Henry Cavendish

How to use this course

Henry Cavendish published fewer than twenty research papers in fifty years. Each was a model of careful measurement, and several changed their subjects: the first precise study of a new gas, the composition of water, the density of the Earth. His unpublished notes held even more, including a sharp test of the inverse-square law of electricity and measurements of capacitance and resistance decades ahead of their time. James Clerk Maxwell spent his last years editing them.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements in modern notation, derivations and exercises with folded solutions. Cavendish worked within the phlogiston theory of chemistry and a one-fluid theory of electricity. The lessons translate his results into modern terms and say where his interpretation differs from ours.

Timeline

A Cavendish born in Nice, 1731–1742

Henry Cavendish belonged to one of the richest and most powerful families in Britain. His father, Lord Charles Cavendish, was the third son of the second Duke of Devonshire. His mother, Lady Anne de Grey, was a daughter of the Duke of Kent. The couple travelled to the Continent for Lady Anne’s health, and Henry was born in Nice, then part of the Kingdom of Sardinia, on 10 October 1731. (One modern chronology gives 31 October; most sources give the 10th.) A brother, Frederick, followed in 1733. Lady Anne died in September 1733, when Henry was not yet two.

Lord Charles turned increasingly to science and administration. In 1738 he moved to a house in Great Marlborough Street, London, which would be Henry’s home for decades. The father was an able experimenter, active in the Royal Society, and interested in thermometers, electricity and meteorology. Henry grew up in a household where instruments were normal furniture and where natural philosophy was a respectable occupation for a gentleman.

Hackney and Cambridge, 1742–1753

At eleven Cavendish entered the Hackney Academy, a private school near London run by Peter Newcome, where many sons of the Whig aristocracy were taught. Little is known of his years there.

On 24 November 1749 he entered St Peter’s College, Cambridge (Peterhouse), as a fellow commoner, a status reserved for wealthy students who dined with the fellows. Cambridge mathematics then centred on Newton’s Principia and Opticks, and the Newtonian programme of explaining nature by forces acting between particles shaped all his later work. He left in February 1753 without taking a degree. This was common for young men of his rank.

He settled in his father’s house in Great Marlborough Street. There he would live and work for the next thirty years.

Apprenticed to his father, 1753–1766

Lord Charles was a careful experimenter. His work on self-registering thermometers earned the Royal Society’s Copley Medal in 1757. Henry assisted him, and the two shared a laboratory and workshop in Great Marlborough Street. Henry’s earliest notes, from the 1750s and early 1760s, deal with heat, arsenic and the solution of metals in acids.

His father brought him into the scientific society of London. In 1760 Henry joined the Royal Society Club, which dined before meetings, and on 1 May 1760 he was elected a Fellow of the Royal Society. From 1765 he sat often on its Council. He attended meetings almost without fail for half a century, and his opinion on papers and instruments carried great weight.

He was painfully shy. He spoke little, disliked being looked at, avoided women, and fled from strangers. He dressed in clothes decades out of fashion. Yet in the company of men of science, on scientific subjects, he could be drawn into conversation, and they respected his judgement deeply. In 1766, aged 34, he published his first paper under his own name. It won him the Copley Medal.

Factitious airs

For the general reader. In the 1760s chemists were learning that “air” is not one substance. Cavendish dissolved metals in acids and collected the gas that came off, a gas lighter than any known, which burned with a pop. He weighed it, measured how much each metal produced, and studied its properties with a precision no one had applied to gases. The gas was hydrogen. The paper also measured the density and solubility of “fixed air”, our carbon dioxide.

The 1766 paper

A “factitious air” was any air contained in bodies in a fixed state and released by art. Cavendish collected gases over water, or over mercury for soluble gases, in vessels he had calibrated. He measured density in two ways: by filling a bladder of known volume and weighing it, and by weighing a flask before and after the gas escaped during a reaction. He found that inflammable air was about one eleventh as dense as common air. He also found that a given weight of zinc, iron or tin always gave the same volume of inflammable air whichever acid he used, dilute sulfuric or hydrochloric. He concluded that the gas came from the metal. Within phlogiston theory, the principle of combustibility that metals were thought to lose on dissolving, he suggested that inflammable air might be phlogiston itself.

