William Gilbert

How to use this course

William Gilbert published one book in his lifetime, and it changed physics. De Magnete (1600) argued from experiment, not from authority, that the Earth itself is a magnet. It explained why a compass needle points north and why it tilts downward, introduced the word electricus for bodies that attract like rubbed amber, and drew a clear line between electrical and magnetic attraction that held for more than two centuries. Galileo and Kepler read it closely.

Each technical lesson opens with a paragraph for the general reader, then sets out what Gilbert found and how he argued, followed by the modern physics that explains it, derivations and exercises with folded solutions. Gilbert wrote no equations, so the mathematics belongs to his successors; the lessons say clearly which claims are his and which are later. The six books of De Magnete map onto Lessons 04 to 09, and Lesson 10 makes his idea of a magnet’s sphere of influence quantitative.

Timeline

Colchester and Cambridge, 1544–1573

William Gilbert was born in Colchester, a prosperous cloth town in Essex, most probably in 1544; the day is often given as 24 May, but it is not certain. His father, Jerome Gilberd, was recorder of the borough, its chief legal officer. The family spelled the name Gilberd, and that form appears on the family monument. His father married more than once, and one of William’s half-brothers, also named William, later edited his unpublished writings.

He matriculated at St John’s College, Cambridge, in 1558, took his BA in 1561 and was elected a fellow of the college the same year. He proceeded MA in 1564 and MD on 13 May 1569, and was made a senior fellow that December. The Cambridge curriculum was built on Aristotle and Galen. Gilbert absorbed both thoroughly, which is why his later attack on the Aristotelian account of magnetism is so detailed: he knew the arguments he was rejecting.

Little is known of his years between the MD and his move to London. Some accounts say he travelled on the Continent; the evidence is thin.

A London physician, 1573–1600

By about 1573 Gilbert had settled in London, where he built a successful practice. He lived at Wingfield House on St Peter’s Hill, near St Paul’s, which he inherited from his stepmother. He never married. In 1577 he was granted a coat of arms.

He rose steadily in the College of Physicians, the body that licensed physicians in London. He was censor, responsible for examining and disciplining practitioners, in 1581 and many later years, treasurer from 1587 to 1594 and again from 1597 to 1599, and consiliarius in the late 1590s. In 1600 he was elected President.

The circle of navigators

Gilbert’s magnetism grew from the practical problems of English navigation. Elizabethan London was full of instrument makers and mathematical practitioners. The compass maker Robert Norman had discovered that a magnetized needle free to turn in a vertical plane tilts downward, and published his measurements in The Newe Attractive (1581). William Borough measured the variation of the compass at Limehouse in 1580. The mathematician Edward Wright, whose Certaine Errors in Navigation (1599) gave the mathematics of the Mercator chart, contributed a preface to De Magnete and probably helped with its navigational chapters. Gilbert used their measurements and corrected their theories.

The making of De Magnete

According to his own preface, Gilbert spent many years and much of his own money on experiments. The book’s full title is De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure; Physiologia Nova, Plurimis et Argumentis et Experimentis Demonstrata: on the magnet, magnetic bodies, and the great magnet the Earth; a new natural philosophy, demonstrated by many arguments and experiments. It was printed in folio by Peter Short in London in 1600.

The book is in six books:

1. History of the lodestone; iron and its ores; the conclusion that the Earth is magnetic.
2. Magnetic motions; the amber effect and electrics; coition (magnetic attraction); the terrella; armed lodestones.
3. Direction: how needles acquire and lose “verticity”, the property of pointing north and south.
4. Variation: the departure of the compass from true north, and its causes.
5. Declination (what we call dip or inclination).
6. The Earth as a magnet; its axis; the daily rotation of the Earth.

Gilbert was unusually explicit about method. He scorned writers who repeated old stories about magnets without testing them, such as the claim that garlic destroys a lodestone’s power. He described his experiments in enough detail to be repeated and marked new discoveries in the margins with asterisks, larger for more important results. He also invented instruments: the terrella, a lodestone turned into a sphere to model the Earth, and the versorium, a light needle on a pivot, which in a magnetized form served as a small compass and in an unmagnetized metal form detected electrical attraction.

