Michael Faraday

How to use this course

Michael Faraday had almost no formal schooling and never used more mathematics than arithmetic. He still discovered electromagnetic induction, the laws of electrolysis, the rotation of light by magnetism and the magnetic response of all matter. He also liquefied gases and isolated benzene. Most important of all, he insisted that electric and magnetic forces live in the space between bodies, carried by lines of force. James Clerk Maxwell turned that picture into equations, and modern physics has been a theory of fields ever since.

Each technical lesson opens with a paragraph for the general reader, then gives the experiment as Faraday did it, a modern statement in a box, a derivation, and exercises with folded solutions. We use SI units throughout. Faraday himself wrote in words and diagrams; the equations are later translations, mostly by Maxwell, Franz Neumann and Hermann von Helmholtz.

Timeline

Newington and the bookbinder’s shop, 1791–1812

Michael Faraday was born on 22 September 1791 at Newington Butts, then a village in Surrey and now part of south London. His father James was a blacksmith from the north of England who had come south looking for work; his mother Margaret Hastwell was a farmer’s daughter. Michael was the third of four children. The family was poor, James was often ill, and the boy’s schooling stopped at reading, writing and arithmetic.

The Faradays belonged to the Sandemanians, a small Christian sect that had split from the Church of Scotland. Sandemanians read the Bible literally, held property loosely, and treated the members of their meeting as a family. Faraday kept this faith all his life. It gave him a strong sense that nature is the work of a single lawgiver, and so that its forces must be connected.

The apprentice

At about thirteen he began running errands for George Riebau, a French émigré bookseller and bookbinder in Blandford Street. In 1805 Riebau took him on as an apprentice bookbinder for seven years. Riebau let him read the books he bound. Two shaped him: the article on electricity in the Encyclopaedia Britannica, and Jane Marcet’s Conversations on Chemistry, a popular textbook that presented the chemistry of Humphry Davy. Faraday did the simple experiments he read about with whatever he could afford, including a small voltaic pile.

From 1810 he paid a shilling a lecture to hear John Tatum on natural philosophy at the City Philosophical Society. He wrote up the lectures in fair copies with his own drawings and bound them. He also worked on his English and taught himself to draw in perspective. He was training himself as a scientist with the means of a tradesman.

Davy’s assistant, 1812–1815

In 1812 a customer of Riebau’s gave Faraday tickets to the last lectures of Humphry Davy at the Royal Institution in Albemarle Street. Davy was the most famous chemist in Britain: he had isolated sodium and potassium by electrolysis and shown that chlorine is an element. Faraday took notes, wrote them up, bound them into a volume of some three hundred pages, and sent it to Davy with a request for any work in science. His apprenticeship ended in October 1812.

Davy replied kindly and met him, but at first had nothing to offer and advised him to stay with bookbinding. Early in 1813 the Royal Institution dismissed its laboratory assistant after a brawl, and on 1 March 1813 Faraday was appointed Chemical Assistant, with a small wage and two rooms in the building. His duties were to clean apparatus, prepare demonstrations and help Davy and the other lecturers.

The European tour

In October 1813 Davy set out for the Continent with his wife, taking Faraday as assistant and, when the valet refused to travel, as servant too. Britain and France were at war, but Napoleon had given Davy a passport. In Paris they met André-Marie Ampère and the French chemists, and Davy worked out that the new substance from seaweed, iodine, was an element. In Florence they used the Grand Duke’s great burning lens to burn diamond in oxygen and showed it was pure carbon. In Milan they met Alessandro Volta. Lady Davy treated Faraday as a servant, which he found hard, but the eighteen months gave him a European education in experimental chemistry. They returned to London in April 1815.

The Royal Institution, 1815–1831

Back in London, Faraday became Davy’s right hand. He helped with the research that led to the miners’ safety lamp in 1815–16, did routine analyses for paying clients, and published his first paper in 1816, on a sample of caustic lime from Tuscany. In the same year he gave his first lectures, to the City Philosophical Society. In 1820–21 he made the first known compounds of carbon and chlorine, hexachloroethane and tetrachloroethylene.

On 12 June 1821 he married Sarah Barnard, the daughter of a Sandemanian silversmith. They had no children and lived for most of their marriage in rooms at the top of the Royal Institution. In the same year he was made Superintendent of the House. In September 1821 he discovered electromagnetic rotation (Lesson 04), the first device to turn electric current into continuous motion.

