Robert Boyle

How to use this course

Robert Boyle is remembered in every physics course for one law, and in every chemistry course as a founder of the subject. Neither memory captures him well. His great contribution was a method: careful experiments with instruments, reported in enough detail that others could repeat them, and witnessed by a community of gentlemen who judged the results. The air pump, built for him by Robert Hooke, was its showpiece. The law of pressure and volume was one result among hundreds.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Where a lesson uses modern ideas that Boyle did not have (moles, molecules, the van der Waals equation), it says so. Dates before 1752 are in the Old Style (Julian) calendar used in England at the time.

Timeline

Lismore, Eton and the Grand Tour, 1627–1644

Robert Boyle was born on 25 January 1627 at Lismore Castle in County Waterford, Ireland. His father, Richard Boyle, had arrived in Ireland as an almost penniless adventurer and became, through land deals in Munster, one of the richest men in the British Isles and the 1st Earl of Cork. Robert was his seventh son and fourteenth child, by his second wife, Catherine Fenton. Twelve of the fifteen children survived childhood. Robert’s mother died when he was small, and the boy was sent out to nurse in the Irish countryside, a practice his father favoured for toughening children.

Around 1635 Robert and his brother Francis were sent to Eton College, whose provost was the diplomat and poet Sir Henry Wotton. He was a bookish boy, and the earl withdrew both sons in 1638. In 1639 the two brothers set out for the Continent with a French tutor. They studied in Geneva, where Robert learned French, Latin, rhetoric, religion and some mathematics. In Geneva, during a violent thunderstorm, he had a religious experience that he later described as a conversion, and his piety shaped the rest of his life.

Florence, 1641–42

In 1641 the brothers travelled into Italy. Robert learned Italian and spent the winter of 1641–42 in Florence. There he read the works of Galileo Galilei, who was living under house arrest at Arcetri, just outside the city, and who died there in January 1642. Boyle later recalled that this encounter with Galileo’s “paradoxes” turned him toward natural philosophy. The family’s fortunes, meanwhile, collapsed with the Irish rebellion of 1641. Money stopped arriving, and the young men were stranded for a time in Marseilles. Robert returned to England in the summer of 1644, in the middle of the Civil War. His father had died in September 1643.

Stalbridge and the Invisible College, 1644–1654

From his father Boyle inherited the manor of Stalbridge in Dorset and estates in Ireland. He lived first with his sister Katherine, Lady Ranelagh, in London. She was thirteen years older, a woman of wide learning and strong Protestant and reforming views, and she remained the closest person in his life. By 1646 he had settled at Stalbridge, where he stayed for about six years.

At Stalbridge he wrote moral and devotional essays and, increasingly, worked with his hands. He had a furnace built and set up a chemical laboratory. Through his sister he joined the circle of reformers around Samuel Hartlib, who promoted useful knowledge, agriculture, medicine and education. In letters of 1646 and 1647 Boyle mentioned an “invisible college” of people who cared about practical learning. Historians still debate exactly whom he meant, but the phrase became attached to the groups that later formed the Royal Society. He read Pierre Gassendi, Marin Mersenne and William Oughtred, admired Copernican astronomy, and began to think of matter as made of small particles in motion.

In 1652 he went to Ireland to secure his estates. Cromwell’s land settlement left him very rich, with an independent income for life. He disliked Ireland, but he used his time there to learn anatomy by dissection with William Petty. In 1653 he met John Wilkins in London, and Wilkins urged him to come to Oxford.

Oxford, Hooke and the air pump, 1654–1668

Boyle settled in Oxford in the mid-1650s, renting rooms at Cross Hall. He never held a university post. Oxford under the Commonwealth had an extraordinary concentration of experimental talent around Wilkins, Warden of Wadham College: the mathematicians John Wallis and Seth Ward, the young Christopher Wren, the physicians Thomas Willis and Richard Lower, and William Petty. Boyle’s private laboratory became one of the centres of this club.