He acknowledged one medieval predecessor with real respect: Peter Peregrinus of Maricourt, whose Epistola de magnete of 1269 had identified magnetic poles, stated that like poles repel and unlike attract, and described a pivoted compass. Gilbert went further by treating the Earth as one of these magnets.

Poles and the terrella

For the general reader. A lodestone is a naturally magnetic rock. Gilbert ground one into a ball and explored it with tiny needles. Each needle lined up along a direction that ran from one point on the ball, its pole, to the opposite one, just as compasses do on Earth. A small model Earth that behaves like the real Earth was a powerful argument: whatever explains the ball explains the planet.

What Gilbert did

He found the poles of the terrella by laying a short needle on its surface and marking the direction it pointed, then drawing great circles through the marks. The circles met at two points, the poles; the circle halfway between was the magnetic equator. He found that attraction was strongest at the poles and weakest at the equator, and that the region around a magnet within which it acts, his orbis virtutis or orb of virtue, extends further from strong stones. He also cut lodestones and showed that each piece has its own north and south poles.

The modern picture

In magnetostatics with no free currents, \(\mathbf H=-\nabla\Phi_M\) and \(\nabla\cdot\mathbf B=0\) with \(\mathbf B=\mu_0(\mathbf H+\mathbf M)\). A magnetization \(\mathbf M\) acts as a source through an effective magnetic charge density \(\rho_M=-\nabla\cdot\mathbf M\) and surface density \(\sigma_M=\mathbf M\cdot\hat{\mathbf n}\).

Derivation. \(\nabla\cdot\mathbf M=0\) inside, so the only source is the surface charge \(\sigma_M=M\cos\theta\). Solve Laplace’s equation inside and outside with \(\Phi_{\text{in}}=Ar\cos\theta\) and \(\Phi_{\text{out}}=B\cos\theta/r^2\). Continuity of \(\Phi\) at \(r=R\) gives \(AR=B/R^2\); the jump in the normal derivative, \(-\partial_r\Phi_{\text{out}}+\partial_r\Phi_{\text{in}}=\sigma_M\), gives \(2B/R^3+A=M\). So \(A=M/3\), \(B=MR^3/3\). The exterior potential \(\Phi=MR^3\cos\theta/(3r^2)=m\cos\theta/(4\pi r^2)\) is that of a dipole. Inside, \(\mathbf H=-\tfrac13\mathbf M\) and \(\mathbf B=\mu_0(\mathbf H+\mathbf M)=\tfrac23\mu_0\mathbf M\).

This is why the terrella works as a model of the Earth. Whatever the internal source, a field dominated by its dipole part looks outside like that of a uniformly magnetized ball.

No isolated poles

Gilbert’s cut lodestones illustrate \(\nabla\cdot\mathbf B=0\). Magnetization comes from aligned atomic moments, each a tiny dipole. Cutting a magnet between two layers of dipoles exposes a north-like surface on one piece and a south-like surface on the other: every piece has total magnetic charge zero.

Verticity and induced magnetism

For the general reader. Iron is not a magnet by itself, but it becomes one when touched by a lodestone, and Gilbert found that it can become one without any lodestone at all: by being hammered, or by cooling from red heat, while it lies north and south. He concluded that the Earth itself magnetizes iron. He also found that capping a lodestone with iron makes it lift far more weight, even though it does not attract from any greater distance.

Gilbert’s findings

• Touch. A needle stroked with a lodestone acquires verticity: it turns to the north and south. Stroking with the opposite pole reverses it.
• Hammering. A bar of iron hammered on an anvil while lying north and south acquires verticity, with its north-seeking end at the end that pointed north (Book III). A 2011 study published by the Royal Society found that this method works only weakly and unreliably.
• Cooling. Iron heated red hot and allowed to cool lying north and south acquires verticity (Book III, chapter 12). Heated past a certain point, a magnet loses its virtue.
• Armed lodestones. A lodestone fitted with iron caps on its poles lifts a much heavier iron weight in contact, yet does not draw iron any more strongly at a distance (Book II, chapters 17–22).

