Châtelet

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chatelet I. Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. – Isaac Newton

“I still don’t understand how it is that these ‘physical sciences’ you study are so important.”

Émilie, the Marquise du Châtelet looked up from her book, stifling a sigh, and smiled at her husband. It was not his fault that he lacked imagination. “Well, consider Newton’s equations regarding gravitational forces. They will, eventually, tell us how fast things will fall if you drop them, but they can also tell us a lot about how the planets orbit the sun, and how the moon orbits the earth. Everything is falling in space, you know, which is why gravity is important.”

The Marquis did not look convinced. “I don’t doubt that this is interesting, and of course it is good to know more about how creation works, but is there any practical application? Do we really need to know how fast things fall?”

Émilie considered her husband again. “My dear Marquis, you are a soldier. Surely you have noticed how when a musket is fired, its path through the air describes an arc? Knowing how fast it will fall as it travels forward, and where the end of that arc will be, tells you how to aim the musket. Is that not a practical application?”

Florent-Claude frowned. “Well, yes – but if I had to stand there and calculate the effect of gravity on the bullet’s flight before I pulled the trigger, I would never fire my weapon at all. Besides, good aim is as much about having a good eye as anything else.”

“But that good eye you describe is simply you unconsciously calculating the path of the bullet. You may not be able to show its arc on paper, but you have learned by experience to accommodate gravity, to fire a little higher, perhaps, than your target, depending on how far away you are. You are a better student of the physical sciences than you realise.”

Her husband laughed. “And yet, I fire my musket without once thinking of a number – and I think that were we to shoot against each other in a competition, all your knowledge of mathematics would not prove you a better shot than I.”

Émilie smiled, a little reluctantly. “Indeed not. There is a matter of muscular knowledge, for one thing, and knowing the initial velocity of the bullet, which I do not – and the small defects in any machine, which its master knows and a borrower would not. But I think if you were to pit me against an absolute beginner, my knowledge of force and velocity and gravity would stand me in good stead, and I would shoot better than him, at least.”

Florent-Claude patted her hand, kindly. “Indeed, I think my prodigy of a wife would fare far better than a beginner in many fields, though I’m not sure if it would be her knowledge of physics that made it so.”

Émilie shook her head, impatiently. “Another example, then. Newton’s first law tells us that an object that is moving at a constant speed and in a straight line – much like this carriage we now travel in – will continue to do so, unless stopped by an external force.”

“Such as highwaymen?”

“Not precisely. But think what would happen if the carriage hit a rock, and stopped suddenly. What would happen to us, travelling inside the carriage?”

Florent-Claude frowned. “By your logic we should stop. But that makes no sense – we would be flung forward, would we not?”

She smiled her approval. “You are quite correct – but we would not be flung, as you say. It is simply that we, like the carriage, are travelling at a constant speed, and so if the carriage hits a rock and stops, and nothing stops us, we will keep travelling forward until either we collide with something, or gravity pulls us to the ground. This creates the sensation of being flung, but in fact, we are simply continuing our journey a little way without the carriage.”

“But surely this is a matter of observation? We hardly need calculations to know that if the carriage stops, we will land on the floor.”

“Ah, but that is precisely the point. A scientist’s job is to observe, and to consider, and to observe again. Only after making observations can he begin to formulate the rules which underlie the constants of the universe.”

Her husband settled back in his seat opposite her. “A noble goal. But I am still not certain that I see any practical application for it.” He shrugged. “Still, my dear, it makes me very proud to know that my beautiful wife has had her essay on the properties of fire published by the Paris Academy, even if I did not understand three words in ten. Study the universe, if that gives you pleasure. I am content to be the moon in your orbit.”

Émilie leaned forward to squeeze his hands in genuine affection. “You give me far more than the moon, my dear. You give me the freedom to use my mind. And that is indeed a very great pleasure.”

Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, was a lady of many accomplishments. She sang beautifully, moved gracefully, and danced like an angel. She knew how to dress stylishly, to flirt with charm and modesty, and converse with wit and good taste. She also spoke Latin, Greek, German, Italian and English, knew how to fence and to dress like a man, was a keen student of mathematics and astronomy, and had mastered the new calculus of Newton. The only accomplishment that she had never mastered was the art of pretending to be stupid.

Her father, conveniently forgetting that it was his own salons and tutors that had guided Émilie’s first steps in these unwomanly achievements, had been heard to complain that she frightened away suitors with her intelligence. But she had, in the end, caught the one that mattered – the Marquis Florent-Claude du Chastellet-Lomont, a member of the upper nobility and a King’s Musketeer; a man whose wits were no match for hers, but a kind man nonetheless, and both proud and indulgent of his clever wife.

Émilie knew that she was very fortunate in her husband, and so she took care to be kind to him in turn, bearing him the proper number of children, exercising her connections to advance his career, managing his estates when he was engaged in military affairs, and being as discreet in her love affairs as her temperament would allow.

Naturally, when Florent-Claude asked her to come with him to Paris for the celebrations surrounding the birth of the royal princess, she agreed, even though this meant interrupting some very interesting experiments involving pendulums and dynamics. It was not so great a sacrifice. Émilie’s studies of natural philosophy had not destroyed her enjoyment of the dancing and card playing that had delighted her as a young bride, and she was fond of Queen Marie.  Moreover, her dame de chambre had grown adept at sewing Émilie into her court finery while Madame read over her notes on the textbook she was writing for her son, or worked problems in geometry. Perhaps she could even make time to visit Gradot and meet with M. Maupertuis or M. Koenig while she was in Paris. This would be a great advantage. And even if it were not, the loss of a few weeks in her Academie at Cirey was a small price to pay to please so accommodating a husband.

She smiled at said husband again, and squeezed his hand briefly before releasing it, and returning to her book. The journey to Paris would take several days, and she could not afford to waste them.nd1

Nôtre Dame de Paris was not the most fashionable of churches, located as it was in one of the more dubious areas of the Île de la Cité. But the Queen had chosen to hear Mass there this Sunday, and the King, in an indulgent frame of mind, had taken a whim to accompany her, and suddenly the whole court, moved by a sudden excess of religious sensibility, had ordered up carriages and horses for the journey from Versailles.

The Mass was well-sung, and the cathedral pleasantly cool after twenty-two miles in a carriage under the hot August sun. After Mass was over, the Queen remained kneeling in prayer for some time in the chapel of Our Lady of Sorrows. It was an open secret among the ladies of the court that the Queen had come very close to death during the birth of Madame Septième, and was still unwell. Indeed, the only person who seemed unaware of this fact was the King.

Twenty two miles was not an insignificant distance, particularly over the bad roads, and few were willing to make the return journey to Versailles so soon. Those courtiers with houses in Paris dispersed to visit them; others chose to remain on the Île de la Cité, availing themselves of the more disreputable services provided in the area, even on a Sunday. The King himself had made plans to spend the the night, and perhaps even the week, at his Château at Vincennes.  As a palace, it was a little less comfortable than Versailles, but the hunting in the Bois de Vincennes was always a pleasure at this time of year, and a man deserved some reward for indulging his wife.

The King spent a few minutes in conversation with the Archbishop, then, seeing that the Queen was still deep in prayerful contemplation and likely to remain so for some time, charmed the Dean into a tour of the cathedral, taking a few of the more energetic and culturally-inclined courtiers with him. They could soon be heard conversing loudly overhead in the bell towers.

At last, the Queen’s devotions were complete. Émilie assisted her to rise, and she and the other ladies accompanied her out of the church, pausing for a moment to let their eyes adjust to the bright sunlight. The Queen sighed, then raised her skirts slightly to avoid the mud, leading the ladies towards the waiting carriages.