His value of 1/11 was too heavy because his hydrogen was wet: it carried water vapour from the reaction. He knew this and tried to correct for it by drying the gas through potash. For fixed air he found a density about 1.57 times that of common air, close to the modern 1.52, and measured its solubility in water.

An elastic electric fluid

For the general reader. In 1771 Cavendish published a mathematical theory of electricity modelled on Newton’s account of an elastic gas. Electricity was a fluid whose particles repel each other and are attracted by ordinary matter. From this he drew a distinction that later became fundamental: the quantity of electricity in a body differs from its degree of electrification. In modern terms, he separated charge from potential.

The model

Cavendish adopted Benjamin Franklin’s single fluid. Particles of the electric fluid repel one another; particles of matter attract the fluid; and, to make an uncharged body exert no force, particles of matter must also repel one another. A body with more fluid than its natural share is positively charged, and one with less is negative. He left the force law general, an inverse power \(r^{-n}\) of the distance with \(n\) less than 3, and showed that an inverse first power could not account for the facts. He judged \(n=2\) the likely case, and the hollow-globe experiment of Lesson 06 settled it. Later physicists showed the one-fluid and two-fluid descriptions to be mathematically equivalent.

Degree and quantity

When two conductors are joined by a long thin wire, fluid flows until no more is pushed along the wire. Cavendish called the common state that the bodies then share their degree of electrification. The fluid in each body is then proportional to a property of its size and shape, its capacity. This is the modern picture.

Cavendish measured capacities by sharing charge. He charged a body, connected it to a standard globe, and judged by an electrometer which of two bodies took the same degree of electrification. Comparing many shapes, he found that capacity grows with linear size, not area, as the inverse-square law predicts.

The hollow globe: testing the inverse square

For the general reader. If electric force falls exactly as the square of distance, a charged hollow metal shell exerts no force inside, so no charge can be drawn onto an object inside it. Cavendish turned this into an experiment of great sensitivity. He enclosed a globe inside two hemispheres, connected them, charged the outside and then looked for charge on the inner globe. He found none, and concluded that the exponent in the force law differs from 2 by less than one part in fifty. He never published the result.

The experiment (c. 1773)

A globe about a foot in diameter was mounted on an insulating stick of glass inside two hollow hemispheres a little larger, which could close around it. A wire connected the inner globe to the hemispheres. Cavendish charged the hemispheres with a Leyden jar, withdrew the connecting wire by a silk string, opened the hemispheres, and tested the inner globe with a pith-ball electrometer. The pith balls did not separate. He then calibrated how small a charge the electrometer could reveal by giving the globe a known fraction of the hemispheres’ charge.

The potential inside a shell

Let the force law be \(F\propto r^{-(2+q)}\), with point potential \(\varphi(s)=s^{-(1+q)}/(1+q)\) (up to a constant factor). A shell of radius \(a\) with charge \(Q\) spread uniformly, seen from a point at distance \(r\lt a\) from the centre, contains a ring of charge \(Q\,\frac{s\,ds}{2ar}\) at distance between \(s\) and \(s+ds\), for \(a-r\le s\le a+r\). So

For \(q=0\) this gives \(V=Q/a\) for every \(r\): the shell theorem. For \(q\neq0\), compare the centre and the shell:

So the interior is not an equipotential. When the inner globe is joined to the shell, charge flows onto it in proportion to \(q\). After the shell is discharged, the globe keeps a charge of order \(q\) times the shell’s charge, with a coefficient set by the geometry.

A modern reading: a nonzero photon mass would give the potential a Yukawa form \(e^{-\mu r}/r\), and the same kind of null experiment bounds \(\mu\). The idea is Cavendish’s.

