Count Rumford

How to use this course

Benjamin Thompson, Count Rumford, is remembered by physicists for one experiment. While boring cannon in the Munich arsenal he boiled water by friction alone and argued that heat could not be a material fluid. That experiment is a milestone on the road to the first law of thermodynamics. Yet Rumford was also a soldier, a spy, a social reformer, a designer of stoves and fireplaces, a pioneer of photometry and the founder of the Royal Institution in London. His physics was always practical, and his practical work was always physics.

Each technical lesson opens with a paragraph for the general reader, then states the physics precisely, works through Rumford’s data where we have it, and ends with exercises whose solutions are folded. Throughout, we separate what Rumford measured and claimed from the modern understanding that later physicists built on it. He was right about the nature of heat, wrong about fluids being non-conductors, and shrewd about almost everything that could be tested in a kitchen.

Timeline

Woburn and Concord, 1753–1775

Benjamin Thompson was born on 26 March 1753 in Woburn, a farming town north of Boston in the Province of Massachusetts Bay. His parents, Benjamin Thompson and Ruth Simonds, worked a small farm. The house where he was born still stands and is kept as a museum. He had little formal schooling beyond the village school, and he educated himself with help from friends and local clergymen.

At about 13 he was apprenticed to John Appleton, a merchant in Salem. Shop work bored him; he spent his time on mechanical gadgets, fireworks and reading. With his friend Loammi Baldwin, later an engineer, he sometimes walked the roughly ten miles from Woburn to Cambridge to hear John Winthrop lecture on natural philosophy at Harvard College. Winthrop was the leading American astronomer and physicist of his generation, and these lectures were the closest Thompson came to a university education. In 1769, recovering at home from an injury, he made his first recorded experiments on heat.

A fortunate marriage

He took up school-teaching, and a teaching post brought him to Concord, New Hampshire, a town whose older name was Rumford. There in 1772 he married Sarah Rolfe, a wealthy widow some fourteen years older than he was, the daughter of a minister. The marriage gave him land, money and access to the royal governor of New Hampshire, John Wentworth, who made the nineteen-year-old a major in the provincial militia. A daughter, Sarah, was born in 1774.

The rapid promotion of a newcomer over older officers made him enemies. As the conflict with Britain sharpened, he was accused of sympathy for the Crown, and he was in fact reporting to the British command in Boston. In 1775 a crowd gathered at his house, and he fled. He left his wife and daughter behind and never saw his wife again; she died in 1792. Thompson later took the name of her town for his title.

Loyalist in London, 1776–1784

After the British evacuated Boston in March 1776, Thompson sailed for England. He brought information about the rebel army and quickly gained the confidence of Lord George Germain, the Secretary of State responsible for the American war. Within four years the farm boy from Woburn was Under-Secretary of State in Germain’s department (1780–81).

Science went alongside politics. With Germain’s backing he carried out a long series of experiments on gunpowder and the velocity of musket balls, which he published in the Philosophical Transactions in 1781 (Lesson 04). The work earned him election as a Fellow of the Royal Society in 1779, before the paper had appeared in print. He noticed in these trials that gun barrels grew hot, and the question of where that heat came from stayed with him.

Soldier

In 1781 he left the ministry abruptly and raised a Loyalist cavalry regiment, the King’s American Dragoons, as its lieutenant colonel. After brief service in South Carolina he was stationed on Long Island in 1782–83. At Huntington his men demolished a church and dug up a burial ground to build a fort, an episode still remembered locally. When the war ended he returned to England as a colonel on half pay. Thomas Gainsborough painted his portrait in 1783, and on 23 February 1784 George III knighted him.

Munich: soldiers, beggars and gardens, 1784–1798

On a journey through Europe in late 1783, Sir Benjamin met members of the circle of Karl Theodor, Elector Palatine and of Bavaria, in Strasbourg. In 1784 he entered the Elector’s service in Munich as a colonel and aide-de-camp. Promotions followed fast: chamberlain in 1785, privy councillor in 1787, and in 1788 major general and head of the war department. For more than a decade he was, in practice, one of the most powerful men in Bavaria.