There was no warning – just a loud, wet thud behind them, and several ladies shrieked as their dresses were spattered with mud. Turning, Émilie gasped. A large cannonball lay in a muddy crater where the Queen had been standing only moments earlier. She heard shouts from above, and looked up. Several men were struggling together on the summit of the south tower, high above them, but as Émilie looked, she had the fleeting impression of movement from the balcony between the towers below. She frowned, watching closely for a moment, but nothing else stirred.

And then there was no time for further observation, because while the Queen herself remained standing, pale and stoic and unharmed, one of the younger ladies had taken one look at the cannonball and fainted, and two more were wringing their hands and weeping loudly. Émilie grimaced. She did not enjoy this sort of fuss, but evidently it was to be her fate for the next few minutes at least.

The more interesting question was, who had just tried to kill the Queen?

nd2

II. The alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d. – Isaac Newton

The answer, apparently, was Florent-Claude’s friend and fellow Musketeer, d’Artagnan.

Florent-Claude refused to believe it.

“He didn’t do it,” he exclaimed, pacing up and down through Émilie’s dressing room as her maid did her hair. “I know D’Artagnan, and he would never do something like that.”

Émilie frowned, sympathetically. “Were you with him at the time?”

Florent-Claude scowled. “No, unfortunately. I was on the stairs when it happened, and so I saw nothing at all. But he didn’t do it. D’Artagnan is a King’s Musketeer – he is absolutely loyal to the King.”

Émilie raised an eyebrow, but said nothing. The rumour she had heard that morning was that the Queen feared another pregnancy, and was considering barring the King from her bed. Loyalty to the King might not be the same as loyalty to the Queen for much longer… But surely this was an extreme reaction to what was, after all, still rumour?

“Do you know where the cannonball was dropped from?” she asked, suddenly. The mud was not unlike the clay she used for her pendulum experiments, but she had never swung or dropped anything from such a distance…

Florent-Claude did not, thankfully, realise that her mind had returned to mathematics. “Presumably the south tower. That’s where most of the men were, I think. Though how anyone could have got a cannonball up there unseen, I don’t know.”

“Hmm…” Émilie thought about this while her maid powdered her hair.

“I should like to see that crater again. If you mean the very top of that tower, I would have thought that it was a bit high. I mean, for an object to make that sort of crater… though perhaps the cannonball was heavier than it looks? I’d be interested to measure it, in any case. Can anyone climb the towers, do you know?”

Florent-Claude frowned. “My dear, you forget yourself. I realise that the physical sciences are important to you, but a man’s life is at stake, here. D’Artagnan will be executed if they can’t find out who really tried to kill the Queen. And if that doesn’t matter to you, recall that executing the wrong man will leave the Queen’s killer still at large. This is no time for mathematics.”

Émilie stood, and moved to take his hands in hers. “This is precisely the time for mathematics, my dear Marquis. I am almost certain I saw someone moving on that balcony below the towers, just after the cannonball fell. If I can prove, mathematically, that the ball could not have fallen from where d’Artagnan was standing, that it must have come from lower down, then your friend’s innocence will be proven.”

Florent-Claude’s face lightened, then he frowned again. “And if you prove, mathematically, that the ball did fall from where d’Artagnan stood?”

Émilie sighed. “Then your friend is no worse off than he is now. There were other people on that balcony, and one of them, surely, must have seen who actually dropped that cannonball. But I hope that we can exclude him entirely.”

nd3

The mud outside Nôtre Dame did not have quite the same consistency as clay, Émilie thought, and the cannonball was a little heavier than she had thought, though light enough to lift. Nobody seemed to care much about evidence, so she had Florent-Claude remove the ball from the crater and set it down a little way away while she measured the dimensions of the hole and calculated its capacity. She frowned. A single data point was not very revealing, especially since she didn’t know how well this particular mud tended to displace itself when a force was exerted on it.