The quarrel with Davy

The rotation paper caused trouble. William Hyde Wollaston had earlier tried to make a current-carrying wire rotate about its own axis, and some Fellows of the Royal Society believed Faraday had used Wollaston’s idea without credit. Faraday cleared himself with Wollaston directly, but relations with Davy cooled. When Faraday was proposed for the Royal Society in 1823, Davy, then its President, opposed the election. Faraday was elected in January 1824 all the same.

In 1823 he liquefied chlorine and other gases, and in 1825 he isolated benzene (Lesson 10). That year he became Director of the Laboratory and founded the Friday Evening Discourses, lectures on current science for members and guests that still continue. From 1825 to 1829 much of his time went into a commission to improve optical glass for telescopes. The work produced little for astronomy, but it left him a block of very dense lead borate glass that later revealed both the Faraday effect and diamagnetism. In 1830 he became professor of chemistry at the Royal Military Academy at Woolwich. Davy died in 1829. In the summer of 1831, free of the glass commission, Faraday returned to electricity.

Electromagnetic rotation (1821)

For the general reader. In 1820 Hans Christian Ørsted found that an electric current deflects a compass needle. Faraday noticed that the force between a current and a magnet pole does not push them together or apart. It pushes sideways, around the wire. So a pole should be able to go round a wire forever, and a wire round a pole. He built the device that did this, the first electric motor.

The experiment

Ørsted’s discovery of July 1820 set off a year of work across Europe. Ampère showed that currents attract and repel one another, and Davy and Wollaston looked for rotations. Asked to write a review of the new subject for the Annals of Philosophy, Faraday repeated every experiment. On 3–4 September 1821 he mapped the force on a magnet pole near a vertical wire and found it was circular.

He then built two cups side by side, each filled with mercury and wired to a battery. In the first, a bar magnet stood upright, fixed at the bottom, and a wire hung freely from above with its lower end dipping into the mercury. With current flowing, the wire’s end swept round the magnet. In the second, the wire was fixed and the magnet, tethered at its lower end, floated upright and swept round the wire. The paper appeared in the Quarterly Journal of Science in October 1821.

Why it turns

Near the top of the fixed magnet the field points roughly radially away from the pole, \(\mathbf B\approx B_r\,\hat{\mathbf r}\). A vertical current \(I\hat{\mathbf z}\) in that field feels \(I L\,\hat{\mathbf z}\times B_r\hat{\mathbf r}=ILB_r\,\hat{\boldsymbol\varphi}\): a force along the circle around the magnet. The force is always tangential, so the wire never reaches equilibrium and keeps going round. Reversing either the current or the pole reverses the sense of rotation.

The mercury matters. A rigid closed circuit in the field of a fixed magnet cannot rotate continuously, because the work done by the magnetic force over a full turn would have to come from a change of flux linked by the circuit, and after a full turn the flux returns to its starting value. The mercury lets the circuit slide over the magnet, so that the current path crosses the field lines on every turn. Every continuous-rotation homopolar device, from Peter Barlow’s star wheel of 1822 to Faraday’s own disk generator of 1831, uses a sliding contact for this reason.

Electromagnetic induction (1831)

For the general reader. If a current makes magnetism, can magnetism make a current? Many tried and failed, because they looked for a steady effect. Faraday found in 1831 that a current appears only while the magnetism changes. Every generator and transformer in the world rests on this discovery.

The experiments

On 29 August 1831 Faraday wound two separate coils of insulated wire on opposite sides of a soft iron ring about 15 cm across. One coil went to a battery, the other to a galvanometer. When he closed the battery circuit, the needle jumped and returned to zero. When he opened it, the needle jumped the other way. A steady current did nothing. On 17 October he plunged a bar magnet into a coil and saw the same transient current, reversing on withdrawal. On 28 October, at the Royal Society’s great horseshoe magnet, he spun a copper disk between the poles, took current off the axle and the rim with sliding contacts, and obtained a steady current: the first dynamo. He read the first series of his Experimental Researches in Electricity to the Royal Society on 24 November 1831. Joseph Henry in Albany made similar observations independently but published later.

Faraday described induction in terms of lines of magnetic force. A current is induced in a conductor when it cuts lines of force, and its strength depends on the rate at which they are cut. The same idea explained a puzzle from 1824, François Arago’s rotating copper disk that dragged a magnetic needle round with it: eddy currents induced in the moving disk.

Derivation: one law or two?