Capacity, resistance and the torpedo

For the general reader. The torpedo is a fish that stuns its prey with an electric shock, yet produces no spark and cannot be detected by the electrometers of the day. Many doubted that the shock was electrical at all. Cavendish built an artificial fish of wood and leather, wired to Leyden jars, and showed that a large quantity of electricity at low intensity gives exactly the torpedo’s effects. In the same years he measured the capacity of plates and the conducting power of salt water, using his own body as the detector.

The artificial torpedo (1776)

John Walsh had shown in 1772–73 that the torpedo’s shock passes through conductors and is stopped by insulators. The puzzle was that it never produced a spark. Cavendish’s answer used his 1771 distinction. A spark needs a high degree of electrification (potential). A shock needs enough fluid (charge) to pass through the body. A battery of many large jars charged to a low potential stores a large charge at low potential: it gives a strong shock and no spark. His model fish, soaked in salt water, reproduced the effect. In modern terms, energy \(\tfrac12CV^2\) can be large while \(V\) stays below the breakdown potential of air, if \(C\) is large.

Capacities

His notes record the capacities of many conductors measured against globes: discs, squares, cylinders, and coated plates of glass with different thicknesses. He found that coated plates have capacities proportional to area divided by thickness, and that glass, shellac and other materials give larger capacity than air for the same geometry. That is the effect of what Michael Faraday later called the specific inductive capacity, now the dielectric constant.

Resistance by the shock

Lacking any current meter, Cavendish discharged a jar through a tube of salt solution and then through his own body, adjusting the length of a comparison tube until the shocks felt equal. In this way he compared the conducting power of solutions of different strengths, and of iron wire against water. Maxwell, editing the notes, read some of these results as an early experimental form of Ohm’s law, that resistance is independent of current. A recent study of the manuscripts argues that Cavendish’s calculations from 1773 and 1781 point in different directions on this question, so the attribution should be made with care.

The composition of water and air

For the general reader. Is water an element? For two thousand years most thought so. In 1781 Cavendish exploded inflammable air with common air and with dephlogisticated air (oxygen) in closed glass vessels. Nothing but water was produced, and its weight equalled the weight of the gases consumed. His 1784 paper showed that water forms from two volumes of hydrogen and one of oxygen. A year later, sparking air for weeks, he made nitric acid from its nitrogen and found a tiny bubble that would not react, later identified as argon.

Water

Using his eudiometer, Cavendish found that common air loses about 20.8% of its volume when its oxygen is consumed, and that this proportion hardly varies from day to day or place to place. He found that about 423 measures of inflammable air consume the oxygen in 1000 measures of common air. That is a volume ratio near 2 : 1. He interpreted the result in phlogiston terms: water was dephlogisticated air united with phlogiston. Antoine-Laurent Lavoisier, who heard of the result in 1783 and repeated it, read it as the combination of two elements, hydrogen and oxygen, and made it a pillar of the new chemistry. James Watt had also proposed water’s compound nature in 1783, and a long priority dispute followed, mostly among their admirers.

Nitric acid and the residue

In 1785 Cavendish passed electric sparks through mixtures of common air and oxygen confined over a solution of potash. The volume shrank and nitrate formed. He concluded that phlogisticated air (nitrogen) combines with oxygen to give nitrous acid. He wanted to know whether all of the phlogisticated air could be converted. After prolonged sparking a small bubble remained, which he estimated at no more than 1/120 of the whole. He drew the cautious conclusion that if the phlogisticated air of the atmosphere was not uniform, the different part was not more than this fraction.

In the early 1890s Lord Rayleigh found that nitrogen from the air was denser than nitrogen made chemically. With William Ramsay, he isolated the cause in 1894, a new inert gas, argon, now known to form 0.93% of air by volume. Rayleigh and Ramsay drew attention to Cavendish’s bubble.

Heat

For the general reader. Why does ice stay at the same temperature while it melts, even though it absorbs heat? Cavendish and, independently, the Scottish chemist Joseph Black found the answer in the 1760s: melting and boiling absorb heat without changing temperature, and different substances need different amounts of heat to warm by one degree. Cavendish published almost none of this. One paper, on the freezing of mercury in the Canadian winter, shows how well he understood it.