The physics

Iron is ferromagnetic. Below its Curie temperature (about 770 °C for iron, 580 °C for magnetite) it consists of domains, each spontaneously magnetized. An applied field \(\mathbf H\) grows favourably oriented domains, giving an induced magnetization far larger than the applied field, \(\mathbf M=\chi\mathbf H\) with \(\chi\) up to \(10^3\) or more in soft iron. Part of it remains when the field is removed: the remanence.

Hammering shakes domain walls loose from the defects that pin them, letting the weak Earth field (about 50 μT at London) bias the domain structure. Cooling through the Curie point in a field is far more effective: domains form already aligned, and the resulting thermoremanent magnetization is the basis of palaeomagnetism. Volcanic rocks record the field in which they cooled, and that record revealed reversals of the Earth’s field and sea-floor spreading. Gilbert’s chapter on cooled iron is its first description.

Derivation. Open a small gap \(dx\). The field in the gap stores energy density \(B^2/(2\mu_0)\) in volume \(A\,dx\); with flux held fixed, the work done must equal this energy, so \(F\,dx=\frac{B^2}{2\mu_0}A\,dx\). An iron cap collects the flux spread over the lodestone’s surface and concentrates it onto a smaller contact face. Since \(F\) grows as \(B^2\), concentrating the same flux \(\Phi=BA\) onto a smaller area multiplies the force: \(F=\Phi^2/(2\mu_0A)\). At a distance, though, what matters is the stone’s total moment, which the cap barely changes. Gilbert’s two observations, more holding force and no more reach, are both explained.

A unit of magnetomotive force in the CGS system, the gilbert, is named after him: \(1\ \mathrm{Gb}=\frac{10}{4\pi}\) ampere-turns.

The Earth as a magnet: dip

For the general reader. A compass needle that can tilt does not stay level. In London it points down at a steep angle. Gilbert found that a needle moved over his terrella does the same: level at the equator, steeper further north, vertical at the pole. He concluded that the Earth is a giant magnet and that the dip could be used to find latitude. The modern formula relating dip to latitude follows from the field of a dipole.

From terrella to Earth

Robert Norman had measured the dip at London in 1581 and found it steep, more than 70 degrees. He thought the needle was drawn toward a point, not pulled by the Earth as a whole. Gilbert showed that on a terrella the tilt depends on position in exactly the same way as on Earth, and argued that the force is a property of the whole Earth, whose interior he took to be magnetic. He built improved dipping instruments and proposed that sailors use dip to find latitude when the sky was overcast. His own geometrical rule for dip as a function of latitude, constructed from arcs on a diagram, gives dips larger than the latitude, as observed, but it is not the dipole law.

The dipole law

Treat the Earth’s field as that of a centred dipole aligned with the rotation axis, pointing south (so that north-seeking needle ends point north). At the surface, at magnetic latitude \(\lambda\), the horizontal (northward) and vertical (downward) components are

where \(B_0\approx30\ \mu\mathrm T\) is the equatorial field strength.

Derivation. The dipole potential is \(\Phi_M=\frac{m\cos\theta}{4\pi r^2}\). Then \(B_r=-\mu_0\partial_r\Phi_M=\frac{\mu_0m}{4\pi r^3}2\cos\theta\) and \(B_\theta=-\frac{\mu_0}{r}\partial_\theta\Phi_M=\frac{\mu_0m}{4\pi r^3}\sin\theta\). With \(\theta=90^\circ-\lambda\), the ratio of radial to tangential components is \(2\cos\theta/\sin\theta=2\tan\lambda\). For the Earth the dipole points southward, which flips both components and makes the field point down and north in the northern hemisphere.

Field lines

The field lines of a dipole satisfy \(r=L\,R\cos^2\lambda\), where \(L\) is the distance at which the line crosses the equator, in Earth radii. This simple formula organizes much of space physics: the van Allen belts and the aurora are labelled by \(L\).

Variation and the changing field

For the general reader. A compass rarely points exactly to true north. The difference, called variation by sailors and declination by modern scientists, changes from place to place. Gilbert thought it was caused by the pull of continents and that at any one place it never changes. The first idea was a reasonable guess; the second was proved wrong within a generation, and the discovery that the Earth’s field drifts over time opened a new branch of geophysics.