Florent-Claude watched the proceedings with gloomy fascination. D’Artagnan could be executed as early as tomorrow, and if they were to prevent this, Émilie would need better proof of what she suspected.

“My dear, would you help me for one moment?”

Florent-Claude looked up, hopefully.

She smiled at him. “I need to compare the craters if the same ball is dropped from a different height. Would you be able to lift the ball just above your head, and drop it for me?”

“As my lady wife wishes.”   He lifted the ball with admirable ease, then dropped it, jumping back to avoid the mud spatter.

“Thank you.” She bent to measure the new crater, then stood. “Now we shall need the height of the gallery, and your height, and I shall be able to make my calculations. Though it really would be faster and easier to simply climb up there and drop another cannonball, to see what sort of a crater it made… No?”

Florent-Claude was already shaking his head. “They do not approve of laypersons climbing about the cathedral. Even the King had to exert all of his charm to be allowed up there.”

The King was not known for his charm, but Émilie took his point.  She sighed. “A pity. Well then, we shall simply have to do this the hard way. Perhaps, once I have shown the King my calculations, he will be able to obtain dispensation for me to test my theories.”

Florent-Claude looked so woebegone that she left it at that. She was not ashamed to admit to herself that a chance to measure the momentum and energy of falling objects from such a height would be something indeed! But Florent Claude was distressed enough already.

“Never mind, my dear Marquis. Now remind me, you are, what, 5.8 pieds du roi?”

Her husband looked bemused. “That’s right.”

“And the crater you created was 18 possons in capacity. The first crater was 430 possons, perhaps a touch more. We can take a cast and measure it later, though some of the mud might have replaced itself since yesterday. How much would that cannonball weigh, do you think?”

Florent-Claude almost smiled. “That, my dear, is a 24 livre cannonball. Standard army issue.”

Émilie made a note, nodding approvingly. “Excellent. And of course, the energy of the cannonball hitting the ground would be half the mass of the cannonball, multiplied by the square of its final velocity, whatever that is. It’s the energy of the ball falling that makes the crater, you understand.”

“Hardly at all, in fact, but you evidently do, so please continue.”

“Well, consider all that speed and weight from the falling ball. It doesn’t just stop – no more than we stop when our carriage does. Think – if we are thrown forward into the wall of the carriage, the energy of our movement transfers back to us. We bounce back towards the carriage seat, but we don’t quite bounce back as forcefully as we first went forward, because some of the energy of the collision was absorbed by the wall of the carriage, which will either buckle as we hit it and then recoil back into place, or perhaps break, and the rest was absorbed by our bodies.”

“As bruises?”

“More or less. And you see, when the cannonball hit the ground, the same thing happened. The energy of the fall had to go somewhere. The mud is not elastic enough to allow the cannonball to bounce, and the cannonball is too small, in the scheme of things, to make the earth itself move in any way we can discern, and so the majority of the cannonball’s energy is transferred into the mud, compacting it and pushing it out of the way. Hence, the crater.”

Florent-Claude looked at his wife with some amusement. “You are a fine tutor, my dear, but I fear your pupil is a dunce. I fail to see how this translates into a simple equation.”

Simple?  Émilie smiled and shook her head. “If you please, would you fetch my portable writing desk from the coach? I think I’m going to require more paper.” She took out a slide rule from her reticule, and began making calculations. Ideally, she would need the height of both the gargoyle balcony, and the tower above.

Her writing desk appeared in front of her, and a chair behind her. She sat down, gratefully, barely pausing in her work. The lower balcony must be around 24 toises high; the upper, nearly 36 toises – certainly enough of a difference to make the crater sizes distinct. Since Florent-Claude, even with his arms lifted above his head, was no more than one toise, the proper equation was quite simple – the volume of the first crater divided by that of the second. She didn’t even need a slide rule for that.