The flux through a moving surface changes for two reasons. Using \(\nabla\cdot\mathbf B=0\), the transport theorem gives

By Stokes’s theorem and \(\nabla\times\mathbf E=-\partial_t\mathbf B\), the first term is \(-\oint\mathbf E\cdot d\boldsymbol\ell\). So \(-d\Phi/dt=\oint(\mathbf E+\mathbf v\times\mathbf B)\cdot d\boldsymbol\ell\). The flux rule thus combines two different physical mechanisms: a transformer emf from the induced electric field and a motional emf from the magnetic force on moving charges. Einstein opened his 1905 relativity paper by pointing out that physics treated these two cases differently although only relative motion mattered.

The Faraday disk

A disk of radius \(R\) turns at angular speed \(\omega\) in a uniform axial field \(B\). A charge at radius \(r\) moves at \(v=\omega r\) and feels \(\mathbf v\times\mathbf B\) directed radially. The emf between axle and rim is

Here the flux rule must be applied with care: the circuit through the brushes does not change shape, so a naive count of flux gives zero. The correct path follows the moving material of the disk, and then the swept area grows at rate \(\tfrac12\omega R^2\). Richard Feynman used the disk as his standard warning about the flux rule.

The laws of electrolysis (1832–1834)

For the general reader. Passing a current through salt water or a molten salt splits it into its elements. Faraday measured how much. He found that the amount of chemical change depends only on how much electricity passes, and that the same quantity of electricity always liberates chemically equivalent amounts of different substances. The laws imply, though he would not say so, that electricity comes in fixed units.

One electricity

In 1832 Faraday asked whether “voltaic”, “common” (frictional), “magneto”, “thermo” and “animal” electricity were the same thing. He showed that each could heat a wire, deflect a needle, give a spark, decompose a solution and shock an animal, and concluded that there is one electricity whatever its source. To compare quantities he needed a measure, and chemical decomposition gave him one.

The laws

He built a “volta-electrometer” (later shortened to voltameter): a tube of acidulated water in which the current releases hydrogen and oxygen that can be collected and measured. Placing voltameters and other cells in series, so that the same current passed through each, he found the gas produced did not depend on the size of the electrodes, the strength of the acid or the intensity of the battery. It depended only on the quantity of electricity. The results appeared in the seventh series of the Experimental Researches (1834).

Words

Faraday disliked the word “pole”, which suggested a centre of attraction, because he saw the decomposition as happening throughout the liquid. With advice from the Cambridge polymath William Whewell he introduced electrode, anode and cathode (the “way in” and “way out” for the current), electrolyte, electrolysis, and ion, with anion and cation for the particles moving to each electrode. All are still in use.

An atom of electricity

The combined law says that one mole of univalent ions always carries the same charge \(F\). If matter is made of atoms, each univalent ion carries charge \(F/N_A\), and a \(z\)-valent ion carries \(z\) times that. Faraday was cautious about atoms and did not draw this conclusion. Hermann von Helmholtz drew it in his Faraday Lecture to the Chemical Society in 1881: electricity, like matter, is divided into definite elementary portions. George Johnstone Stoney named the unit the electron in 1891, and J. J. Thomson found the particle in 1897.

Lines of force and the field

For the general reader. Newton’s gravity acts across empty space instantly, and most physicists in 1830 thought electric and magnetic forces did the same. Faraday did not. He thought of space around magnets and charges as filled with lines of force that have tension and pressure and carry the action from place to place. The idea seemed vague to the mathematicians of his day. Maxwell showed that it was exact.

Counting lines

Faraday’s lines start on positive charge and end on negative charge (for electricity) or form closed loops (for magnetism). Their density measures the strength of the force. If a fixed number of lines leave a point charge, the number crossing any sphere around it is the same, so the density falls as \(1/r^2\). The inverse square law becomes a conservation law for lines.

Cage and ice pail

In January 1836 Faraday built a cube about 12 feet on a side, a wooden frame covered with wire and paper, insulated it from the ground and charged it heavily from an electrical machine. He went inside with his most sensitive electroscopes and found no trace of charge or force, even while sparks flew from the outside. This is the Faraday cage. In 1843 he lowered a charged metal ball into an insulated ice pail connected to an electroscope. The electroscope’s reading rose as the ball went in, then stayed the same whether the ball touched the inside or not. The pail’s outer surface always carried exactly the charge of the ball. Both results follow from Gauss’s law applied to a surface inside the conductor, where \(\mathbf E=0\).