Mixing experiments

Cavendish’s unpublished notes describe mixing measured quantities of substances at different temperatures and recording the final temperature. He found that equal weights of different substances need different amounts of heat for the same rise in temperature, and that ice absorbs a fixed quantity of heat in melting at constant temperature. He measured these quantities with care.

The freezing point of mercury (1783)

In 1759 in St Petersburg, Joseph Adam Braun froze mercury in a freezing mixture, and mercury thermometers then read hundreds of degrees below zero. Cavendish suspected the readings were false: mercury contracts sharply when it solidifies, so the column drops far below the true temperature. He designed an apparatus in which a thermometer stood in a cup of mercury that was allowed to freeze slowly, so that it read the temperature of the solid–liquid mixture. Thomas Hutchins used it at Albany Fort on Hudson Bay in the winter of 1781–82. While the mercury froze, the thermometer held steady near 39 degrees below zero on Fahrenheit’s scale. Cavendish’s analysis fixed the freezing point there, close to the modern value of \(-38.8\ ^\circ\mathrm C\) (\(-37.9\ ^\circ\mathrm F\)), and explained the earlier error.

Heat as motion

In an unpublished manuscript on heat, tentatively dated to the 1780s, Cavendish argued against the caloric theory that heat is a fluid. He took heat to be the motion of the particles of bodies and used a quantity equivalent to kinetic energy, conserved in exchanges, to reason about it. The theory was not developed fully until the mid-nineteenth century.

Weighing the world

For the general reader. Newton’s law of gravitation says every two masses attract, but the attraction between ordinary objects is fantastically weak. In 1797–98, at the age of 67, Cavendish measured the pull between lead spheres in a shed at Clapham. Comparing it with the pull of the whole Earth on the same balls, he found that the Earth is about five and a half times as dense as water. Every later value of Newton’s gravitational constant descends from his method.

The apparatus

The Reverend John Michell, geologist and astronomer, designed and built a torsion balance for the purpose but died in 1793 before using it. It passed to Francis John Hyde Wollaston and then to Cavendish, who rebuilt most of it. A wooden rod 6 feet long hung horizontally from a wire, with a lead ball 2 inches in diameter at each end. Two lead spheres 12 inches in diameter, about 158 kg each, hung from a frame that could swing them close to the small balls on opposite sides, so that both torques twisted the rod the same way. To shut out air currents and the warmth of his own body, Cavendish enclosed the balance in a sealed room and watched it from outside through telescopes, reading vernier scales lit by lamps.

Analysis

Let the rod have length \(L\), small balls of mass \(m\), large spheres of mass \(M\) at distance \(r\) from the small balls. The gravitational torque \(2\cdot\frac{GMm}{r^2}\cdot\frac L2\) balances the wire’s torque \(\kappa\theta\). The period of free oscillation is \(T=2\pi\sqrt{I/\kappa}\) with \(I=2m(L/2)^2=\tfrac12mL^2\). Eliminating \(\kappa\):

The small mass \(m\) cancels, and the wire’s stiffness is measured by the period. Cavendish did not write \(G\). He compared the attraction of the large sphere with the weight of the small ball, \(mg=Gm M_E/R^2\), which gives the Earth’s mean density directly.

Cavendish analysed his errors with unusual care: the attraction of the large spheres on the rod and the far ball, the effect of temperature differences, magnetism in the lead, and drift of the rest position. He noticed that the rod’s zero drifted when the large spheres were warmer than the case, which causes air convection, and controlled it. Geologists welcomed the result. Since surface rocks have densities around 2.5 to 3, the Earth’s interior must be much denser, a first clue to its iron core.

Bedford Square and Clapham, 1783–1810

Lord Charles Cavendish died in April 1783 and left Henry nearly all his estate. Further inheritances made Henry one of the richest men in Britain; at his death he was said to be the largest holder of Bank of England stock. He spent little on himself. He bought a house in Bedford Square in 1784 for his library, which he lent freely to scholars, and in 1785 a house on Clapham Common, south of London, which he turned largely into laboratory and workshop. The density experiment was done in an outbuilding there.