She smiled up into her husband’s anxious face. “It’s 24 toises,” she told him, with quiet triumph, and, when he still looked confused, she pointed at the cathedral. “Look. The tower is far higher than that. The ball must have been dropped from the balcony below.”

nd4

III. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Of course, nothing is ever that simple. Not at court, and certainly not if one has the misfortune to be female.

M. Maupertuis, damn his eyes, tried to wave away her calculations. “All this talk of energy and forces! I know you have been doing excellent work with pendulums and such, my dear Marquise, but on this occasion, you are letting your affection for your husband run away with you. As the speed is proportional to the square root of height, so the ratio between the heights should be equal to the square of the ratio of the craters.”

Émilie had already tried that equation, so she smiled sweetly at her former tutor. “Very well, then sir. Here are the volumes of the two craters. Would you care to calculate the true height of the fall?”

Maupertuis was neither stupid enough nor vain enough to trust that tone of voice. He received her notes and the slide rule with a suspicious gaze, then made the calculations.

“571 toises? But that is ridiculous! The cannonball did not fall from the clouds! No, you must certainly have measured the craters incorrectly.” But his voice was uncertain.

“I do know the basics of geometry,” Émilie retorted, trying to curb her irritation. “But by all means, feel free to measure the craters again yourself. I left a man guarding them, to prevent anyone destroying the data by walking on it. Obviously, the first crater was not preserved absolutely perfectly, but it is sufficient to make it very clear what height the cannonball could not possibly have fallen from. You might even repeat the experiment of dropping the ball from a lower height, as I did, if you do not trust my experimental skills.”

A throat was cleared behind them, and Émilie turned, then curtseyed very low. “Madame la Reine,” she said. Beside her, Maupertuis bowed equally deeply.

“Marquise. M. Maupertuis. Do I understand that there is some disagreement about the… mechanics of my attempted assassination yesterday?”

Émilie curtseyed again. “Madame, there is,” she said, just as Maupertuis spoke “No, Madame, of course not.”

The Queen raised an eyebrow. “That certainly does not sound like perfect agreement to me. I gather that the Marquise is not certain of the guilt of our prisoner?”

“Indeed, Madame, I am certain that he is not guilty. You know I have a strong interest in mathematics. I have been back to Nôtre Dame, and measured the crater where the ball fell, and I am absolutely convinced that it could not have been dropped from that tower.”

Maupertuis pursed his lips and shook his head, but said nothing.

The Queen eyed them both. “The crime was against my person,” she said, at last, “And so I have an interest in seeing that justice is done. I myself am not satisfied of M. d’Artagnan’s guilt – I do not believe he has any reason to harm me. But the King is adamant that it must have been him.”

“If you please, Madame, a simple experiment would settle the question, at least of where the cannonball came from. If we were to enter the cathedral and drop two cannonballs, one from the gargoyle balcony and one from the tower, we could see where each of them landed, and how deep the craters were, and compare these with the original crater. If d’Artagnan is innocent, we could establish this in a matter of moments.”

“And if he is guilty?”

Émilie bowed her head. “If we learn that the cannonball was dropped from the upper level and not the lower, his guilt would remain unproven. There are some questions even geometry cannot resolve.   But there is no possible way the cannonball could have fallen from the upper tower and left the crater it did. I would stake my own life on it.”

“It seems you are staking D’Artagnan’s.”

“On the contrary, Madame. His life is already at stake – my experiment cannot make matters worse. And it may spare an innocent man from execution.”

Marie Leszczyńska raised an eyebrow to indicate that she understood precisely what Émilie was not quite saying. Émilie gazed steadily back, and she smiled very slightly.

“Very well then. I shall speak to the King, and to the Archbishop. Far be it from me to condemn a man when proof of his innocence could so easily be obtained. You shall have your experiment.” She eyed Émilie drily. “I shall even permit you to have a servant stand somewhere safe, to calculate the time the cannonballs take to fall. I am well aware that a lead weight and soft mud are an irresistible delight to you.”