To run his experiments he hired assistants. The most important was Robert Hooke, who had come to Oxford as a poor chorister and worked for Willis. In 1657 Boyle read of Otto von Guericke’s experiments in Magdeburg with an evacuated vessel. Guericke’s pump had to be worked under water and was hard to use. Boyle asked Hooke to design a better one. The “pneumatical engine” was finished in 1659: a glass receiver on top of a brass cylinder, with a piston worked by a rack and pinion, and a stopcock and valve to let air out stroke by stroke.

The book that came out of it, New Experiments Physico-Mechanicall, Touching the Spring of the Air and its Effects (1660), reported forty-three experiments in the form of letters to his nephew. It was written so that readers could follow, judge and repeat every step. Two critics replied. The Jesuit Franciscus Linus denied that air could exert such force and proposed an invisible membrane, the funiculus, that pulled the mercury up. Thomas Hobbes denied that experiments with a leaky machine could settle anything about the vacuum. Boyle’s answer to Linus in 1662 contained the law of Lesson 05. The quarrel with Hobbes was about what counts as knowledge, and it is the subject of a celebrated study by Steven Shapin and Simon Schaffer.

On 28 November 1660, after a lecture by Wren at Gresham College, twelve men including Boyle, Wilkins and Wren agreed to found a society for promoting physico-mathematical experimental learning. It became the Royal Society, chartered in 1662 and again in 1663, when Boyle was named to its council. In November 1662, on Boyle’s recommendation, Hooke became its Curator of Experiments. In 1668 Boyle left Oxford for London.

The pneumatical engine

For the general reader. Evangelista Torricelli had shown in 1644 that the atmosphere holds up a column of mercury about 76 cm tall. Boyle wanted to know what happens when the air is taken away. With Hooke’s pump he put candles, bells, barometers, animals and bladders inside a glass globe and pumped it out. Flames went out, sound faded, mercury fell and animals died. Air, it turned out, was a material with weight and springiness, and it was needed for fire and life.

Stroke by stroke

Let the receiver have volume \(V\) and the cylinder swept volume \(v\). At the start of a stroke the receiver holds air at pressure \(p_k\). The valve between them opens and the piston is drawn down, so the same air fills \(V+v\). Then the valve closes and the cylinder is emptied to the atmosphere. If the temperature does not change, Boyle’s law (Lesson 05) gives

A real pump also has a dead volume \(d\) between valve and piston, which still holds air at atmospheric pressure \(p_0\) when the piston returns. Mixing that air with the receiver’s gives the recurrence \(p_{k+1}=(p_kV+p_0d)/(V+v+d)\). Its fixed point satisfies \(p_\ast(v+d)=p_0d\), so \(p_\ast=p_0\,d/(v+d)\approx p_0\,d/v\). Leaks around the piston and stopcock set a similar floor. Hobbes made the most of these imperfections.

The barometer in the receiver

In one of the most famous experiments of the 1660 book, Boyle placed a Torricellian tube with its dish of mercury inside the receiver and sealed it in. As he pumped, the mercury column sank; when he let air back in, it rose again. The height of the column measures the pressure of the air on the dish:

This settled for Boyle that the column is held up by the air outside, against those who said nature abhors a vacuum. He never got the column all the way down, which he attributed to the pump’s leaks.

Weight versus spring

Inside a sealed receiver there is no tall column of air above the dish, yet the barometer stands at full height until the pumping begins. So it cannot simply be the weight of the air in the receiver that supports the mercury. Boyle’s explanation was that the enclosed air keeps the pressure it had when sealed, because air acts like a compressed spring. In the open atmosphere the spring of the lower air is wound up by the weight of all the air above it. The two descriptions agree in equilibrium: pressure is the spring of the local air, and it equals the weight of the column above per unit area.

The spring of the air: Boyle’s law

For the general reader. Squeeze a sealed bicycle pump and it pushes back harder the more you squeeze. Boyle measured how much harder. Halve the volume of a fixed amount of air and its pressure doubles; reduce the volume to a third and the pressure triples. He published this in 1662, to answer a critic who doubted that air could push so strongly.

The J-tube

Boyle and his assistants took a long glass tube bent into a J, with the short arm sealed. Mercury poured into the open long arm trapped air in the short arm. At first the levels were equal, so the trapped air was at atmospheric pressure, measured as \(29\tfrac18\) inches of mercury. As more mercury was added, the trapped column shortened. Because the short arm had uniform bore, the volume of the air was proportional to its length, measured in “spaces” of a quarter of an inch, starting from 48.