Gilbert’s theory

In Book IV Gilbert argued that variation is not caused by a magnetic mountain or a point in the heavens, as earlier writers had suggested. Instead, the great land masses, being more magnetic than the sea, draw the needle aside: near a large continent the needle bends toward it. He insisted that the variation at a given place is constant. He also discussed, sceptically, the hope of finding longitude from variation.

Secular variation

William Borough had measured the variation at Limehouse in 1580 as about 11° east. Edmund Gunter found about 6° in 1622, and in 1634 Henry Gellibrand, Gresham Professor of Astronomy, repeated the measurement at the same place and found about 4°. He published the result in 1635. The variation at a fixed place changes slowly with time, contrary to Gilbert. At London it later became westerly, reaching about 24° W around 1820, and is now close to zero again. Edmond Halley published the first chart of lines of equal variation over the Atlantic in 1701.

The modern description

Outside the Earth’s core and below the ionosphere there are no currents, so \(\mathbf B=-\nabla V\) with \(\nabla^2V=0\). Carl Friedrich Gauss showed in 1839 that the field can be expanded as

with Schmidt semi-normalized associated Legendre functions \(P_n^m\). He showed from data that the field is almost entirely of internal origin, confirming Gilbert’s central claim in quantitative form. The \(n=1\) terms describe a dipole: \(g_1^0\approx-29.4\ \mu\mathrm T\) at present, and the dipole axis is tilted about 10° from the rotation axis. The higher terms produce the irregularities Gilbert attributed to continents. Today we know the field is generated by convection in the liquid iron outer core, a dynamo, and that its pattern drifts and occasionally reverses.

For a dipole, the horizontal field points along the great circle toward the geomagnetic pole, so the formula is the standard spherical-trigonometry bearing.

Electrics and the versorium

For the general reader. Since antiquity people knew that rubbed amber picks up straws. Many writers lumped this together with the lodestone’s pull on iron. Gilbert showed they are different. He found that many substances, glass, sulphur, gems and resins, attract like amber when rubbed, and he called them electrica, from the Greek for amber. To test them he built the first electrical instrument, a light needle on a point that swings toward a charged body.

Gilbert’s results (Book II, chapter 2)

With the versorium Gilbert surveyed many materials. Those that attract after rubbing included amber, jet, diamond, sapphire, glass, sulphur, mastic, sealing wax and hard resin. Others, among them emerald, pearl, coral, and metals such as silver, gold, copper and iron, did not; he grouped them as non-electrics. He listed differences between the two kinds of attraction:

• Electrics attract almost everything light: chaff, metal foil, water and smoke. A lodestone attracts only iron and magnetic bodies.
• Electrics need rubbing; a lodestone acts by itself.
• Electrical attraction is weakened by moist air; it is strongest in cold, clear winter weather.
• Electrical attraction is one-sided and only an attraction; magnetic coition is mutual, and magnets both attract and repel by their poles.

He explained the electric effect by an effluvium, a fine material emanation released by rubbing that reaches out and draws bodies back as it returns. He showed that the effect was not carried by moving air, since a candle flame placed nearby did not flicker. He also noticed that rubbed amber held near a drop of water draws it into a cone.

The physics

Rubbing transfers charge between surfaces: the triboelectric effect. The charged body then attracts any neutral object, because its field polarizes the object. In a conductor free charges move; in an insulator molecules polarize. Either way, the near side acquires charge opposite to the source and the far side the same charge, and since the field is stronger on the near side, the net force is attractive. Gilbert’s claim that electrical attraction is always attraction is true for neutral objects; repulsion appears only after the object picks up charge of the same sign, an effect noted by later experimenters such as Niccolò Cabeo in 1629.

Derivation. A grounded or neutral conducting sphere in a uniform field \(E\) has induced dipole \(p=4\pi\varepsilon_0a^3E\) (from the boundary condition that the surface is equipotential). In a non-uniform field \(E(r)=q/(4\pi\varepsilon_0r^2)\), the force on an induced dipole is \(F=p\,|dE/dr|=4\pi\varepsilon_0a^3E\cdot2E/r\). Substituting gives the result. The steep \(r^{-5}\) dependence explains why rubbed amber must be held close.

