Émilie du Châtelet: A Life in Five Chapters

Chapter 1 · A Father Who Had Her Taught

Latin, mathematics and metaphysics, for a girl

1706 – 1733 · Paris · Versailles

Gabrielle Émilie Le Tonnelier de Breteuil was born in Paris in December 1706. Her father Louis Nicolas was Principal Secretary and Introducer of Ambassadors at the court of Louis XIV, and he did something unusual: he had his *daughter* educated.

She was taught Latin and Greek, which she read fluently — she is said to have translated the *Aeneid* — and German, Italian and English. She was taught mathematics, and she was taught metaphysics. Her father reportedly noticed her ability early and arranged for tutors.

This was not what happened to girls of her class, who were educated for marriage, conversation and the management of a household. Her mother is said to have disapproved strongly.

She was tall, awkward as a girl, and became a considerable figure at court: a serious gambler, an excellent horsewoman, fond of clothes and of the opera, and by every account extremely quick.

At nineteen she married the Marquis Florent-Claude du Châtelet, a soldier some twelve years older, who was largely absent on campaign and who tolerated — and in some accounts got on well with — the arrangements she made afterwards. They had three children.

At around twenty-six, having discharged what was expected of her, she returned seriously to mathematics, taking lessons from *Pierre-Louis Maupertuis* and then *Alexis Clairaut*, two of the best mathematicians in France.

And she ran into the walls. The *Académie des Sciences* did not admit women. The *Café Gradot*, where the mathematicians met and argued, did not admit women — the story is that she had a suit of men's clothes made and walked in, and was served.

“Judge me for my own merits, or lack of them, but do not look upon me as a mere appendage.”

— Émilie du Châtelet, in her correspondence

Why this matters

Du Châtelet's education was the result of one father's unusual decision, and it is the only reason a first-rate mind of that generation was trained at all.

You have the education and the doors that were shut. What would you ask her?

Ask Du Châtelet

• “Why did your father have you taught Latin and mathematics?”
• “Did you really get into the Café Gradot in men's clothes?”
• “What did the Academy's refusal actually cost you?”
• “How did you go back to mathematics at twenty-six?”
• “What did your mother make of it?”

Chapter 2 · Cirey

Twenty thousand books, and a laboratory in a country house

1733 – 1749 · Cirey-sur-Blaise · Champagne

In 1733 she met *Voltaire*, who was then in serious trouble with the authorities over his *Lettres philosophiques* and faced arrest.

She offered him refuge at the du Châtelet family château at *Cirey* in Champagne, a semi-ruined house on the family estate. Voltaire paid for its restoration. He lived there for about fifteen years.

What they built is remarkable, and it was hers. Cirey became a private research institution: a library of some *twenty thousand volumes* — comparable to a major university library of the period — laboratory rooms with apparatus imported from England and Holland, instruments, and a scientific correspondence reaching across Europe.

The working regime was severe. She rose late, worked until deep into the night, and reportedly plunged her hands into ice water to stay awake. Visitors complained that meals were at unpredictable hours and that one was expected to work.

The relationship with Voltaire was a genuine intellectual partnership, and it was competitive. He was the more famous by far; she was the better mathematician, and he said so — he wrote that she was a great man whose only fault was being a woman, which is a compliment with a substantial defect in it.

In 1738 the Académie des Sciences announced a prize essay competition on the *nature of fire*. Voltaire entered. Du Châtelet also entered — *secretly*, without telling him, working at night after he had gone to bed, because she disagreed with his approach.

Neither won. But the Academy was impressed enough to publish *both* essays, which made her one of the first women to have a scientific paper published under the Academy's imprint.

Her essay proposed, among other things, that different colours of light carry *different heating powers* — which is essentially right, and was demonstrated by Herschel's discovery of infrared sixty years later.

Why this matters

Cirey was a private scientific institution with a twenty-thousand-volume library and imported apparatus, assembled by a woman excluded from every public one.

You have the library, the ice water and the secret essay. What is your question?

Ask Du Châtelet

• “What did you build at Cirey?”
• “Why enter the fire competition without telling Voltaire?”
• “What did you propose about the colours of light?”
• “How would you describe your partnership with Voltaire?”
• “What did Voltaire mean by calling you a great man?”

Chapter 3 · Vis Viva

Brass balls dropped into clay, and the square of the speed

1740 – 1741 · Cirey · Paris

There was a long-running argument in European physics about what quantity measures the *force* of a moving body.

The *Newtonians* — which in France meant almost everyone who mattered — said it is the *mass times the velocity*: the quantity Descartes had called the quantity of motion, and which we call momentum.

The *Leibnizians* said it is the *vis viva*, the living force: mass times the *square* of the velocity.

The two camps had been arguing for decades and it looked like a dispute about definitions.

Du Châtelet's contribution was to bring *evidence*. She marshalled the experiments of the Dutch natural philosopher *Willem 's Gravesande*, who had dropped brass balls of known mass from known heights into a bed of soft clay and measured how deep they sank.

The result: the depth of the impression goes as the *square of the speed*, not as the speed. A ball moving twice as fast makes an impression four times as deep, not twice as deep.

So if you are asking what a moving body can *do* — how much deformation it can produce, how much work it can accomplish — the answer goes as v², and the Newtonian quantity does not describe it.

She published the argument in her *Institutions de Physique* in 1740 and defended it in a public exchange with *Jean-Jacques Dortous de Mairan*, secretary of the Academy, in 1741. She had the better of it, and contemporaries said so.

The resolution, understood later, is that *both* quantities are conserved and they describe *different things*. Momentum is conserved in collisions. The v² quantity — with a factor of one half — is *kinetic energy*, and it is the one that measures capacity to do work.