The army and the poor

He reformed the Bavarian army along practical lines: better pay, better food, schools for soldiers’ children, and military gardens where troops grew vegetables. On 1 January 1790 he had the beggars of Munich rounded up in a single day and put to work in a military workhouse that made uniforms for the army. The workhouse was a laboratory as well as a factory. To feed hundreds of people cheaply he studied cooking scientifically, designed closed ranges that used far less wood, and developed a nourishing soup of barley, peas and potatoes, still known as Rumford soup. He promoted the potato, then distrusted, as a staple food.

The English Garden

In 1789 he began turning a hunting ground beside the Isar into a public park, the Englischer Garten, opened to the public in 1792. It remains one of the largest urban parks in the world. In 1792, during the interregnum in which Karl Theodor acted as imperial vicar, Thompson was made a count of the Holy Roman Empire and a lieutenant general. He chose the title Rumford, after the old name of Concord.

Rumford travelled to Italy in 1793–94 and was seriously ill in Naples. He returned to London in 1795, where he published the first volume of his Essays, Political, Economical and Philosophical (1796) and endowed his two prizes for research on heat and light (Lesson 12). In the autumn of 1796 he was back in Munich as French and Austrian armies approached; he commanded the city’s defence and kept it out of the fighting. In the winter of 1797–98, as superintendent of the arsenal, he made the cannon-boring experiments of Lesson 05.

Gunpowder and the ballistic pendulum

For the general reader. How fast does a musket ball fly? In the eighteenth century no clock could time it. The answer was to fire the ball into a heavy wooden block hung as a pendulum and measure how far the block swung. Thompson used this device, invented by Benjamin Robins in 1742, to compare powders and charges for the British army. His 1781 paper made his scientific name.

The method

A ball of mass \(m\) and speed \(v\) embeds itself in a block of mass \(M\) hanging at rest. The collision is short compared with the pendulum’s period, so the block barely moves during it, the string stays vertical, and there is no horizontal external impulse. Afterwards the block and ball swing up together until they come momentarily to rest at height \(h\).

Derivation

During the impact, horizontal momentum is conserved: \(mv=(m+M)V\). During the swing, mechanical energy is conserved: \(\tfrac12(m+M)V^2=(m+M)gh\), so \(V=\sqrt{2gh}\). Combining the two gives the formula. Kinetic energy is not conserved in the impact. The fraction that survives is

so for a heavy block almost all of the ball’s kinetic energy is lost to deformation of wood and lead, and ultimately to heat. Rumford did not phrase it this way, because the concept of energy did not yet exist. But the observation that violent mechanical processes, from firing to impact, produce heat ran through his work on gunpowder and led directly to the arsenal in Munich.

Rumford’s questions

Thompson used the pendulum to study how muzzle velocity depends on the quantity of powder, the windage (gap between ball and bore) and the position of the vent. He also made the gun barrel itself into a pendulum to measure its recoil. Later, in 1797, he published experiments on the force of fired gunpowder, and a device for proving powder that was adopted by the British and Bavarian armies.

Boring cannon: heat as motion

For the general reader. Around 1800 most chemists thought heat was a weightless fluid, caloric, that flowed from hot bodies to cold ones. Rumford noticed that boring a cannon with a blunt drill produced heat apparently without limit. A fluid stored in the metal should run out; motion can be supplied for ever. He concluded that heat is a kind of motion. Half a century later James Prescott Joule used Rumford’s numbers to estimate how much work makes how much heat.

The caloric theory

In Antoine Lavoisier’s chemistry, caloric was an element. Joseph Black’s work on latent and specific heat fitted the picture well: a body’s capacity for caloric could change, so caloric could be released without a change in temperature, or absorbed in melting. Friction was explained by supposing that abrading a metal reduced its heat capacity, squeezing out caloric, or that the abraded powder held less caloric than the solid.