Magnetic philosophy and the turning Earth

For the general reader. The last book of De Magnete leaves the laboratory. Gilbert argued that the Earth spins once a day rather than the whole heavens spinning around it, and suggested that magnetism is involved in that motion. He also denied that the stars sit on a single sphere. These claims went beyond his evidence, but they made magnetism part of the new astronomy, and Kepler built on them.

Gilbert’s arguments

In Book VI Gilbert held that the Earth’s magnetic axis is fixed in direction and that the Earth turns on its axis daily. It is absurd, he argued, that the vast heavens, with the stars at immense and varied distances, should whirl around the small Earth at inconceivable speeds every day; it is simpler that the Earth turns. He answered the classical objections, for instance that a turning Earth would fling off loose objects or leave the air behind. He described the Earth’s magnetic virtue as a kind of soul or form, the source of its motion and of its orderly orientation in space. On the larger Copernican question of the Earth’s orbit around the Sun he was largely silent in this book, though he was sympathetic to Copernicus. In his posthumous De Mundo he discussed the Moon as bound to the Earth by a mutual magnetic attraction and included a map of the Moon drawn without a telescope in the 1590s, with light areas he took to be seas.

Kepler’s magnetic celestial physics

Johannes Kepler, in Astronomia Nova (1609), proposed that the Sun turns and sends out a magnetic-like “motive virtue” that sweeps the planets around, and that each planet is a magnet whose axis keeps a fixed direction, so that it is alternately attracted and repelled by the Sun, producing an elliptical orbit. He cited Gilbert explicitly. The theory failed: a dipole’s field falls as \(r^{-3}\), not in the way the orbits require, and there was no mechanism for the sweeping force. But the idea that a physical force from the Sun governs the planets survived and led, through Newton, to universal gravitation.

The orb of virtue: how far a magnet reaches

For the general reader. Gilbert said that every magnet is surrounded by an “orb of virtue”, a region within which it acts on iron and outside which it does nothing. Strong stones have larger orbs. He did not measure how the force weakens with distance; the law was found in the eighteenth century. The answer explains his observations: a magnet’s pull dies away very quickly, so that it seems to have an edge.

What Gilbert observed

In Book II Gilbert described the orb of virtue as spherical around a spherical stone and larger for stronger or larger stones. He noted that a needle inside it is both turned and drawn, and that the turning (direction) acts at greater distances than the pulling (coition). He also found that interposed bodies such as paper, wood or glass do not block the magnetic virtue (Book II, chapter 21 and following).

Dipole forces

Derivation. On the axis of \(m_1\), \(B=\mu_0m_1/(2\pi r^3)\). Then \(U=-m_2B\) and \(F=-dU/dr\) has magnitude \(3\mu_0m_1m_2/(2\pi r^4)\). The torque on a needle at right angles to the field is \(m_2B\), falling only as \(r^{-3}\). Because the torque falls more slowly than the force, a needle at a distance is turned long after it has ceased to be noticeably drawn. This is exactly Gilbert’s observation that direction reaches further than coition.

Soft iron

A piece of soft iron has no permanent moment; the magnet induces one, \(m_{\text{ind}}\propto B\). Its energy is then \(U\propto-B^2\), so on the axis \(U\propto r^{-6}\) and \(F\propto r^{-7}\). A lodestone that lifts a nail in contact may barely stir it at a few centimetres. The steepness of this fall-off makes the orb of virtue appear to have a sharp edge: the radius at which the force drops below friction or weight.

Court physician and death, 1600–1603

In the year De Magnete appeared Gilbert was elected President of the College of Physicians, and in 1601 he became one of the physicians to Queen Elizabeth I. When the Queen died in March 1603, James I reappointed him. He had little time left. He died on 30 November 1603, most probably in the plague epidemic that struck London that year, aged about 59. He was buried in the chancel of Holy Trinity Church in Colchester, where a monument put up by his brothers survives.

He left his library, globes, instruments and mineral collection to the College of Physicians. They were destroyed when the College building burned in the Great Fire of London in 1666.

His other writings, notes on cosmology and meteorology, were gathered by his half-brother William Gilbert of Melford and presented to Henry, Prince of Wales. They were published in Amsterdam in 1651 as De Mundo Nostro Sublunari Philosophia Nova. The book rejects the four Aristotelian elements in favour of a single magnetic earth, treats comets, winds and the rainbow, and contains the Moon map.