Boyle’s table gave, for each length \(A\) of the air column, the mercury difference, the atmosphere’s \(29\tfrac18\) inches, their sum \(D\) (the total pressure), and a final column of what “that pressure should be according to the hypothesis” that pressures and volumes are reciprocal. A selection:

Across all 25 rows the product \(A\cdot D\) lies between about 1396 and 1415, a spread of roughly ±0.7% about its mean, while the pressure itself varies by a factor of four. Boyle published a second table for rarefaction, in which air trapped at the top of a tube dipped in a deep cistern of mercury was expanded by raising the tube. It showed the same law at pressures below one atmosphere.

Who found it

Boyle credited the hypothesis to Richard Towneley, who had read an account of experiments made by Henry Power in Yorkshire and Lancashire. Hooke built and probably operated the apparatus. Edme Mariotte found the same relation independently in France in the 1670s and added the observation that air expands when heated, so in France the law often carries his name. What Boyle contributed was the decisive published test, against a theory (Linus’s funiculus) that predicted something else.

Modern consequences

Combined with the later laws of Charles and Gay-Lussac and with Avogadro’s hypothesis, Boyle’s law becomes the ideal gas law \(pV=nRT\). Two consequences at fixed \(T\):

The first says that air becomes stiffer exactly in proportion to how hard it is already squeezed. The second is the work done on the gas in an isothermal compression.

Hydrostatical paradoxes and specific gravity

For the general reader. Water in a narrow tube can balance a much larger mass of water in a wide vessel, as long as the surfaces stand at the same height. This looked paradoxical in the seventeenth century. In Hydrostatical Paradoxes (1666) Boyle demonstrated such effects with real apparatus. At the end of his life, in Medicina Hydrostatica (1690), he turned the same principles into a practical test for detecting fake gems, debased coins and adulterated drugs: weigh them in air and in water.

Pressure depends only on depth

Consider a small vertical prism of fluid of cross-section \(dA\) and height \(dz\) at rest. Balance of forces gives \(dp/dz=-\rho g\). For an incompressible fluid,

Hence the force on the base of a vessel equals \(p\cdot(\text{base area})\), which can be far more or far less than the weight of the water in it. That is the hydrostatic paradox, discussed by Simon Stevin and Blaise Pascal. Pascal’s treatise on the equilibrium of liquids, published in 1663 after his death, argued partly from experiments that could hardly be performed, such as men sitting twenty feet under water. Boyle admired the reasoning but insisted on experiments that he and others had actually done.

Specific gravity by double weighing

By Archimedes’ principle a body immersed in water is buoyed up by the weight of the water it displaces. If a body weighs \(W_a\) in air and \(W_w\) when suspended in water, the displaced water weighs \(W_a-W_w\), so

The Sceptical Chymist: what is an element?

For the general reader. In 1661 most learned people believed that everything was made of four elements (earth, water, air and fire) or of the three “principles” of the chemists (salt, sulphur and mercury). Boyle asked how anyone knew. When you burn wood you get ash, water, smoke and flame, but did those things exist inside the wood, or did the fire make them? His book is an argument that chemistry must rest on experiment, and it gave the operational idea of an element that chemists later used.

The dialogue

The Sceptical Chymist is a conversation in a garden. Carneades, the sceptic, speaks largely for Boyle; Themistius defends Aristotle’s four elements; Philoponus defends the chemists’ three principles, derived from Paracelsus; Eleutherius moderates. Carneades argues that:

• fire does not merely separate pre-existing ingredients; it can produce new substances, as when sand and alkali fuse into glass, which no one claims was hidden in either;
• different methods of analysis yield different numbers and kinds of products from the same body, so the number of elements cannot be read off from analysis by fire;
• some bodies, such as gold, cannot be decomposed by fire at all, which would make them elements on the chemists’ own test.

Having stated this, Carneades doubts that any such bodies have been shown to exist. Boyle was a corpuscularian (Lesson 08): he thought all matter was one universal stuff, differentiated by the size, shape and motion of its particles. The definition was a tool to clear away the old systems, not a list. More than a century later Antoine Lavoisier made it operational: an element is a substance that has not yet been decomposed by any means of analysis. His 1789 list had 33 entries, including light and caloric.