The experiment

Cannon were cast with an extra cylinder of metal beyond the muzzle, which was cut off and discarded. Rumford used this piece. He had a deliberately blunt steel borer pressed against the bottom of a bore in the cylinder, which was turned by horses. In his most famous trial he enclosed the cylinder in a watertight wooden box filled with cold water. After about two and a half hours the water boiled. He recorded the astonishment of the bystanders at seeing a large quantity of cold water boil without any fire.

His arguments were two. First, he measured the specific heat of the metal chips and found it the same as that of the solid metal, so no caloric could have been released by a change of capacity. Second, the heat seemed inexhaustible: as long as the horses turned the cylinder, heat kept coming. Something that a body can supply without limit cannot be a material substance. The only thing communicated to the metal was motion.

Rumford did not measure the equivalence. Many of his contemporaries, including William Henry and Thomas Thomson, held that caloric theory could absorb his results, and the inexhaustibility claim was an extrapolation. The decisive quantitative experiments came in the 1840s from Julius Robert Mayer and Joule.

Joule’s reanalysis (1850)

In his 1850 paper on the mechanical equivalent of heat, Joule took Rumford’s own estimate: the heat produced in two and a half hours would have raised 26.58 lb of ice-cold water by 180 °F, to boiling. Rumford had remarked that one horse could have turned the machinery. Using James Watt’s horsepower of 33 000 ft·lbf per minute,

Joule’s own best value was 772 ft·lbf. He judged Rumford’s figure not very different and attributed the excess to heat lost to the apparatus and surroundings, which Rumford acknowledged he had not measured.

Does heat weigh anything?

For the general reader. If heat were a substance, a hot body might weigh more than a cold one. Rumford sealed water, alcohol and mercury in flasks, balanced them, and froze the water. Freezing removes a great deal of heat, yet the balance did not move. He concluded that heat has no measurable weight. Relativity says it does have weight, but far too little for any balance.

The experiment (read 2 May 1799)

Rumford sealed about 4214 grains (273 g) each of water, spirit of wine and mercury in three similar flasks and balanced them. He chose alcohol and mercury as controls because they do not freeze at the temperatures he used, so any effect of freezing would show up as a difference between the water and the others. He left the flasks at about 30 °F for 48 hours. The water froze; nothing in the balance changed, and nothing changed on thawing. He estimated that his balance would have detected a change of one part in a million. An earlier trial had shown an apparent gain on freezing, which he traced to air currents and moisture, and which disappeared when he improved his method.

The water lost its latent heat of fusion, about 334 J/g, so \(E\approx273\times334\approx9.1\times10^{4}\) J and

That is six orders of magnitude below Rumford’s sensitivity. His null result was correct, and his inference that heat is not a ponderable fluid was sound. The calculation is also a lesson in how to report a null experiment: the right statement is an upper bound, not a claim of exactly zero.

Convection, conduction and insulation

For the general reader. Why are fur, wool and down so warm? Rumford showed that they work by trapping air and stopping it from moving. Moving fluid carries heat far faster than still fluid conducts it. He then went too far and claimed that still fluids conduct no heat at all. Both the insight and the error are instructive.

Rumford’s observations

In Munich Rumford tested the insulating power of fur, eiderdown, wool, cotton and silk by surrounding a thermometer with them and timing its cooling. He found that the best insulators were those that held the most air in the finest spaces. In his essay on the propagation of heat in fluids (1797) he described convection currents made visible by suspended particles in heated liquids, and he showed that thick or viscous liquids, in which currents are hindered, cool much more slowly. From this he concluded, wrongly, that air and liquids are perfect non-conductors and transfer heat only by carrying it. John Dalton and John Leslie objected. Rumford also emphasised that water has its maximum density near 4 °C, so that lakes freeze from the top while their depths stay above freezing.