Reception and legacy

De Magnete was reprinted in Stettin in 1628 and 1633 and read across Europe. Galileo, in his Dialogue Concerning the Two Chief World Systems (1632), praised Gilbert’s many new and true observations and wished only that he had been more of a mathematician. Kepler adopted his magnetism as a model for celestial forces. Francis Bacon, who knew Gilbert’s work, was more critical: he complained that Gilbert had built a whole philosophy on the lodestone. René Descartes devoted a long section of his Principles of Philosophy (1644) to explaining Gilbert’s magnetic phenomena by mechanical particles.

The English word “electricity” first appears in Thomas Browne’s Pseudodoxia Epidemica (1646), derived from Gilbert’s electricus. Later electrical work, from Otto von Guericke’s sulphur globe to Benjamin Franklin’s one-fluid theory, grew from his distinction between electrics and non-electrics.

Legacy

• Geomagnetism: the Earth as a magnet, the terrella model, the explanation of dip and the systematic study of variation. Gauss’s 1839 analysis confirmed that the field originates inside the Earth.
• Electricity: the word, the first instrument (the versorium), the first systematic list of electrics, and the separation of electric from magnetic attraction, which lasted until Hans Christian Ørsted’s discovery of 1820 reunited them.
• Method: one of the earliest books in natural philosophy to rest its case on repeatable experiments described in detail, a generation before Bacon’s programme and Galileo’s mechanics.
• Honours: the CGS unit of magnetomotive force, the gilbert; a lunar crater. The Gilbert Club, founded for the tercentenary, produced Silvanus Thompson’s 1900 translation.

Connections

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

Influenced by

• Peter Peregrinus of Maricourt
• Robert Norman

Influenced

• Carl Friedrich Gauss
• Galileo Galilei
• Johannes Kepler
• Otto von Guericke
• René Descartes
• Francis Bacon
• Henry Gellibrand

Colleagues and collaborators

• Edward Wright 1600

Also mentioned in this life

• Aristotle
• Nicolaus Copernicus
• Benjamin Franklin
• G. I. Taylor
• Edmond Halley
• Pierre-Simon Laplace
• Adrien-Marie Legendre
• Isaac Newton
• Hans Christian Ørsted

Fields

• magnetism 5 lives
• electricity 5 lives
• geomagnetism 3 lives
• medicine 8 lives

Sources and further reading

Biography

1. William Gilbert (physicist), Wikipedia.
2. Royal College of Physicians, Inspiring Physicians: William Gilbert (Munk’s Roll).
3. Gilbert, William, Complete Dictionary of Scientific Biography, via Encyclopedia.com.
4. William Gilbert, Encyclopaedia Britannica.
5. S. P. Thompson, William Gilbert, and Terrestrial Magnetism in the Time of Queen Elizabeth, London, 1903.
6. S. Pumfrey, Latitude and the Magnetic Earth, Icon Books, 2002.

Science

1. W. Gilbert, De Magnete, London, 1600. English translation by S. P. Thompson and the Gilbert Club, 1900: On the Magnet, Project Gutenberg.
2. W. Gilbert, On the Loadstone and Magnetic Bodies, trans. P. F. Mottelay, 1893 (Dover reprint).
3. De Magnete, Wikipedia.
4. Petrus Peregrinus, Epistola de magnete (1269).
5. R. Norman, The Newe Attractive, London, 1581.
6. H. Gellibrand, A Discourse Mathematical on the Variation of the Magneticall Needle, London, 1635.
7. C. F. Gauss, Allgemeine Theorie des Erdmagnetismus, in Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1838, Leipzig, 1839.
8. D. Jiles, Introduction to Magnetism and Magnetic Materials, CRC Press (domains, remanence, pole-piece forces).
9. R. T. Merrill, M. W. McElhinny and P. L. McFadden, The Magnetic Field of the Earth, Academic Press, 1996.
10. J. Plaice, William Gilbert compares electric bodies and magnetic bodies and William Gilbert calculates the magnetic declination.
11. J. L. Heilbron, Electricity in the 17th and 18th Centuries, University of California Press, 1979.