Charles-Augustin de Coulomb

Chapter 1 · Nine Years at Fort Bourbon

An engineering education that cost his health

1736 – 1772 · Angoulême · Mézières · Martinique

Charles-Augustin de Coulomb was born at Angoulême in June 1736, into a family of some standing; his father lost the family money in speculation and the household moved to Montpellier.

He trained at the *École du génie* at Mézières, the French school of military engineering — a serious institution that taught mathematics, statics and the analysis of structures, and which produced a remarkable number of scientists.

In 1764 he was posted to *Martinique* to supervise the construction of *Fort Bourbon*.

He was there nine years. He had responsibility for the design and execution of a major fortification in a tropical climate, with a workforce that included enslaved people, in conditions of disease and heat that were lethal to Europeans.

It ruined his health permanently. He suffered recurrent illness for the rest of his life.

And it was an apprenticeship in *what materials actually do*. A designer of fortifications has to know how a masonry wall fails, how earth behaves when it is retained, how a beam breaks, how much friction there is between surfaces. These are not abstract questions; getting them wrong brings down a wall and kills people.

His first major memoir, in 1773, is *on the application of the rules of maxima and minima to problems of statics relating to architecture*. It treats the failure of masonry piers, the design of retaining walls and the stability of arches, and it is a founding document of structural engineering.

He came to physics as an engineer, and the habits show throughout: check the instrument, quote the range you actually measured over, and do not speculate past the data.

“The repulsive force between two small spheres charged with the same sort of electricity is in the inverse ratio of the squares of the distances.”

— Charles-Augustin de Coulomb, Premier mémoire sur l'électricité et le magnétisme (1785)

Why this matters

Coulomb learned physics as a military engineer responsible for structures that would kill people if they failed, and the caution shows in everything he published.

You have Fort Bourbon and the ruined health. What would you ask him?

Ask Coulomb

• “What did nine years in Martinique cost you?”
• “What does an engineer have to know that a physicist does not?”
• “What was the École du génie like?”
• “How does a masonry pier actually fail?”
• “Who built Fort Bourbon?”

Chapter 2 · The Theory of Friction

A prize memoir that stood for a century and a half

1779 – 1781 · Rochefort · Paris

In 1781 Coulomb won the grand prize of the Académie des Sciences for a memoir on the *theory of simple machines*, and its core is friction.

He had done the experimental work at the naval dockyard at Rochefort, dragging loaded sledges of various materials over various surfaces, measuring the forces required, and varying every parameter he could.

What he established has three parts and they are still taught in engineering.

The frictional force is proportional to the *normal force* pressing the surfaces together. Double the load, double the friction.

It is *independent of the apparent area of contact*. This is counter-intuitive — a wider sledge does not drag harder — and the explanation is that real contact occurs only at microscopic asperities, whose total area depends on load rather than on apparent area.

And *static friction* exceeds *kinetic friction*: it takes more force to start something sliding than to keep it sliding. Everybody who has pushed furniture knows this, and Coulomb quantified it.

He also distinguished friction between dry surfaces from the resistance in a lubricated bearing, and worked on the stiffness of ropes.

This is now called *Coulomb friction*, and it remained the standard account for about a century and a half — arguably longer, since it is still what any engineer uses for a first calculation.

He thought it as important as the electrical work, and said so. Friction determines whether a machine works, how much power is lost, whether a brake holds, whether a rope slips, whether a wall stands.

It is worth noticing that the most-used result of his career is the unglamorous one.

Why this matters

Friction is independent of apparent contact area because real contact happens only at microscopic high points — Coulomb established this by dragging sledges around a naval dockyard.

You have the sledges and the three rules. What is your question?

Ask Coulomb

• “Why doesn't a wider block have more friction?”
• “Why is it harder to start something sliding than to keep it going?”
• “How do you measure friction with eighteenth-century equipment?”
• “Do you consider the friction work your best?”
• “Where does your friction law break down?”

Chapter 3 · Prove the Instrument First

The torsion balance, and why it can be trusted

1784 · Paris

Coulomb wanted to measure a force too small for any balance then existing.

His instrument is the *torsion balance*: a light horizontal arm suspended by a fine wire, so that a tiny sideways force on the end of the arm twists the wire, and the *angle* of twist is read off a scale.

The idea is not original to him — Michell had proposed something similar — and the instrument is useless unless one thing is known: *how the wire's restoring force depends on the angle*.

If you do not know that relationship, an angle tells you nothing about a force.

So Coulomb did the preliminary work first, and published it separately in 1784.

He hung a weight from a wire, twisted it, and let it *oscillate* — turning back and forth like a torsional pendulum. He timed the oscillations.

The key result: the *period of oscillation is independent of the amplitude*. Twist it a little or twist it a lot, and each swing takes the same time.

That is the signature of a restoring force *exactly proportional to the displacement* — the same relationship that makes a pendulum isochronous. If the wire's restoring couple grew faster or slower than the angle, the period would depend on how far you twisted it.

He also established how the stiffness depends on the wire's length, diameter and material.

Only *then* did he trust it with a question.

This is the part that makes his electrical work a measurement rather than an assertion, and it is a general principle: an instrument must be calibrated against something known before its readings mean anything.

Why this matters

Coulomb established that his wire's restoring force is exactly proportional to the twist before using it, which is what makes an angle on a scale into a measurement of force.