The \(L^3\) dependence explains Rumford’s insulators. Divide a thick air layer into many fine cells and \(\mathrm{Ra}\) in each cell drops by the cube of the subdivision, far below \(\mathrm{Ra}_c\). Convection stops, and heat crosses only by conduction through air (\(k\approx0.026\) W/(m·K)) and by radiation, both slow. Fibres also block radiation. Rumford’s mistake was the opposite extreme: still water does conduct, with \(k\approx0.6\) W/(m·K), more than twenty times air. Conduction in liquids is small compared with convection, which is why his experiments seemed to show none.

Thermal resistance

For steady conduction through a slab of thickness \(d\) and area \(A\), the heat flow is \(P=kA\Delta T/d\). Layers in series add their resistances \(R_i=d_i/(k_iA)\), like electrical resistors.

Radiant heat and “frigorific rays”

For the general reader. In 1790 the Genevan physicist Marc-Auguste Pictet put a lump of ice at the focus of one concave mirror and a thermometer at the focus of another, facing it across a room. The thermometer cooled. Was cold a thing that could be radiated? Rumford thought so for a time. The modern answer, first given by Pierre Prévost in 1791, is that every body radiates, and a thermometer facing ice simply receives less than it sends out.

Rumford on radiation

In a long paper of 1804 on the nature of heat and its communication, Rumford reported experiments with paired metal vessels whose surfaces were polished, blackened or covered with linen or varnish. Blackened or covered surfaces gave off heat faster than bright metal. John Leslie found the same with his famous cube in the same year. Rumford interpreted Pictet’s experiment in terms of “calorific” and “frigorific” rays: vibrations from a hot body warm, those from a cold body cool. Because he held a wave theory of heat, he could treat cold as an emitted influence in its own right. Prévost’s exchange theory turned out to be simpler and correct.

Prévost’s insight is the minus sign: the body always emits, and the surroundings always send radiation back. In Pictet’s experiment the mirrors make the ice fill much of the thermometer’s field of view, lowering the effective \(T_s\). The thermometer’s emission is unchanged, its absorption drops, and it cools. No frigorific rays are needed.

For small temperature differences, \(T^4-T_s^4\approx4T^3(T-T_s)\), so radiation behaves like Newtonian cooling with a coefficient \(h_r=4\varepsilon\sigma T^3\), about 6 W/(m²·K) for a black surface near room temperature.

Photometry and the standard candle

For the general reader. To light a workhouse cheaply, Rumford needed to know which lamps gave the most light per unit of fuel. The eye cannot judge brightness on an absolute scale, but it can tell very well when two patches look equally bright. Rumford built an instrument around that fact and proposed a candle as a standard of light, an ancestor of today’s SI unit, the candela.

The shadow photometer (1794)

A vertical rod stands in front of a white screen. Two lamps light the screen from slightly different directions, so the rod casts two shadows side by side. Each shadow is lit only by the other lamp. The observer moves one lamp until the two shadows look equally dark, which means the screen receives equal illuminance from each lamp. Rumford used the instrument to compare wax and tallow candles, oil lamps and the new Argand lamp, and to measure how much light glass and other materials absorb. He also observed the vivid complementary colours of shadows cast by daylight and candlelight together, a phenomenon later explained by Michel-Eugène Chevreul’s law of simultaneous contrast (1839).

The law follows from conservation of light: the flux \(I\,d\Omega\) into a small cone spreads over an area \(r^2 d\Omega/\cos\theta\). Johann Heinrich Lambert had stated it, with the cosine factor, in his Photometria of 1760. Rumford’s contribution was a practical instrument and a programme of measurement aimed at efficiency.

From candles to the candela

Rumford proposed a standard candle as a reference source. A legal British standard followed in 1860: a spermaceti candle burning 120 grains per hour. Candle standards were replaced by flame lamps and then by a platinum blackbody at its freezing point (the “new candle”, adopted internationally in 1948 as the candela). Since 1979 the candela is defined through radiation of frequency \(540\times10^{12}\) Hz with radiant intensity \(1/683\) W per steradian. An ordinary candle still gives roughly one candela.

