Réponse à la lettre de M. de Mairan sur la question des forces vives

(lit.: Reply to the Letter of M. de Mairan on the Question of Living Forces)

Accused in print by the Académie's own secretary of misreading him, she answers charge by charge and holds to Leibniz's measure of a body's force.

by Émilie du Châtelet41 passages held

French, the original language

First published: 1741(aged 35)
Original language: French

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Overview

Jean-Jacques Dortous de Mairan, perpetual secretary of the Académie des sciences in Paris, had argued in a memoir of 1728 that the force of a moving body should be measured by its mass multiplied by its speed, as Newton too appeared to hold. Leibniz had measured it by the mass multiplied by the square of the speed, and called it vis viva, living force. In her Institutions de physique of 1740, Émilie du Châtelet took Leibniz's side and abridged Mairan's memoir to refute it. Mairan answered with a printed letter to her, dated 18 February 1741. He charged that she had not read his memoir properly, that she had cut and distorted it, and that her views came from people who had stayed with her at Cirey, her country house. Her reply, printed in Brussels the next month with his letter, takes the charges one at a time. Any reader, she writes, can lay her abridgement beside his six pages and judge. She came round to living forces by reading a discourse on the laws of motion that Johann Bernoulli, the Swiss mathematician, had presented to the Académie, and the correction recording her change of mind was in print long before the guests he blamed arrived. On the physics she will not move: however he frames the case, a force able to close four springs will never close six. He objects to arguments from authority, she notes, yet leans on Newton's; and the question, in her view, has become a mathematical one. Mairan withdrew from the dispute. Luise Gottsched, a writer and translator, put the two letters into German at Leipzig in 1741; they were added to the 1742 Amsterdam edition of the Institutions, translated into Italian in 1743, and printed at the back of the Paris edition of her essay on fire in 1744. In 1747 the young Kant discussed the debate in his first published work.

Key concepts

What is living force in the dispute with Mairan?

It is Leibniz's measure of the force of a moving body: its mass multiplied by the square of its speed, not by the speed alone. Double the speed and the force is four times as great. The reply's plainest case is a body thrown upward against gravity: with a speed of 2 it rises to a height of 4, and nothing in the effect suggests the speed counts only once.

How did Mairan propose to measure the force of a moving body?

By what it fails to do. As a body slows, it closes springs or pushes matter aside. Mairan compared that with what it would have done had its force stayed constant, and took the obstacles left untouched as the measure of the force it spent. That comparison gives mass times simple speed. The reply calls it measuring a force by the effects it does not produce.

What is the difference between uniform and retarded motion here?

Uniform motion keeps the same speed, as a body would in space offering no resistance, and it spends no force at all. Retarded motion slows down because the body is overcoming obstacles, such as springs to close or the pull of weight. Du Châtelet's point is that their effects are of different kinds, one a distance crossed with nothing displaced, the other a displacement of obstacles, so neither can measure the other.

What counts as a refutation for du Châtelet in the Reply?

Showing that the claim implies a contradiction. When Mairan says she has not refuted him, she asks what refuting could mean if not that. A proposition that requires the same springs to be closed and not closed at once is finished, whatever the experiments say, because what implies a contradiction can never become true. Even if force were simply mass times speed, his argument for it would still be false.

Themes of the book

What this book returns to, gathered into themes and ordered by how much of the text each one occupies.

Who misread whom

When a scholar says his work has been cut and distorted, how should the quarrel be settled? Du Châtelet's answer is to set both texts before the reader and let the reader judge.

Mairan charged that she had not read his memoir properly, that her abridgement mangled it, and that her opinions came from guests at her house. Du Châtelet answers each charge with texts. She prints her abridgement beside his words so the reader can weigh the differences, confesses with mock gravity to leaving out the words 'or lasts forever', and turns the charge back on him for cutting the words that limit her own claim. The guests could not have taught her: she changed her mind on reading Johann Bernoulli, and her correction was printed before they came. Authority, she adds, decides nothing in a question that has become mathematical.

textual accuracy
quotation
interpretation
textual interpretation
reading
rhetoric
argumentation
authority
exposition of opposing views
philosophical debate
refutation
assent

Enter a dialogue

Four springs will never close six

Is the force of a moving body its mass times its speed, or its mass times the square of its speed? The reply defends Leibniz's living force against a measure built on what a body does not do.

Mairan proposed to estimate a body's force not by the springs it actually closes as it slows, but by the springs it would have closed had its force stayed constant. Du Châtelet calls this supposing contradictories at once: the force cannot both be spent on the springs and still be there to close more. Her comparison is a man with forty thousand francs who buys four diamonds at ten thousand each, and nobody measures his fortune by the two he could not buy. Force is measured by the obstacles a body overcomes. In the mathematician Hermann's collision of balls, she shows, the square comes out every time.

living force
force measurement
collision mechanics
mechanics
force
motion
gravity
time
counterfactual reasoning
contradiction
measurement
mathematical physics
philosophy of physics
scientific evidence
resistance
analogy
fallacy

Enter a dialogue

Within this work

passages held: 41
distinct concepts: 61
by passages held, corpus-wide: #678

What this book thinks together

The wheel takes this book’s leading concepts and shows how often they come up together. The wider the band between two, the more of its passages speak of both. Among them, most often together: “living force” and “mechanics”.

Concept co-occurrence, strongest first 8 concepts, joined by 13 pairings. 28 pairings reach beyond these concepts and are not drawn.
Concept	Paired concept	Shared passages
living force	mechanics	10
force measurement	living force	8
force measurement	mechanics	7
collision mechanics	living force	6
force	motion	4
argumentation	living force	3
force	living force	2
living force	motion	2
argumentation	force measurement	1
argumentation	motion	1
argumentation	rhetoric	1
force	mechanics	1
mechanics	motion	1

Works held

The author's work in order, this book marked in place. Your-language title first, the original beneath it where the two differ; side chips show which full texts are held.

1738 Dissertation on the Nature and Propagation of Fire (Dissertation sur la nature et la propagation du feu)
Written for the Académie des sciences' prize of 1738 and printed by the Académie in 1739, then revised for a separate Paris edition in 1744.
FR
1741 Réponse à la lettre de M. de Mairan sur la question des forces vives you are here FR
1746 Discourse on Happiness (Discours sur le bonheur)
Unlike her physics, a private essay on how to live, written in the mid-1740s and put into print thirty years after her death.
FR

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