You have the oscillating wire and the constant period. What would you ask?

Ask Coulomb

• “Why does a constant period prove the force is proportional to the angle?”
• “What would happen if the wire did not behave that way?”
• “How small a force can the balance measure?”
• “Why publish the wire work separately?”
• “Should every instrument be proved before it is used?”

Chapter 4 · Halve the Distance, Quadruple the Force

The memoirs of 1785

1785 – 1789 · Paris

With the instrument proved, Coulomb put it to the question.

He fixed a small gilt pith ball inside the apparatus, and mounted another on the end of the suspended arm. He charged them both with the same kind of electricity so that they *repelled*. The arm swung away, twisting the wire, until the electrical repulsion balanced the wire's restoring couple.

Read the angle, and you have the force.

Then change the separation and read again.

The result, in the first memoir of 1785: *halve the separation and the force becomes four times as great*. Reduce it to a third and the force is nine times. The force varies as the *inverse square* of the distance.

In the second memoir he obtained the same inverse-square dependence for *magnetic poles*, using a different method — timing the oscillations of a magnetised needle in the field of another magnet, since magnetic poles cannot be isolated and separated the way charges can.

He also showed that the force is proportional to the *product of the two charges*. To vary a charge in a known way without any means of measuring charge, he used a beautiful trick: touch a charged sphere to an identical uncharged one, and by symmetry the charge divides *equally*. Repeat, and you have a half, a quarter, an eighth.

He further measured how charge *leaks away* along imperfect insulating supports and through damp air — a source of error he had to characterise and fight, and which limited his accuracy.

Henry Cavendish had established the inverse-square law more precisely around 1771, by an entirely different and more elegant method, and had left it in a drawer where Maxwell found it a century later. Coulomb published, and the law and the unit carry his name.

He worked with *two electric fluids*, vitreous and resinous — and said plainly that he used them as a way of calculating rather than as a claim about what exists.

Why this matters

Coulomb varied charge without being able to measure it, by touching a charged sphere to an identical uncharged one so the charge divided in half by symmetry.

You have the repelling balls and the halved charges. What is your question?

Ask Coulomb

• “How do you halve a charge you cannot measure?”
• “Why measure magnetism by oscillation instead?”
• “How much did leakage limit your accuracy?”
• “Cavendish had the law first — does that matter?”
• “What did you think electricity actually was?”

Chapter 5 · The Revolution, and a Unit

Retirement, return, and 1881

1789 – 1806 and after · Blois · Paris

Coulomb was an officer of the *ancien régime* and a member of the Académie des Sciences, both dangerous positions after 1789.

He resigned his engineering appointments, and when the Académie was suppressed in 1793 he retired to a house at Blois, near Orléans, and stayed out of Paris through the Terror. Several of his colleagues did not survive it; Lavoisier was guillotined in 1794.

He was recalled in 1795 when the Institut de France was established, and served on the commission that determined the new *metric* system of weights and measures — one of the more constructive results of the Revolution.

Under Napoleon he became an inspector-general of public instruction, and travelled the country organising the new lycées, which occupied his final years.

His personal life is unusual for the period. He lived for years with *Louise Françoise LeProust Desormeaux* and had two sons by her, and married her formally in 1802 — legal changes during the Revolution having made it possible. He legitimised both boys.

He died in Paris in August 1806, aged seventy, of a fever.

In 1881, at the International Congress of Electricians, the unit of *electric charge* was named the *coulomb*.

That is a slightly odd memorial, because Coulomb had no concept of a quantity of charge in the modern sense. He worked in relative charges and ratios, with two hypothetical fluids he did not believe in.

What he actually did was establish, by measurement over a real range, that a force falls off as the inverse square — and prove his instrument first. The whole of electrostatics is built on that law, and Poisson, Gauss and Maxwell built the mathematical theory of fields on top of it.

His friction theory, meanwhile, is still what an engineer uses on a Tuesday.

Why this matters

Coulomb established a law by measurement over a range he had actually covered, and refused to speculate about what electricity is — which is why the law outlived every theory of his period.

You have the Terror, the metric commission and the unit. What would you ask?

Ask Coulomb

• “How did you survive the Terror when Lavoisier did not?”
• “What did the metric commission actually decide?”
• “Why refuse to say what electricity is?”
• “What would you make of a unit of charge named after you?”
• “Which mattered more — the fort, the friction or the force?”

What Coulomb changed

The inverse-square law of electrostatics is the foundation of the whole of electrical theory, and the unit of charge carries Coulomb's name; Poisson, Gauss and Maxwell built the mathematics of fields on top of it. His theory of dry friction stood as the standard account for a century and a half and is still what an engineer uses for a first calculation.

A debate that continues

Henry Cavendish had established the inverse-square law more precisely around 1771 by a more elegant method and left it unpublished, so the attribution is an accident of publication rather than of priority.

Keep exploring — ask Coulomb

• “Which of your instruments took longest to trust?”
• “What is the honest range of a measurement?”
• “Would you rather be remembered for friction?”

Related lives

• Henry Cavendish — Who Made Acid Out of Air
• Alessandro Volta — Who Built A Battery Without A Frog
• Michael Faraday — Discoverer of Electromagnetic Induction
• James Clerk Maxwell — Who Bound Light to Electromagnetism

Related themes

Electrostatic force · Friction · Measurement and instruments