Fireplaces, chimneys and draught

For the general reader. Eighteenth-century London fireplaces were deep, square boxes that sent most of their heat up the chimney and much of their smoke into the room. Rumford redesigned them with a shallow hearth, angled sides and a narrow throat. The fire threw more heat into the room and the smoke went up. His design, still built today as the Rumford fireplace, is applied physics of radiation and buoyancy.

Rumford’s rules (1796)

In his essay Of Chimney Fire-places Rumford gave proportions for the most perfect form: the back as wide as the fireplace is deep; the opening three times the width of the back; the sides (covings) set at 135° to the back, which he judged the best position for throwing heat into the room; and a throat about four inches wide. He also advised lowering the opening whenever its width is reduced. Builders added the smoke shelf behind the throat, which turns back down-drafts.

The draught is a pressure difference, so the flow it can sustain is limited. A wide, open throat lets cold room air rush in to fill the flue, which cools the column, lowers \(\Delta p\) and lets eddies carry smoke back into the room. A narrow throat keeps the gas hot and the upward velocity high, so smoke cannot fall back. The rest of the fireplace can then be made shallow and wide to radiate into the room.

Geometry of the covings

With back width \(b\), depth \(b\) and opening \(3b\), each coving runs from a back corner to a front corner offset by \(b\) sideways and \(b\) forward: it makes 45° with the line of the back, so the angle inside the fireplace between back and coving is 135°. The hero figure above shows rays from the fire reflected by the covings into the room.

The Royal Institution and Paris, 1798–1814

In August 1798 the Elector named Rumford Bavarian envoy to Great Britain, but the British government refused to receive a British subject as a foreign minister. He stayed in London anyway. Karl Theodor died in February 1799, and with him Rumford’s secure position in Munich.

Founding the Royal Institution

In March 1799, at the house of Sir Joseph Banks, President of the Royal Society, Rumford and a group of wealthy subscribers founded the Royal Institution of Great Britain. Its purpose, in Rumford’s plan, was to spread knowledge of useful mechanical inventions and to teach the application of science to everyday life through lectures and experiments. It received a royal charter in 1800 and took a house in Albemarle Street, where it still is. Rumford chose the staff and supervised everything, including the kitchens, which displayed his stoves.

In 1801 the Institution engaged a young chemist from Bristol, Humphry Davy, as assistant lecturer, and Thomas Young as professor of natural philosophy. Davy’s lectures made the Institution fashionable, and Davy later brought Michael Faraday there. Rumford’s autocratic manner caused friction with the managers, and he left London in 1802. The Institution he founded became, through Davy and Faraday, one of the great laboratories of nineteenth-century physics and chemistry.

Paris

Rumford settled in Paris in 1803 on a Bavarian pension. He was elected to the Institut National, where he presented papers on radiation, the conduction of heat and the heat of combustion. In 1805 he married Marie-Anne Paulze Lavoisier, the widow of Antoine Lavoisier, executed in 1794, and herself a skilled collaborator in her husband’s chemistry. The marriage was unhappy; she kept the name Lavoisier, they separated, and it was formally dissolved on 30 June 1809. Rumford retired to a villa in Auteuil, then a village west of Paris, where he continued experimenting on lamps, coffee-making and the heat of combustion.

Death and legacy

Rumford died of a fever at Auteuil on 21 August 1814, aged 61, and was buried in the cemetery there. The Académie des sciences placed a monument on his grave. His daughter Sarah, who had joined him in Europe, inherited his title as Countess Rumford.

Prizes and professorships

• Rumford Medal. In 1796 he gave the Royal Society £1000 in stock, the interest to reward discoveries on heat and light. The medal was first awarded in 1800, to Rumford himself; early recipients include John Leslie, Étienne-Louis Malus, Davy, David Brewster, Augustin Fresnel and Faraday.
• Rumford Prize. In the same year he gave the American Academy of Arts and Sciences 5000 dollars for the same purpose. The first award was made only in 1839, to Robert Hare for the oxy-hydrogen blowpipe.
• Harvard. He left most of his estate to Harvard to found a professorship on the application of science to the useful arts; the Rumford chair still exists.