The willow tree

Boyle discussed Jan Baptist van Helmont’s experiment with a willow, which seemed to show that water could be turned into wood and so was the one true element. Van Helmont planted a 5-pound willow in 200 pounds of dried earth and gave it only rainwater. After five years the tree weighed about 169 pounds, while the earth had lost only about 2 ounces. Boyle repeated growth experiments with plants in water and took them seriously as evidence that substances transform.

Corpuscles, qualities and the kinetic theory

For the general reader. Boyle thought the world was a machine made of tiny particles. Colour, heat, taste and smell were not separate things in objects but effects of the particles’ size, shape, motion and arrangement on our senses. He could not see the particles, but he could show that his machine-picture explained experiments. Seventy-six years after his law, Daniel Bernoulli showed how particles in motion produce exactly that law.

The corpuscular philosophy

Boyle coined the phrase “corpuscular philosophy” and used it interchangeably with “mechanical philosophy”. In The Origin of Forms and Qualities (1666) he argued that matter is one and the same everywhere, and that bodies differ only in the size, shape and motion of their parts and their arrangement, which he called the mechanical affections of matter. Other qualities, such as colour and heat, arise from these together with the structure of our sense organs. John Locke, Boyle’s friend, made the terms primary and secondary qualities standard. Boyle avoided committing himself to Descartes’ plenum or to Gassendi’s atoms in the void; he wanted a framework that experiments could fill in.

Two pictures of the spring

In 1660 Boyle offered two possible explanations of the air’s elasticity without choosing between them. In the first, the particles of air are like tiny springs, or like a fleece of wool, that resist being pressed together. In the second, following Descartes, the particles are kept in rapid whirling motion by a subtle fluid and fly apart when given room. The second is closer to the explanation that won.

Bernoulli’s derivation (1738)

In Hydrodynamica Daniel Bernoulli modelled a gas as many small particles moving rapidly and bouncing off the walls. In modern form: let \(N\) particles of mass \(m\) move in a cube of side \(L\). A particle with velocity component \(v_x\) hits a given wall every \(2L/|v_x|\) and transfers momentum \(2m|v_x|\) each time.

Derivation. The average force on one wall of area \(L^2\) is \(\sum_i 2m v_{x,i}^2/(2L)=Nm\langle v_x^2\rangle/L\), so \(p=Nm\langle v_x^2\rangle/L^3\). Isotropy gives \(\langle v_x^2\rangle=\tfrac13\langle v^2\rangle\). Comparing with \(pV=Nk_BT\) identifies \(\tfrac12m\langle v^2\rangle=\tfrac32k_BT\). Bernoulli also saw that compressing the gas faster than heat can escape would raise the speeds and the pressure, the adiabatic correction to Boyle’s law.

Fire, air, phosphorus and indicators

For the general reader. Boyle showed that a candle and a mouse both die in an exhausted receiver, and he found that metals gain weight when they are heated in air. He made a new “factitious air” that burned, prepared the glowing substance phosphorus, and used plant juices that change colour to tell acids from alkalis. He drew the wrong conclusion about the weight gain, and the story of how it was corrected leads straight to Lavoisier.

Calcination and the fire particles

When tin or lead is heated strongly in air it turns into a powdery calx that weighs more than the metal. Boyle heated metals in sealed glass retorts, broke them open, and weighed the products. He found the gain and, in work published in 1673, attributed it to particles of fire that passed through the glass and fixed themselves in the metal. Lavoisier in 1774 repeated the experiment with tin in a sealed vessel and weighed the whole vessel before and after. Its total weight did not change. When the vessel was opened, air rushed in, and the weight of that air equalled the gain of the tin. Boyle had weighed the calx after air had entered.

Factitious air, flame and life

Boyle dissolved iron filings in dilute acid and collected an air that burned; we call it hydrogen. His 1660 experiments showed that flame and animal life both require air, and that a small animal in a closed vessel dies as the air is “spent”, long before it is all used up. Later he described a viper placed in an exhausted receiver with a bubble visible in the fluid of its eye, the first recorded description of decompression sickness.

