joly noted that this undermines the calculation, and in 1904 Ernest Rutherford said so in a lecture at the Royal Institution with Kelvin present.
• The Sun. Thomson’s independent limit from the Sun’s heat (Lesson 05) failed because the Sun is powered by fusion.

Radiometric dating now gives the Earth an age of about 4.5 billion years. Thomson’s method was sound physics applied with incomplete knowledge of the materials, and his insistence that geology must obey thermodynamics changed the subject.

Vortex atoms and circulation

For the general reader. In 1858 Helmholtz proved that in a perfect fluid a vortex ring can never be created or destroyed. In 1867 Thomson watched Peter Guthrie Tait’s smoke rings bounce off one another and had a bold idea: perhaps atoms are permanent knotted vortex rings in a perfect fluid filling space, with chemical elements corresponding to different knots. The theory failed, but it produced a cornerstone of fluid dynamics and started the mathematical theory of knots.

Circulation

For a velocity field \(\mathbf u\), the circulation around a closed curve \(\mathcal C\) is \(\Gamma=\oint_{\mathcal C}\mathbf u\cdot d\mathbf l\). By the Kelvin–Stokes theorem it equals the flux of vorticity \(\boldsymbol\omega=\nabla\times\mathbf u\) through any surface bounded by \(\mathcal C\).

Proof. For a material curve, \(\frac{d}{dt}\oint\mathbf u\cdot d\mathbf l=\oint\frac{D\mathbf u}{Dt}\cdot d\mathbf l+\oint\mathbf u\cdot d\mathbf u\). The last integral is \(\oint d(\tfrac12|\mathbf u|^2)=0\). In the first, \(\nabla\Phi\) integrates to zero round a closed loop, and \(\frac1\rho\nabla p=\nabla P\) with \(P(p)=\int dp/\rho\), which also integrates to zero. Hence \(d\Gamma/dt=0\).

Consequences: vortex lines move with the fluid, the strength of a vortex tube is constant along it and in time, and vorticity can neither appear nor disappear in such a fluid. These are Helmholtz’s theorems of 1858. Thomson’s paper On Vortex Motion, read in 1867 and published in 1869, gave the circulation form and much else.

The vortex atom

Thomson saw in Helmholtz’s results what an atom needs: permanence, distinct identities, and capacity for vibration, which might explain spectral lines. A vortex ring knotted in a perfect fluid can never untie itself, so knot type could label the elements. The idea, set out in On Vortex Atoms (1867), was widely discussed for two decades. It prompted Tait’s systematic tabulation of knots from the late 1870s, the first knot tables. The theory foundered on stability: Thomson could never show that the required vortex configurations were stable, and he gave it up by the end of the century. Knot theory survived and returned to physics a century later.

Kelvin–Helmholtz instability

When two fluid layers slide past each other, their interface is unstable. Helmholtz noted this in 1868 and Thomson analysed it in 1871, applying it to wind raising waves. Take a lower fluid of density \(\rho_1\) moving with speed \(U_1\) and an upper fluid of density \(\rho_2<\rho_1\) moving with \(U_2\), with gravity \(g\) and surface tension \(\sigma\).

Without surface tension, short enough waves are always unstable. With it, the right side has a minimum over \(k\) of \(2\sqrt{g\sigma(\rho_1-\rho_2)}\), so there is a threshold shear.

Instruments: galvanometer and tide predictor

For the general reader. Thomson took out about 70 patent applications and built a substantial instrument business. His devices share one idea: get the physics right, then make the measurement light, fast and readable. A galvanometer with a tiny mirror could read the faint signals from the Atlantic cable. A machine of pulleys and wire could add up the dozens of rhythms that make up the tide and print a year of tide tables in hours.

The mirror galvanometer (1858)

In a moving-magnet galvanometer, the current \(I\) in a coil of \(N\) turns produces a field \(B_c=\beta NI\) at the needle, where \(\beta\) depends on the coil’s geometry. A magnet of moment \(m\), held by a restoring field \(B_0\) (or a fibre), turns until the torques balance. Thomson made the magnet tiny, a few small magnets glued to the back of a light mirror hung by a silk fibre, so that it responds in a fraction of a second. A lamp beam reflected from the mirror onto a scale forms an optical lever with no inertia.

The mirror galvanometer was the receiver that read the 1858 cable. Its successor, the siphon recorder patented in 1867, used a fine glass siphon to write the signal in ink on a moving paper tape, giving a permanent record. Thomson and Fleeming Jenkin, his partner in cable engineering, also devised automatic senders. In 1861 Thomson proposed the British Association committee on electrical standards, which with Jenkin and Maxwell established practical absolute units including the ohm.