Scientific legacy

• The nature of heat: the cannon-boring paper became the standard historical argument against caloric. Davy took up the motion theory; Joule cited Rumford’s data in 1850; Hermann von Helmholtz and Rudolf Clausius placed it in the prehistory of energy conservation.
• Heat transfer: his demonstration that insulation works by suppressing convection is the principle of every modern insulating fabric and wall cavity.
• Photometry: the shadow photometer and the idea of a standard candle.
• Engineering: the Rumford fireplace, the closed kitchen range, the double boiler, the drip coffee pot, improved lime kilns; the Royal Institution itself.
• Memorials: the English Garden in Munich, with a monument to him; a statue on the Maximilianstraße; a lunar crater; and the name of Rumford baking powder, invented by a later holder of his Harvard chair, Eben Norton Horsford.

Contemporaries found Rumford brilliant, vain and cold. He abandoned one family, tried to bend every institution he joined to his will, and served whichever state would advance him. He also fed the poor of Munich, gave his inventions away without patents, and endowed two of the oldest prizes in science. His physics was of a piece with his social engineering: measure, improve, and make it work.

Connections

People linked to Count Rumford across this collection. A name without a link has no page here yet. See Count Rumford in the network of all 337 lives →

Influenced by

• Joseph Black
• John Winthrop

Influenced

• James Prescott Joule
• Julius Robert Mayer
• Michael Faraday

Colleagues and collaborators

• Humphry Davy 1801-1802
• Thomas Young 1801-1802
• Joseph Banks 1799
• Marc-Auguste Pictet

Rivals

• Antoine Lavoisier
• John Dalton
• John Leslie

Family

• Marie-Anne Paulze Lavoisier 1805-1809

Also mentioned in this life

• Ludwig Boltzmann
• David Brewster
• Rudolf Clausius
• Albert Einstein
• Joseph Fourier
• Augustin-Jean Fresnel
• Hermann von Helmholtz
• Gustav Kirchhoff
• Johann Heinrich Lambert
• Étienne-Louis Malus
• Lord Rayleigh
• James Watt

Sources and further reading

Biography

1. Benjamin Thompson, Wikipedia (with references).
2. Rumford, Benjamin Thompson Graf von, Neue Deutsche Biographie and Allgemeine Deutsche Biographie.
3. Thompson, Benjamin (Count Rumford), Complete Dictionary of Scientific Biography, via Encyclopedia.com.
4. S. C. Brown, Benjamin Thompson, Count Rumford, MIT Press, 1979.
5. G. I. Brown, Count Rumford: The Extraordinary Life of a Scientific Genius, Sutton, 1999.
6. Rumford Medal and Rumford Prize, Wikipedia.

Physics

1. B. Thompson, New experiments upon gun-powder, Phil. Trans. R. Soc. 71 (1781).
2. B. Count of Rumford, An inquiry concerning the source of the heat which is excited by friction, Phil. Trans. R. Soc. 88 (1798). Overview.
3. B. Count of Rumford, An inquiry concerning the weight ascribed to heat, Phil. Trans. R. Soc. 89 (1799).
4. B. Count of Rumford, Essays, Political, Economical and Philosophical, London, 1796–1802; includes Of Chimney Fire-places.
5. S. C. Brown (ed.), Collected Works of Count Rumford, 5 vols., Harvard University Press, 1968–70; Complete Works (1870–75 edition, vol. 3) at the Internet Archive.
6. J. P. Joule, On the mechanical equivalent of heat, Phil. Trans. R. Soc. 140 (1850).
7. Mechanical equivalent of heat, Wikipedia.
8. About the evolution of the concept of heat and thermal energy, arXiv:2201.13206.