Phosphorus

The Hamburg alchemist Hennig Brand obtained white phosphorus from urine in 1669. The secret was sold to Johann Daniel Kraft, who demonstrated it in London, where Boyle saw it. Boyle worked out a preparation for himself and in 1680 published his method, together with observations of its cold glow in air. He was the first to use phosphorus to ignite splints tipped with sulphur, ancestors of the match. His assistant Ambrose Godfrey later made a business of manufacturing phosphorus.

Indicators

In Experiments and Considerations Touching Colours (1664) Boyle reported that syrup of violets and other plant extracts turn one colour with acids and another with alkaline salts, and he proposed such colour changes as a test to sort substances into acid, alkaline and neither. This was a precursor of litmus paper. The modern explanation: the dye is a weak acid \(\mathrm{HIn}\) whose two forms have different colours.

Beyond the ideal: the Boyle temperature

For the general reader. Boyle’s law is exact only for an imaginary gas whose molecules have no size and do not attract each other. Real gases deviate. Molecules attract at a distance, which lowers the pressure, and they take up room, which raises it. At one special temperature, named the Boyle temperature, the two effects cancel and a real gas obeys Boyle’s law over a wide range of pressures.

The virial expansion

For a real gas, the compressibility factor \(Z=pV_m/RT\) can be expanded in powers of the molar density:

The second virial coefficient \(B(T)\) comes from interactions between pairs of molecules. It is negative at low temperature, where attraction dominates, and positive at high temperature, where the excluded volume dominates.

Derivation. Solve for \(p=\dfrac{RT}{V_m-b}-\dfrac{a}{V_m^2}\) and expand \(\dfrac{1}{V_m-b}=\dfrac{1}{V_m}\big(1+\tfrac{b}{V_m}+\cdots\big)\). Then \(Z=1+\dfrac{1}{V_m}\Big(b-\dfrac{a}{RT}\Big)+O(V_m^{-2})\). The critical temperature follows from the inflection conditions \(\partial p/\partial V_m=\partial^2p/\partial V_m^2=0\).

Pall Mall and the Royal Society, 1668–1691

In 1668 Boyle moved to London and lived for the rest of his life in his sister Katherine’s house in Pall Mall, where he built a laboratory. Visitors came to see experiments and to consult him. His health had never been strong. In June 1670 he suffered a stroke that left him paralysed for a time. He recovered slowly, cut back his public engagements, and kept writing, often by dictation to secretaries, at an enormous rate.

He remained the Royal Society’s most celebrated experimental Fellow. His papers filled the early Philosophical Transactions, and his presence lent the Society the respectability of a pious, aristocratic gentleman. In 1680 the Fellows elected him President. He declined, explaining that he had scruples about taking the oaths required by the charter. Christopher Wren was elected in his place.

Chymistry and alchemy

Boyle’s chemistry included what historians now call chymistry: work on the transmutation of metals that we would classify as alchemy. He believed that a properly prepared mercury could act on gold, and he lobbied successfully for the repeal of the medieval statute that forbade the multiplication of gold and silver. Lawrence Principe’s studies of his manuscripts have shown how central this work was to him. It belongs to the same project as his corpuscular philosophy: if all matter is one stuff differently arranged, then rearrangement into gold is not absurd. Isaac Newton, who shared these interests, corresponded with him, including a long letter on the aether in 1679.

Religion and the wider world

Boyle saw experimental philosophy as a form of worship: the “Christian virtuoso” studied the creation to know the creator. A Free Enquiry into the Vulgarly Received Notion of Nature (1686) attacked the idea of Nature as a quasi-intelligent agent, arguing that the world is a mechanism whose laws God made and sustains. He was governor of the Corporation for the Propagation of the Gospel in New England and a director of the East India Company, and he paid for translations and printings of the Bible, including the Bible in Irish in the 1680s. He also employed and trained assistants who became natural philosophers in their own right, among them the Frenchman Denis Papin, who worked on the air pump with him in the later 1670s and went on to invent the steam digester.