Physical lines

From the 1840s Faraday argued that the lines are physical things. In the 1846 Friday Evening Discourse later published as “Thoughts on ray-vibrations”, filling in at short notice for Charles Wheatstone, he speculated that light might be a vibration of the lines of force themselves, with no need for an ether. In 1852 he wrote “On the physical character of the lines of magnetic force”: the lines behave as if under tension along their length and repel one another sideways.

Maxwell read the Experimental Researches as a young man and resolved to translate them into mathematics. His paper “On Faraday’s lines of force” (1855–56) treated the lines as tubes of an incompressible fluid. “On physical lines of force” (1861–62) built a mechanical model of the field and found that it carried waves at the speed of light. Maxwell judged that Faraday’s methods showed him to be a mathematician of a very high order, though he wrote no equations.

The Faraday effect (1845)

For the general reader. Faraday was sure that light, electricity and magnetism were connected. After years of failure he sent polarized light through a block of heavy glass placed in a strong magnetic field and saw the plane of polarization twist. It was the first evidence that light and magnetism interact, and a clue that light is itself electromagnetic.

The experiment

In August 1845 William Thomson (later Lord Kelvin) wrote to ask whether a transparent dielectric under electrical strain would affect polarized light. Faraday tried electric fields again without success, then turned to magnets. On 13 September 1845 he placed a bar of his lead borate glass from the 1820s between the poles of an electromagnet, with the light travelling along the field. When the magnet was switched on, the plane of polarization rotated, and the rotation reversed when the field reversed. He wrote in his notebook that he had magnetized a ray of light. The work became the nineteenth series of the Experimental Researches.

Derivation

Write linear polarization as the sum of left and right circular components. Model the medium as electrons (charge \(-e\), mass \(m\), density \(N\)) bound with natural frequency \(\omega_0\). In a static field \(B\hat{\mathbf z}\), a circularly polarized wave \(\mathbf E=E_0(\hat{\mathbf x}\pm i\hat{\mathbf y})e^{-i\omega t}\) drives circular motion, and the magnetic force adds or subtracts from the restoring force. With \(\omega_c=eB/m\), the equation of motion \(m\ddot{\mathbf r}=-m\omega_0^2\mathbf r-e\mathbf E-e\dot{\mathbf r}\times\mathbf B\) gives

with the sign labelling the two circular senses. The two components travel at different speeds. After a distance \(d\) they have acquired a phase difference \((\omega d/c)(n_+-n_-)\), and when recombined the plane of polarization has turned by half that:

For small \(\omega_c\), \(n_\pm(\omega)\approx n(\omega\pm\omega_c/2)\), which gives Henri Becquerel’s relation of 1897, \(|V|=\dfrac{e}{2mc}\,\lambda\,\Big|\dfrac{dn}{d\lambda}\Big|\). Strongly dispersive glasses rotate most, which is why Faraday’s heavy glass succeeded where ordinary glass would have shown little.

Non-reciprocity

Natural optical activity in a sugar solution undoes itself if light is reflected back through the sample. The Faraday rotation does not: a beam that returns through the medium is rotated by the same sense relative to \(\mathbf B\), so the total doubles. A rotator giving 45°, between polarizers set 45° apart, passes light one way and blocks it the other way. Such optical isolators, often made of terbium gallium garnet (\(V\approx-134\) rad T\(^{-1}\) m\(^{-1}\) at 632 nm), protect lasers from their own reflections.

Diamagnetism (1845–1850)

For the general reader. Everyone knew that iron is attracted by a magnet. In 1845 Faraday found that a bar of his heavy glass is weakly repelled, and that so are water, bismuth, wood, flesh and almost everything else. Every substance responds to magnetism, either by attraction or by repulsion. The repulsion is strong enough today to float a living frog in a powerful magnet.

The observations

With the new electromagnet that had rotated light, Faraday hung the bar of heavy glass by a silk thread between the poles. When the magnet was switched on, the bar turned to lie across the line joining the poles, the “equatorial” position, while an iron bar lies along it, “axially”. Anton Brugmans had seen bismuth repelled in 1778, but the observation had been forgotten. Faraday tested a long list of materials and found the same repulsion in most of them, strongest in bismuth. He sorted substances into two classes, the attracted and the repelled; at Whewell’s suggestion the latter were called diamagnetic. By 1850 he had also shown that oxygen gas is attracted by a magnet.

