The French translation of Newton’s Principia that scientists use today was completed in 1749 by a marquise working against the clock, convinced she would not survive the birth of her fourth child. She was right. Émilie du Châtelet finished the manuscript, deposited it with the Royal Librarian, and died six days after the delivery, aged forty two.
Two hundred and seventy years later, it remains the only complete French translation of the Principia, and it is not a period curiosity. It is still the edition French speaking physicists and historians reach for, because it does considerably more than translate.
An Unusual Education
Gabrielle Émilie Le Tonnelier de Breteuil was born in Paris in 1706 into a family at court. Her father, in a decision that was atypical for the period, provided her with tutors in Latin, Greek, Italian, and English, and did not stop when the mathematics began.
She married the Marquis du Châtelet at nineteen, had three children, and returned to serious study in her mid twenties. Her teachers included Pierre Louis Maupertuis and Alexis Clairaut, two of the leading mathematicians in France and both committed Newtonians, which was still a minority position there.
From 1734 she lived largely at the château of Cirey in Champagne, which she and Voltaire turned into a working establishment with a library of some twenty one thousand volumes and rooms fitted out for experiments. The arrangement was a scientific partnership as much as a domestic one, and the two of them competed as well as collaborated.
France Against Newton
Understanding what du Châtelet did requires knowing that Newtonian physics was not accepted in France. The dominant system was Descartes’s, in which space is filled with a subtle matter forming vortices that carry the planets around, and all action is by direct contact.
Newtonian gravity, a force acting instantaneously across empty space with no mechanism, struck French natural philosophers as a return to the occult qualities that the mechanical philosophy had been designed to eliminate. Fontenelle, the long serving secretary of the Académie des Sciences, defended Cartesian vortices into the 1750s.
The dispute had a decidable case. Newtonian theory predicts that a rotating Earth should bulge at the equator and flatten at the poles. Cartesian vortex theory implied the opposite, an Earth elongated towards the poles. Expeditions were sent to Lapland under Maupertuis and to Peru to measure the length of a degree of latitude at high and low latitudes. The results favoured Newton.
Du Châtelet worked on this material as it happened, and both she and Voltaire submitted essays to the Académie’s 1737 prize competition on the nature of fire. Neither won, but hers was published, and it contains a striking suggestion: that light and radiant heat are the same kind of thing, and that heat radiation might be detectable beyond the visible colours. Infrared radiation was identified by William Herschel in 1800.
Institutions de Physique
In 1740 she published Institutions de Physique, presented as a textbook for her thirteen year old son. It is a good deal more ambitious than that description suggests.
The book sets out to reconcile three systems that were usually treated as incompatible: Newton’s mathematical account of forces, Descartes’s mechanics, and Leibniz’s metaphysics, including the principle of sufficient reason and the conservation of vis viva. It was one of the main routes by which Leibnizian ideas entered French scientific discussion, and it was translated into German and Italian.
The Vis Viva Dispute
The most substantial physics in her work concerns a question that had been argued since the 1680s. What is the correct measure of the quantity of motion in a moving body?
The Newtonian and Cartesian answer was mass times velocity, the quantity we call momentum. The Leibnizian answer was mass times velocity squared, vis viva or living force, which corresponds to what we call kinetic energy.
Du Châtelet argued for the Leibnizian measure and, crucially, marshalled experimental support. Willem ‘s Gravesande in Leiden had dropped brass spheres from various heights into soft clay and measured the depth of the impressions. A ball dropped from four times the height, arriving at twice the speed, does not make a hole twice as deep. It makes one four times as deep. The effect scales with the square of the velocity.
She published this argument and defended it in a public exchange with Dortous de Mairan, the secretary of the Académie, in 1741. The dispute is often written up as a confusion that was later dissolved when physicists realised that momentum and energy are both real and conserved in different senses. That is true, but it undersells her position. She was arguing that a quantity proportional to mv² is physically fundamental, at a time when energy had no place in mechanics at all, and she was right.
The Translation
She began work on the Principia around 1745, and the finished book is in two parts.
The first is a complete French translation of Newton’s Latin, including the geometric proofs. This alone was a considerable task, since Newton’s presentation is deliberately austere and his Latin is compressed.
The second is her Commentaire, which runs to nearly two hundred pages and is where the real work lies. It contains:
- An explanation of the Principia’s main results restated in the analytical calculus of Leibniz and the Bernoullis, rather than Newton’s geometry. This is what made the book usable, since continental mathematicians worked in that notation and Newton’s proofs were nearly unreadable to them
- A summary of the analytical solution to the system of the world, incorporating the work Clairaut had done on the three body problem and the motion of the Moon
- Her own account of the shape of the Earth, of tides, and of the precession of the equinoxes
The result is not a translation with notes. It is a bridge between two mathematical traditions that had been diverging for half a century since the calculus priority dispute poisoned relations between British and continental mathematics.
Our edition of the Principia presents Newton’s three books as he structured them, which is the text du Châtelet worked from, and Halley’s role in getting it printed in the first place is a reminder of how narrowly the whole tradition survived its publication.
The Race Against Time
In 1748 she began a relationship with the poet Saint Lambert and became pregnant the following year. For a woman of forty two in the eighteenth century this was a serious danger, and she said plainly that she expected to die.
She worked on the translation through the pregnancy, reportedly for long hours daily, and completed the manuscript in the late summer of 1749. She gave birth to a daughter on 4 September and died of a pulmonary embolism on 10 September. The child died shortly afterwards.
Voltaire, who had been present, wrote that he had not lost a mistress but half of himself, a soul for which his own had been made.
The book appeared in a partial edition in 1756 and in full in 1759, with a preface by Voltaire. The timing was fortunate. Halley’s comet returned on schedule in early 1759, precisely as Newtonian theory required, and Clairaut had calculated the date of its perihelion in advance. Newtonian physics arrived in French translation at the exact moment its most spectacular prediction came true.
The Frontispiece
Voltaire’s Éléments de la philosophie de Newton of 1738, written with her assistance, carries one of the most quoted frontispieces in the history of science publishing. Voltaire sits writing at a desk. Above him Newton looks down from the clouds, and a beam of light descends from Newton and strikes a mirror held by du Châtelet, who directs it onto Voltaire’s page.
The image is usually read as a compliment, and it is one. It also puts her in the position of the intermediary rather than the source, which was how the eighteenth century preferred to think of her and is not what the record supports. This is the kind of visual argument about who counts as a scientist that runs through Portraying Science, our collection of the images through which science has presented its practitioners.
What She Left
Her reputation suffered for two centuries from being written about mainly as Voltaire’s companion, and the recovery has been recent. The evidence is not ambiguous: an original contribution to the vis viva question, an early suggestion of infrared radiation, a textbook that brought Leibniz into French physics, and a translation with commentary that remains standard.
The last of these is the most unusual achievement. Scientific translations are typically superseded within a generation. Hers has not been replaced because nobody has produced anything better, and because the commentary did work that the original did not do: it made Newton’s results available in the mathematical language the rest of Europe was actually using.
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