Émilie had the grace to blush.

nd5

What is left to say? The experiment was performed that very afternoon, and the resulting crater exonerated d’Artagnan completely. The Archbishop was disgusted with the proceedings, but the Queen placated him with a promise to pave the area surrounding the cathedral.

The King interrogated his gentlemen in waiting and courtiers to try to discover who had stood on the balcony of gargoyles that day, but nobody had seen anything of relevance. However, two nights later, a junior priest, distantly connected through his mother to the King’s former advisor, the Duc de Bourbon, disappeared from Nôtre Dame cathedral. No other proof of his responsibility was found, and he was never seen again, however his guilt was taken as certain.  The King, furious with all concerned, fined the Duc heavily for the supposed offense, and the Archbishop never did get his paving.

No further attempts were made on the Queen’s life.  Fearing another pregnancy, she banished the King from her bed, and he promptly turned his affections elsewhere.  The Queen consoled herself with music, religion, and acts of philanthropy, and became beloved by the French people, if not by her King and court.

Florent-Claude was prouder than ever of his clever wife. While he never grew to share her enthusiasm for geometry, he supported her in all her scientific endeavours, and never once complained about the cost to the estate, nor her unorthodox relationship with a certain controversial poet. D’Artagnan was a frequent visitor to the estate at Cirey, and even deigned to participate in the operas that Émilie wrote for the household, though his voice was not noted for its tunefulness.

The time taken for the cannonball to drop from the top tower was just under four seconds. It took three seconds to drop from the balcony of gargoyles. Neither of these numbers were exact enough for Émilie’s purposes, but the Archbishop absolutely refused to permit a second test, and the Queen, while amused, felt that there had been enough sacrilegious mathematics in the cathedral for one day.

Resigned, Émilie noted down her two imperfect numbers, along with the measurements she had surreptitiously taken with her barometer on both levels, and returned to Cirey and her experiments. Her barometric measurements allowed her to calculate more exact heights for each level of the cathedral, and her Nôtre Dame data, when plotted with the data from her other experiments, provided excellent graphical evidence for her theory that kinetic energy was proportional to the square of an object’s velocity, rather than being directly proportional to it.

The question of kinetic energy settled to her satisfaction, Émilie began work on a calculus proof of Newton’s theory of gravity.

It was a good life.

nd6

With profound thanks to Geoffrey Brent, mathematician and statistician extraordinaire, who checked my equations and helped me with the physics in this story.  A lot.  Because it is nearly 25 years since I last studied physics and it turns out that I remember almost nothing.  Any errors that remain are my own.