Force on a weakly magnetic body

A small body of volume \(V\) and susceptibility \(\chi\) with \(|\chi|\ll1\) acquires magnetization \(\mathbf M=\chi\mathbf B/\mu_0\). Its energy in the field is \(U=-\chi VB^2/(2\mu_0)\), so

A paramagnet (\(\chi>0\)) moves toward strong field; a diamagnet (\(\chi<0\)) moves toward weak field. An elongated diamagnet sets itself equatorially because that places its ends where the field is weaker.

Origin

When a field is switched on, the induced electric field (Lesson 05) speeds up or slows down each electron’s orbit so as to oppose the change, in line with Lenz’s law. The result is Larmor precession at \(\omega_L=eB/2m\) and an induced moment opposite to \(\mathbf B\). For atoms with closed shells this gives Paul Langevin’s formula (1905)

with \(N\) atoms per unit volume and the sum over electrons. Yet the Bohr–van Leeuwen theorem (Niels Bohr 1911, Hendrika van Leeuwen 1919) shows that in strictly classical statistical mechanics all magnetic susceptibility vanishes: the surface currents of electrons bouncing off the walls cancel the bulk effect exactly. Langevin’s answer is right because atoms are quantum systems with fixed orbits. Faraday’s weakest effect turned out to need quantum mechanics.

Chemistry: liquefying gases and isolating benzene

For the general reader. Before he was a physicist Faraday was a chemist, and a very good one. In 1823 he turned chlorine gas into a liquid using nothing more than a sealed glass tube and a little heat, and showed that many other “gases” were vapours of liquids that boil at low temperatures. In 1825 he isolated from lamp gas residues a new liquid, benzene, which became the foundation of aromatic chemistry.

Liquid chlorine (1823)

In 1810 Davy had found a solid hydrate of chlorine that forms when chlorine is bubbled through cold water. Early in 1823 Faraday analysed it, and at Davy’s suggestion heated the crystals to about 100 °F (38 °C) in one arm of a sealed, bent glass tube. The hydrate decomposed, the pressure inside rose, and a yellow oily liquid collected in the cool arm: chlorine, condensed by its own pressure. He confirmed it by compressing dry chlorine to a few atmospheres with a pump. Over the next weeks he liquefied by similar means sulfur dioxide, hydrogen sulfide, carbon dioxide, nitrous oxide, cyanogen, ammonia and hydrogen chloride. A tube exploded in his face during this work. He failed with hydrogen and oxygen.

Faraday’s conclusion, that gases like chlorine are vapours of volatile liquids above their boiling points, follows: any vapour condenses when its pressure exceeds the vapour pressure at that temperature.

The permanent gases (1844–45)

In 1844–45 he returned to the problem with a cooling bath of solid carbon dioxide and ether, evacuated with an air pump, which reached about \(-110\) °C, and with pumps giving up to about 50 atmospheres. He liquefied or solidified many more gases, but oxygen, nitrogen and hydrogen still would not condense. Thomas Andrews explained why in 1869: above a critical temperature no pressure can liquefy a gas. The critical temperatures of oxygen (154.6 K), nitrogen (126.2 K) and hydrogen (33.2 K) all lie below Faraday’s bath (about 163 K). Louis Cailletet and Raoul Pictet finally liquefied oxygen in 1877.

Benzene (1825)

Illuminating gas made by heating oils was stored compressed in cylinders, where an oily liquid condensed. Faraday separated from it by careful distillation a colourless liquid that froze at about 5 °C and boiled near 80 °C, and analysed it as containing carbon and hydrogen in equal numbers of atoms. He called it bicarburet of hydrogen. With the atomic weight of carbon then taken as 6, his formula looked different from today’s C\(_6\)H\(_6\), but the composition was right. Eilhard Mitscherlich made the same compound from benzoic acid in 1833 and named it benzin, and August Kekulé proposed the ring structure in 1865.

Lecturer and public scientist

In February 1833 Faraday became the first Fullerian Professor of Chemistry at the Royal Institution, a chair endowed by the eccentric MP John Fuller with no obligation to lecture. He lectured anyway, and superbly. He had studied the craft since his days with Tatum: clear demonstrations, a slow pace, nothing that could fail. He gave nineteen of the Christmas lectures for young people between 1827 and 1860. The 1860–61 series, The Chemical History of a Candle, was published from a shorthand record and is still in print.