His domestic life was ordered to avoid contact. He ordered his dinner by notes left for his housekeeper, and he is said to have had a second staircase built so that he need not meet them. At the Royal Society, his sharp remarks were feared and valued. He served as a trustee of the British Museum from 1773 and, from 1800, as one of the managers of the new Royal Institution, where he followed Humphry Davy’s chemical work closely. In 1803 he was elected a foreign associate of the Institut de France.

He kept working to the end. His last paper, in 1809, described a method for dividing the scales of astronomical instruments. He died at Clapham on 24 February 1810, aged 78, after a short illness. He was buried in the family vault in All Saints’ Church, Derby, now Derby Cathedral.

The papers, the laboratory, the legend

Cavendish left about twenty packets of unpublished electrical papers. In 1874 they were entrusted to James Clerk Maxwell, first Cavendish Professor of Experimental Physics at Cambridge. Maxwell repeated several experiments, translated the notation and added long commentaries. The Electrical Researches of the Honourable Henry Cavendish appeared in October 1879, weeks before Maxwell’s death. It revealed that Cavendish had anticipated Coulomb on the inverse-square law, Faraday on dielectric constants, and others on capacity and conduction. Because he had not published, those laws carry other names.

The Cavendish Laboratory at Cambridge, opened in 1874, was paid for by William Cavendish, seventh Duke of Devonshire, a distant relative and Chancellor of the University, and is named for the family and for Henry. Its directors have included Maxwell, Lord Rayleigh, J. J. Thomson and Ernest Rutherford, and it became one of the great laboratories of modern physics.

Legacy

• Gravity: the torsion-balance measurement of gravitational attraction; refined versions still test Newton’s law and measure \(G\), the least precisely known fundamental constant.
• Electricity: the distinction between charge and potential; the null test of the inverse-square law; capacity and dielectric measurements.
• Chemistry: the first precise study of hydrogen; the composition of water; the constancy of the atmosphere’s oxygen fraction; the first trace of argon.
• Method: a standard of quantitative precision and error analysis far ahead of his time.

His extreme shyness has invited retrospective diagnosis. Some modern writers, including the neurologist Oliver Sacks, have suggested he might today be described as autistic. Such diagnoses at a distance of two centuries cannot be confirmed, and they say less than his own work does about the kind of mind he had.

Sources and further reading

Biography

1. Henry Cavendish, Wikipedia.
2. C. Jungnickel and R. McCormmach, Henry Cavendish’s chronology and publications, in Cavendish: The Experimental Life, Edition Open Access, Max Planck Research Library for the History and Development of Knowledge, 2016.
3. R. McCormmach, Cavendish, Henry, Dictionary of Scientific Biography, via Encyclopedia.com.
4. G. Wilson, The Life of the Honourable Henry Cavendish, Cavendish Society, London, 1851.
5. O. Sacks, Henry Cavendish: an early case of Asperger’s syndrome?, Neurology 57 (2001) 1347.

Physics and chemistry

1. H. Cavendish, Three papers, containing experiments on factitious air, Phil. Trans. 56 (1766) 141–184.
2. H. Cavendish, An attempt to explain some of the principal phaenomena of electricity, by means of an elastic fluid, Phil. Trans. 61 (1771) 584–677.
3. H. Cavendish, An account of some attempts to imitate the effects of the torpedo by electricity, Phil. Trans. 66 (1776) 196–225.
4. H. Cavendish, Experiments on air, Phil. Trans. 74 (1784) 119–153; 75 (1785) 372–384.
5. H. Cavendish, Experiments to determine the density of the Earth, Phil. Trans. 88 (1798) 469–526.
6. J. C. Maxwell (ed.), The Electrical Researches of the Honourable Henry Cavendish, Cambridge University Press, 1879.
7. I. Falconer, Editing Cavendish: Maxwell and The Electrical Researches of Henry Cavendish, arXiv:1504.07437.
8. Cavendish experiment, Wikipedia (apparatus and analysis).
9. E. R. Williams, J. E. Faller and H. A. Hill, New experimental test of Coulomb’s law, Physical Review Letters 26 (1971) 721.