The factor of v² in ½mv² is exactly the point she was arguing for.

Why this matters

Brass balls dropped into clay sink to a depth going as the square of the speed, which is the experimental evidence that kinetic energy rather than momentum measures capacity to do work.

You have the clay, the squares and the argument in print. What would you ask?

Ask Du Châtelet

• “What do the balls in the clay actually show?”
• “Why did the Newtonians resist the v² quantity?”
• “Are both quantities conserved?”
• “What was it like arguing publicly with the Academy's secretary?”
• “Was this a dispute about words or about the world?”

Chapter 4 · Translating Newton

Not a translation — a commentary that argues

1745 – 1749 · Cirey · Lunéville

Newton's *Principia* was written in Latin, in a deliberately difficult geometrical style, and there was no French edition. That is a significant obstacle in a country where Cartesian physics was still taught and where Newtonianism had to be argued for.

Du Châtelet undertook it, from about 1745.

And what she produced is not a translation. It is a translation *plus* an extensive *commentaire*, in which she explains the arguments, sets out the mathematics in the more modern analytical notation of Leibniz and the Bernoullis rather than Newton's geometry, and — crucially — incorporates the substantial work done on Newtonian mechanics in the sixty years *since* the *Principia*, particularly by Clairaut and the Bernoullis on the shape of the Earth and the motion of the Moon.

So a French reader gets Newton, made intelligible, brought up to date, and set out in a notation they can actually calculate with.

Doing that requires understanding the *Principia* well enough to reconstruct its arguments in a different mathematical language and to judge which later work is sound. It is not a service task.

In 1748, at forty-one, she began a relationship with the poet *Jean-François de Saint-Lambert*, and in 1749 found herself pregnant.

She was terrified, and said so plainly in letters: a woman of forty-two in 1749 had a serious chance of dying in childbirth, and she knew it.

She worked at the *Principia* through the pregnancy, at extraordinary speed and for very long hours, explicitly in order to finish it before the birth. She completed the manuscript and deposited it with the King's librarian.

She gave birth to a daughter on 4 September 1749, and died six days later, on 10 September, aged forty-two. The child died shortly afterwards.

Voltaire wrote that he had lost half of himself.

Why this matters

Du Châtelet's Principia is a translation with a commentary that recasts Newton's geometry into analytical notation and incorporates sixty years of later work — a scholarly achievement in its own right.

You have the commentary and the race against the birth. What is your question?

Ask Du Châtelet

• “Why was a French Principia needed at all?”
• “What did you add beyond the translation?”
• “Why rewrite Newton's geometry as analysis?”
• “Did you expect to survive the birth?”
• “What made you work at that pace?”

Chapter 5 · A Mere Appendage

What was remembered, and what was not

1759 – present · Paris

The *Principia* translation was published in full in 1759, ten years after her death, with a preface by Voltaire. It remains the *standard French edition* — still in print, still cited, two hundred and sixty years later.

Its publication was timed to coincide with the return of Halley's comet, whose date Clairaut had predicted using exactly the Newtonian mechanics the book presented. That gave French Newtonianism a very public confirmation.

For the next two centuries she was remembered, when she was remembered at all, as *Voltaire's mistress* — a brilliant and eccentric woman attached to a great writer. The physics was treated as an accomplishment rather than as work, and the translation as a service to Newton rather than a contribution.

Serious reassessment came in the twentieth century, and particularly since the 1970s.

The verdict now is fairly clear. She was right about vis viva, against the scientific establishment of her country, and the quantity she defended is kinetic energy. Her *Institutions de Physique* is a genuine attempt to synthesise Newtonian mechanics with Leibnizian metaphysics — an unfashionable project that turned out to contain the more durable insight about energy. And the *Principia* commentary is a scholarly achievement of the first rank.

She also wrote a *Discours sur le bonheur*, on happiness, which argues among other things that study is the resource available to a woman excluded from ambition, power and the ordinary careers, and that it is a good one.

Her own line on the matter, from her correspondence, stands as well as anything: *judge me for my own merits, or lack of them, but do not look upon me as a mere appendage*.

She is one of the clearest cases in history of first-rate science done entirely *outside* the institutions that existed to support it — by someone those institutions would not admit.

Why this matters

Du Châtelet was remembered as Voltaire's companion for two centuries, and the reassessment of her work as science is largely a development of the last fifty years.

You have the standard edition and the two centuries of being an appendage. What would you ask?

Ask Du Châtelet

• “Why is your translation still the standard one?”
• “How would you like to be described?”
• “What does your Discours say about study?”
• “What could you have done inside the Academy?”
• “Which of your works should be read first?”

What Du Châtelet changed

The quantity du Châtelet defended is kinetic energy, and the factor of v² in ½mv² is the point she was arguing for. Her Principia translation carried Newton into French thought and is still the standard French edition nearly three centuries later. Her career is one of the clearest cases of first-rate science done entirely outside the institutions that existed to support it — by someone those institutions would not admit.

A debate that continues

Du Châtelet was remembered chiefly as Voltaire's companion for two centuries, and the reassessment of the Institutions de Physique and the Principia commentary as substantive scientific work is largely a development of the last fifty years.

Keep exploring — ask Du Châtelet

• “Which problem in the Principia would you have taken up next?”
• “Is a translation ever only a translation?”
• “What should a woman without institutions do?”

Related lives

• Voltaire — Philosophe · Voice of the Enlightenment
• Isaac Newton — Lucasian Professor · President of the Royal Society
• James Prescott Joule — Who Weighed Heat Against Work
• Ada Lovelace — Enchantress of Number · First Programmer

Related themes

Kinetic energy · Conservation laws · Women excluded from science