He also served the state. He was professor of chemistry at the Royal Military Academy at Woolwich from 1830 to 1851 and scientific adviser to Trinity House, the lighthouse authority, from 1836 to 1865, where he worked on ventilation, lamps and the first electric lighthouse lamps. With the geologist Charles Lyell he investigated the 1844 explosion at Haswell Colliery, which killed 95 men, and identified coal dust as a cause. He advised on the preservation of the paintings in the National Gallery and on the Great Exhibition of 1851. In 1855 his letter to The Times on the stinking state of the Thames, tested by dropping white cards into the water, drew a famous Punch cartoon. He declined to help prepare poison gas for use in the Crimean War.

Illness

From about 1839 Faraday suffered from giddiness and failures of memory, and for several years he could do little research. He recovered enough to make the great discoveries of 1845, but his memory deteriorated steadily through the 1850s. He was an elder of his Sandemanian church, preaching on Sundays, and kept his religious and scientific lives in separate compartments. He refused a knighthood and twice declined the presidency of the Royal Society, wishing to remain plain Michael Faraday.

Hampton Court, death and legacy

In 1848, on the suggestion of Prince Albert, Queen Victoria granted Faraday a house at Hampton Court; he moved there in 1858. His research continued into the 1860s, though more slowly. In 1862 he looked for a change in the spectral lines of a flame placed in a magnetic field and found none; Pieter Zeeman found the effect in 1896 with better spectroscopes. Faraday gave his last Friday Evening Discourse in 1862 and gradually gave up his posts. John Tyndall, who had joined the Royal Institution in 1853, succeeded him there.

Faraday died at his house at Hampton Court on 25 August 1867, aged 75. He had declined burial in Westminster Abbey and lies in the dissenters’ section of Highgate Cemetery; there is a memorial plaque in the Abbey near Newton’s grave.

Legacy

• The field: Maxwell’s equations are Faraday’s lines of force in mathematical form, and through them every later field theory, from relativity to the Standard Model, descends from his picture. Einstein kept portraits of Faraday, Newton and Maxwell in his study.
• Technology: the electric motor, the dynamo and the transformer all rest on Lessons 04 and 05; electroplating and electrochemical industry rest on Lesson 06.
• Units and words: the farad, the unit of capacitance, and the Faraday constant \(F\) are named for him, as are the Faraday cage and the Faraday effect. Electrode, anode, cathode, ion and electrolyte are his words.
• Records: his laboratory notebooks, numbered paragraph by paragraph, are among the most complete records of experimental discovery ever kept.
• Public science: the Royal Institution Christmas Lectures and Friday Evening Discourses continue. His portrait appeared on the Bank of England £20 note from 1991 to 2001.

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Michael Faraday, MacTutor History of Mathematics.
2. Michael Faraday, Wikipedia (with extensive references).
3. AIM25 archives, Faraday, Michael, 1791–1867, chemist and natural philosopher, authority record.
4. L. Pearce Williams, Michael Faraday: A Biography, Chapman and Hall, 1965.
5. G. Cantor, Michael Faraday: Sandemanian and Scientist, Macmillan, 1991.
6. F. A. J. L. James, Michael Faraday: A Very Short Introduction, Oxford University Press, 2010.
7. J. Tyndall, Faraday as a Discoverer, Longmans, 1868.

Physics and chemistry

1. M. Faraday, Experimental Researches in Electricity, vol. 1, Project Gutenberg.
2. M. Faraday, The Chemical History of a Candle, ed. W. Crookes, Project Gutenberg.
3. M. Faraday, On some new electro-magnetical motions, and on the theory of magnetism, Quarterly Journal of Science 12 (1821).
4. M. Faraday, On fluid chlorine, Phil. Trans. R. Soc. 113 (1823). Text at ChemTeam.
5. M. Faraday, On new compounds of carbon and hydrogen, Phil. Trans. R. Soc. 115 (1825).
6. M. Faraday, Thoughts on ray-vibrations, Phil. Mag. 28 (1846).
7. J. C. Maxwell, On Faraday’s lines of force, Trans. Camb. Phil. Soc. 10 (1856).
8. Encyclopaedia Britannica, 11th ed., Liquid gases (history of Faraday’s liquefaction work).
9. Faraday’s law of induction, Faraday effect, Diamagnetism, Faraday’s laws of electrolysis, Wikipedia.
10. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. II, ch. 17 (the laws of induction and exceptions to the flux rule).
11. D. Gooding, Experiment and the Making of Meaning, Kluwer, 1990 (on Faraday’s laboratory practice).