The tide predictor (1872–73)

From the late 1860s Thomson introduced harmonic analysis of tides. The tide at a port is written as a sum of constituents, each a cosine with a frequency fixed by astronomy and an amplitude and phase fitted to local observations:

The principal lunar semidiurnal constituent M2 has period 12.42 hours, the principal solar S2 exactly 12 hours; others describe diurnal tides, the Moon’s elliptical orbit and seasonal effects. Thomson’s machine, designed in 1872–73 with Edward Roberts and built by Alexander Légé, represents each term by a crank turning at the right rate, which moves a pulley up and down sinusoidally. A single wire passes over all the pulleys, fixed at one end; its free end moves by the sum of the pulley displacements and drives a pen tracing the predicted tide. The machine shown at the British Association in 1873 combined 8 constituents. Later machines handled 10, 20 and more, and tide-predicting machines on his principle were used until the age of electronic computers.

His brother James Thomson invented a disc-globe-cylinder integrator in 1876, and William showed how such integrators could perform the harmonic analysis and even solve linear differential equations mechanically: an early vision of the analogue computer.

For ships he also produced a compass with a light dry card and correcting magnets, adopted by the Admiralty in 1889, and a sounding machine that used piano wire in place of hemp rope, allowing quick deep soundings from a moving ship.

Sir William, 1866–1899

The cable made Thomson famous and rich. He was knighted on 10 November 1866, and his cable patents and consulting fees, including work with Jenkin as engineers to further cables, gave him a large income. In 1867 he and Peter Guthrie Tait published the first volume of the Treatise on Natural Philosophy, known as “T and T′”, which presented mechanics through energy and variational principles and became a standard text. Its planned later volumes were never written.

In 1870, the year his first wife died, he bought the 126-ton schooner Lalla Rookh, which became his summer home and floating laboratory. Sailing to Madeira for cable work in 1873 he met Frances Anna Blandy, and they married on 24 June 1874. He built a house, Netherhall, on the coast at Largs. His instrument work with the Glasgow maker James White, begun in the 1850s, grew into a large factory, which became Kelvin and James White Ltd.

He took a leading place in British science. He was president of the British Association in 1871, three times president of the Royal Society of Edinburgh, and president of the Royal Society from 1890 to 1895. He received the Royal Medal (1856) and the Copley Medal (1883). In 1884 he gave a famous course at Johns Hopkins University in Baltimore on molecular dynamics and the wave theory of light, trying to build mechanical models of the ether. He admired Maxwell and worked with him on electrical units, but he never fully accepted Maxwell’s electromagnetic theory of light, wanting a mechanism he could picture.

In politics he was a Liberal who broke with William Gladstone over Irish Home Rule in 1886 and became a Liberal Unionist. In 1892 he was created Baron Kelvin of Largs, the first British scientist raised to the peerage for science. The title comes from the River Kelvin, which flows past the University of Glasgow. In June 1896 the university celebrated the jubilee of his professorship with delegates from across the world. In his reply he said that one word summed up his fifty-five years of effort to understand the nature of matter, and the word was failure. He retired from the chair in 1899, after 53 years, and characteristically enrolled as a research student to keep his laboratory access.

Clouds, death and legacy, 1899–1907

On 27 April 1900 Kelvin lectured at the Royal Institution on two clouds over the dynamical theory of heat and light. The first was the ether’s apparent motionlessness relative to the Earth, shown by the Michelson–Morley experiment. The second was the failure of the equipartition theorem of Maxwell and Ludwig Boltzmann to predict the specific heats of gases. Within a few years the first cloud gave way to relativity and the second to quantum theory. A remark that physics had nothing new left to discover is often attributed to him, but no source for it has been found.

In 1902 he received the Order of Merit and became a Privy Councillor. In 1904 he became chancellor of the University of Glasgow. That year Ernest Rutherford, lecturing at the Royal Institution on radioactivity, tactfully noted that Kelvin had limited the age of the Earth provided no new source of heat was found, and that radium was such a source; Rutherford later recalled the old man beaming at him. Kelvin never fully conceded. He died at Netherhall on 17 December 1907, after a severe chill, aged 83. He was buried in Westminster Abbey on 23 December, near Isaac Newton.

Legacy

• Thermodynamics: absolute temperature, one of the two classical statements of the second law, the dissipation of energy, available work, and the Joule–Thomson effect, the basis of gas liquefaction.
• Electricity: electrical images, the heat–electricity analogy that Maxwell built on, the theory of cable transmission, the Thomson effect and the Kelvin relations, and absolute electrical units.
• Fluids and geophysics: the circulation theorem, Kelvin–Helmholtz instability, harmonic analysis of tides, and the use of physics to set time scales in geology and astronomy.
• Engineering: the Atlantic cable, the mirror galvanometer and siphon recorder, the tide predictor, the compass and the sounding machine.
• Name: the SI unit of thermodynamic temperature, renamed from “degree Kelvin” to the kelvin (K) in 1967–68.