station

The StationChâtelet Station is situated on the north bank of the Seine, in the middle of medieval Paris.  The station, which opened in 1900, connects five Metro lines, and is itself connected to an RER station serving three more train lines.  Châtelet is named for the castle built on the site in the 12th century by Louis VI, as a final line of defense against any invaders from the North of Paris.  The castle was rendered somewhat obsolete for this purpose by a series of defensive walls, and was eventually pulled down by Napoleon early in the 19th century.The Mathematical Marquise I am not certain whether the Marquisate of Chastellet (the original spelling of the name du Châtelet) refers to this castle or another (the du Châtelet’s do seem to have had a house in Paris that was quite close to the current location of Châtelet station, but I don’t think it was the castle itself), however when I first Googled ‘châtelet’ to see what came up, I discovered this amazing woman.  Émilie du Châtelet was born in 1706, and died in 1749, and in between she did every single thing I referred to in this story and more.  While she is often remembered primarily as the lover of Voltaire (who described her, after her death, as ‘a great man, whose only fault was being a woman’), she really was a brilliant mathematician, whose great contribution to science was her translation, with commentary, of Newton’s Principia Mathematica.  This remains the standard French translation of Newton’s text today. Châtelet believed that Newton’s work was so fundamental to human understanding of the universe that it must be made accessible to the broadest possible audience, and so in addition to her mathematical commentary (which used the new calculus to create more elegant proofs of Newton’s theories), she also wrote a commentary designed to be intelligible to lay people.  And, while she was at it, she corrected some of Newton’s misconceptions about kinetic energy. It is hard for me, at least, to fathom the incredible importance of Newton’s work to du Châtelet and others of her generation.  Debates about mathematics became linked to matters of national pride – the English Newton versus the French Descartes and the German Liebniz – but for du Châtelet, all national allegiances bowed before her allegiance to geometry.  On finding herself pregnant at the dangerously advanced age of 43, du Châtelet determined to complete her work before what she saw as her inevitable death in childbirth; she worked on her translation and commentaries for eighteen hours a day, every day, throughout her pregnancy.  She did, in fact, die of a pulmonary embolism only a few days after giving birth (Voltaire wrote rather flippantly that the baby was born among the papers in her office), and some speculate that the burden of work that she imposed on herself during her pregnancy contributed to her death. In this story, I have hopefully not made too much of a hash of du Châtelet’s most famous discovery, that of conservation of kinetic energy (which, as far as my decidedly non-physics-compliant brain understands it, is essentially, the idea that the energy an object acquires while in motion has to go somewhere when it stops).  Prior to her work, kinetic energy was believed to be the same as momentum (which could be determined by multiplying the mass of an object by its velocity).  Du Châtelet spent a lot of time dropping various ball bearings into soft clay and measuring the amount of clay displaced, and worked out that kinetic energy was actually proportional to the square of velocity, not the product of it, with the equation being E_k = \frac{1}{2} mv^2.  (Obviously, I stole this experiment for the purposes of my story.) If this equation looks a little bit familiar to you, this might be because it’s closely related to Einstein’s famous equation E = mc 2 .  E stands for energy in both equations, as m stands for mass, and du Châtelet’s realisation that an object’s speed was proportional to the square of its velocity was a key step towards Einstein’s discovery of this equation. Émilie’s husband, Florent-Claude really was a King’s Musketeer, however he lived a full century after the Musketeers you are thinking of.  The D’Artagnan of this story was presumably a great-grandson of the original.  There is a contemporary Richelieu, too, who was a good friend of both Florent-Claude and Émilie; alas, I couldn’t find a way to bring him into the story. This story is set in 1737, just after the birth of Madame Septième, the youngest daughter of Louis XV and his Queen, Marie Leszczynska.  I took the liberty of shifting the publication of Émilie’s essay on fire back to just before this event, to give Florent-Claude something concrete to be proud of in his wife; the essay was actually written in 1738. And while I speak of historical liberties, I must also confess that while the area around Nôtre Dame was originally unpaved and difficult to walk through because of the mud, I can no longer find the reference to when it *was* finally paved, which is most frustrating.  I believe this occurred in the time either of Napoleon I or of Louis XV, as they both did fairly major building works in Paris, but if I am wrong and it was paved earlier, we shall simply have to assume that Louis XIV’s (documented!) neglect of Paris had been so egregious that he had allowed the citizens of Paris to carry off the paving stones near Nôtre Dame for their own use, leaving the area around the cathedral muddy and unpaved and ready to provide mathematically interesting craters at the drop of a cannonball… If you would like to read more about Émilie du Châtelet, there is a good brief biography online at Project Continua, and I highly recommend the biography by Judith P. Zinsser.  And if you would like to read her translation of Newton’s Principia Mathematica, it is available here.The illustrations for this story are a detail from The Churches of Paris – from Clovis to Charles X, by S. Sophia Beale, published in 1892 and obtained via Project Gutenberg, which I have of course embellished with a falling object.

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Pont Marie fleur7left Châtelet fleur7right Pont Neuf
11 fleur11left Châtelet fleur11right Hôtel de Ville
Pyramides fleur14left Châtelet fleur14right Gare de Lyon

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