*By Mohsin Khan*

Emilie du Chatelet, regarded for too long as a footnote of history being a mistress of Voltaire, was a driven and passionate physicist, mathematician and translator. She derived the equation for kinetic energy by studying the work of Leibniz and created the only existing French translation of Newton’s *Principia*. Du Chatelet’s scientific work centred on research into the conservation of energy, combustion and light and Newtonian principles. She also contributed to the Enlightenment trend of thought in her literary work, whilst also tackling theology in a commentary of the Bible.

In 1706, Gabrielle Emilie Le Tonnelier de Breteuil was born into a ‘noblesse de robe’ family who recognized and developed her talents. It was decided that she lacked the necessary beauty for the eighteenth century marriage market, so her father ensured that she received the same classical education as her brothers; alongside learning how to ride, dance and fence. Importantly, and most unusually, she received extra lessons in mathematics and metaphysics. Aged 19, she was married to Florent-Claude, Marquis du Chatelet but after only five years, the couple informally separated. At 24, she had an affair with the Duc de Richelieu, who encouraged her to receive lessons in further mathematics so that she could understand Newton’s theories and by 27 she had returned to academic study. It was at this point that Emilie captured the heart of philosopher and writer Voltaire.

In 18th Century France, Newton’s ideas were extremely controversial. They were held up in contrast to the Cartesian scientific model; the theory espoused by the religious order that to a great extent controlled the French education system: the Jesuits. Both Du Chatelet and Voltaire sought to understand Newtonian theories and, at first, supported them – she, it seems, for scientific reasons, he for political. In 1738, Voltaire published the *Elements of the Philosophy of Newton* on the subject, but he wrote in the preface that du Chatelet was his co-author, recognising her important contribution to his intellectual creation. This work helped explain the discoveries made by Newton to the French public. It was a tremendous success, being well illustrated and not requiring alienating advanced knowledge of mathematics. In 1740, she published a work of her own, an integrative review of recent trends in science and philosophy, called *Institutions de Physique*, focusing on the works of Descartes, Leibniz and Newton, with a discussion of free will and theology.

By the time she wrote *Institutions*, du Chatelet had demurred in her support for Newtonian science. This, she wrote, was based on experimental observation, but her judgement also assumed the existence of confliciting scientific laws. Notably, she had found that Newton’s equations for kinetic energy appeared to be false. Newton had stated that ‘vis viva,’ ‘living force,’ (kinetic energy) was equal to the product of mass and velocity i.e. E = mv. Leibniz, however, suggested that kinetic energy was equal to the product of mass and velocity-squared, i.e. E = mv^2. He rationalized this with a thought experiment but did not conduct any actual trials to empirically prove this.

Du Chatelet read about experiments conducted by Willem Gravesande, who dropped weights onto a clay floor. If Newton was correct, as the velocity of descent increased, the depth that the object sank when it hit the ground should also increase by the same proportions. Gravesande – and du Chatelet, when she tested several of Newton’s theories herself – found that this was not the case.

In her review, she combined Gravesande’s results with Leibniz’s ideas, supporting the theory that kinetic energy is equal to mv^2. This is correct (at non-relativistic speeds); the only difference today being that we use the equation E = _mv^2, as our units are different to those used by Leibniz.

Du Chatelet also worked on the nature of fire and what later became known as infrared radiation. She submitted an essay on the topic to a *Grand Prix* contest. Though Euler won the competition, the French Academy of Science published her work, the *Dissertation sur la nature du feu*, in 1739. She wrote that heat and matter were made from the same substance and was also correct in describing infrared radiation: she suggested that the colour of a flame varies with the amount of heat given off.

As well as being an experimentalist and mathematician, Du Chatelet was also a translator. Du Chatelet’s most enduring contribution to science was her French translation of Newton’s *Principia Mathematica* which was reprinted in 1966 and remains the only French translation of *Principia*. She also wrote a commentary to accompany the translation from Latin, *Principes mathematiques de la philosophie naturelle*, re-expressing Newton’s incomprehensible geometric proofs with calculus and explaining the mathematics with refined prose and her own examples. Also, using the mechanics in *Principia*, she inserted a new derivation for conservation of energy. The translation was instrumental in spreading the ideas of Newton throughout France. It was completed in 1745, and was published ten years after her death.

Du Chatelet’s translated works outside of Science and Mathematics cover a myriad of subjects, including Mandeville’s *Fable of the Bees*; which she translated but also edited and noticeably inserted new material. She also translated the Greek tragedy *Oedipus Rex* into French. Besides poetry and drama compositions, she wrote a Biblical commentary, *Examens de la Bible*.

In philosophy, her work *Discours sur le Bonheur (a Treatise on Happiness)* defended her education and intellectual activities, alongside her passions for sexual affairs and gambling! Crucially, she highlighted the importance of education for women as the only means that women could overcome the restrictions that society placed upon them:

‘Of all the passions, the love of learning contributes the most to our happiness. [There lies] a passion from which an elevated soul is never entirely exempt, that of glory; learning is the only way to acquire glory for half of humanity, yet it is precisely this half which is deprived of the means of education, rendering impossible such a taste of glory.’

Becoming pregnant from an affair in her early 40’s, du Chatelet knew that childbirth would most likely be a death sentence. Desperate to finish her translation of *Principia* in time, she worked twenty-four hour days regularly throughout her pregnancy. She died from an embolism a few days after childbirth, at the age of 42.

**References:**

Bodanis. D, *Passionate Minds: The Great Enlightenment Love Affair *(London, 2006)

*http://www.pbs.org/wgbh/nova/einstein/ance-sq.html*

*http://muse.jhu.edu/journals/eighteenth_century_fiction/v019/19.3hutton.html*

*http://www.guardian.co.uk/science/2006/aug/04/peopleinscience.guardianweekly*

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