Death, the Boyle Lectures and legacy

Katherine, Lady Ranelagh, died in December 1691. A week later, on 31 December 1691, Robert Boyle died in her house in Pall Mall, aged 64. He was buried in the chancel of St Martin-in-the-Fields; the church was rebuilt in the eighteenth century and the grave is lost. Gilbert Burnet, Bishop of Salisbury, preached the funeral sermon. John Locke saw his unfinished General History of the Air through the press in 1692.

His will endowed a series of eight sermons a year to defend Christianity against unbelievers, without entering into controversies among Christians. Richard Bentley gave the first Boyle Lectures in 1692, drawing on Newton’s Principia and corresponding with Newton about it. The lectures were revived in 2004 and continue in London.

Legacy

• Physics: the law \(pV=\text{const}\), the first quantitative law of a gas, and the first step to the ideal gas law and kinetic theory. The Boyle temperature of real gases bears his name.
• Chemistry: the critique of the four elements and three principles, the operational spirit later made precise by Lavoisier, careful analysis by reagents and indicators, and the separation of chemistry from medicine as a subject in its own right.
• Method: detailed, repeatable reporting of experiments; the use of instruments to produce new phenomena; the idea that matters of fact are established by witnessed trials. These practices shaped the Royal Society and modern experimental science.
• Honours: the Royal Dublin Society’s Boyle Medal, first awarded in 1899, and the Royal Society of Chemistry’s Robert Boyle Prize for Analytical Science.

Connections

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

Influenced by

• Blaise Pascal
• Evangelista Torricelli
• Galileo Galilei 1641-1642
• Otto von Guericke
• René Descartes
• Jan Baptist van Helmont
• Pierre Gassendi

Influenced

• Antoine Lavoisier
• Daniel Bernoulli
• Richard Bentley

Colleagues and collaborators

• Christiaan Huygens
• Christopher Wren
• Isaac Newton
• Jacob Bernoulli
• John Wallis
• Robert Hooke 1655-1662
• Denis Papin 1675-1679
• Edme Mariotte
• Henry Power
• John Wilkins 1653-1668
• Richard Towneley
• William Petty 1652-1660

Rivals

• Franciscus Linus 1661-1662
• Thomas Hobbes 1661-1674

Friends

• John Locke

Family

• Katherine Jones, Viscountess Ranelagh

Also mentioned in this life

• Archimedes
• Aristotle
• Amedeo Avogadro
• Joseph Louis Gay-Lussac
• Marin Mersenne
• John Philoponus
• Simon Stevin
• Johannes Diderik van der Waals

Fields

• pneumatics 3 lives
• chemistry 21 lives
• natural philosophy 12 lives
• hydrostatics 4 lives

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Robert Boyle, MacTutor History of Mathematics.
2. Robert Boyle, Wikipedia.
3. J. J. MacIntosh and P. Anstey, Robert Boyle, Stanford Encyclopedia of Philosophy.
4. M. Hunter, Boyle: Between God and Science, Yale University Press, 2009.
5. S. Shapin and S. Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life, Princeton University Press, 1985.
6. L. M. Principe, The Aspiring Adept: Robert Boyle and His Alchemical Quest, Princeton University Press, 1998.
7. Linda Hall Library, Scientist of the Day: Robert Boyle.

Physics and chemistry

1. R. Boyle, New Experiments Physico-Mechanicall, Touching the Spring of the Air, and its Effects, Oxford, 1660; 2nd ed. with A Defence of the Doctrine touching the Spring and Weight of the Air, 1662.
2. R. Boyle, The Sceptical Chymist, London, 1661. Project Gutenberg text.
3. R. Boyle, Experiments and Considerations Touching Colours, London, 1664. Project Gutenberg text.
4. R. Boyle, Hydrostatical Paradoxes, Oxford, 1666; Medicina Hydrostatica, London, 1690.
5. M. Hunter and E. B. Davis (eds.), The Works of Robert Boyle, 14 vols., Pickering & Chatto, 1999–2000.
6. Boyle’s 1662 compression table, transcribed at ChemTeam.
7. Boyle’s law and The Sceptical Chymist, Wikipedia.
8. D. Bernoulli, Hydrodynamica, Strasbourg, 1738, section X (kinetic theory of gases).