He published more than 650 scientific papers. He is often remembered for his errors: the age of the Earth, the ether, scepticism about radioactivity. Those errors were made by applying firm physical principles to questions where the materials or mechanisms were unknown. The principles have lasted.

Connections

People linked to William Thomson, Lord Kelvin across this collection. A name without a link has no page here yet. See William Thomson, Lord Kelvin in the network of all 337 lives →

Teachers and advisors

• William Hopkins 1841-1845

Students

• James Alfred Ewing
• John Perry

Influenced by

• Georg Simon Ohm
• George Green
• Joseph Fourier
• Louis Pasteur
• Michael Faraday
• Sadi Carnot
• Henri Victor Regnault 1845

Influenced

• Aleksandr Lyapunov
• C. T. R. Wilson
• Heike Kamerlingh Onnes
• J. J. Thomson
• James Clerk Maxwell
• Oliver Heaviside
• Svante Arrhenius
• William Ramsay 1866-1869

Colleagues and collaborators

• George Boole
• Hermann von Helmholtz
• James Clerk Maxwell
• James Prescott Joule 1847-1862
• John William Strutt, Lord Rayleigh
• Joseph Henry
• Joseph Liouville
• Michael Faraday 1845
• Oliver Heaviside
• Peter Guthrie Tait 1861-1901
• Pierre Curie
• Rudolf Clausius
• Fleeming Jenkin 1859-1885
• William John Macquorn Rankine

Rivals

• Ernest Rutherford
• John Tyndall
• Julius Robert Mayer 1862
• Rudolf Clausius 1850-1856
• Charles Darwin

Friends

• George Gabriel Stokes 1846-1903
• Hermann von Helmholtz

Family

• James Thomson

Also mentioned in this life

• Ludwig Boltzmann
• Leonhard Euler
• Albert A. Michelson
• Isaac Newton
• Johannes Diderik van der Waals

Fields

• thermodynamics 12 lives
• fluid dynamics 6 lives

On CoursesHub

• Thermodynamics
• Fluid Mechanics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, William Thomson (Lord Kelvin), MacTutor History of Mathematics.
2. C. Smith, Thomson, William, Baron Kelvin, Oxford Dictionary of National Biography (reproduced at MacTutor).
3. William Thomson, 1st Baron Kelvin, Wikipedia.
4. University of Glasgow, Lord Kelvin 200.
5. IET Archives, Lord Kelvin 1824–1907.
6. S. P. Thompson, The Life of William Thomson, Baron Kelvin of Largs, 2 vols, Macmillan, 1910.
7. C. Smith and M. N. Wise, Energy and Empire: A Biographical Study of Lord Kelvin, Cambridge University Press, 1989.

Physics

1. W. Thomson, Mathematical and Physical Papers, 6 vols, Cambridge University Press, 1882–1911.
2. W. Thomson, On an absolute thermometric scale founded on Carnot’s theory of the motive power of heat, Proc. Cambridge Phil. Soc. (1848); Phil. Mag. 33 (1848).
3. W. Thomson, On the dynamical theory of heat, Trans. Roy. Soc. Edinburgh 20 (1851).
4. W. Thomson, On a universal tendency in nature to the dissipation of mechanical energy, Phil. Mag. 4 (1852).
5. W. Thomson, On the electro-dynamic qualities of metals (Bakerian Lecture), Phil. Trans. R. Soc. 146 (1856).
6. W. Thomson, On the theory of the electric telegraph, Proc. R. Soc. 7 (1855).
7. W. Thomson, On the secular cooling of the earth, Trans. Roy. Soc. Edinburgh 23 (1864; read 1862).
8. W. Thomson, On vortex atoms, Proc. Roy. Soc. Edinburgh 6 (1867); On vortex motion, Trans. Roy. Soc. Edinburgh 25 (1869).
9. W. Thomson and P. G. Tait, Treatise on Natural Philosophy, Oxford, 1867.
10. J. D. Burchfield, Lord Kelvin and the Age of the Earth, Science History Publications, 1975.
11. P. England, P. Molnar and F. Richter, John Perry’s neglected critique of Kelvin’s age for the Earth, GSA Today 17 (2007).
12. Transatlantic telegraph cable, Tide-predicting machine, Thermoelectric effect, Age of Earth, and Kelvin, Wikipedia.