djtaylor.me

Reflections on the motive power of gunfire

RÉFLEXIONS

SUR LA

PUISSANCE MOTRICE

DU TIRS

Par S. CARNOT

Translated April 2026

[Editors note: [todo: how this treatise was found].

This manuscript is now the last piece of known writing by Carnot before his death in 1832. The most notable thing about this manuscript, from a historical physics perspective, is that Carnot seems to have developed a much more sophisticated and modern understanding of thermodynamics since his 1824 treatise. It's known that Carnot had moved pass his caloric theory by the time of his death. But it was not known until now that Carnot seems to have connected the idea of temperature with microscopic motion, and has some understanding of entropy as a one-way process!

On the other hand, his signature "clarity of thought" is gone. There is a confusion of ideas demonstrated here, relating temperature and pressure of gasses with "temperature" and "pressure" in the social sense. It shouldn't need to be said, but human societies don't obey the ideal gas law. Is this an honest attempt to understand the French Revolution via physical laws, or something else? Is this analogy how he came to think of temperature as microscopic motion? We will probably never know.

The idea of interpreting social movements through a physics lens wasn't unheard of in Carnot's day. For example, this manuscript quotes Lettres d'Un Habitant de Genève À Ses Contemporains, written by Henri Comte de Saint-Simon in 1803, which advocates for scientists to play a larger role in society, and uses words like "la force d'inertie" to describe social "inertia". But honestly, trying to draw a line between these two works feels reductionist. This manuscript is on a whole other level. I'm not aware of any contemporary work with remotely similar subject matter. [todo: find a better example]

The other striking thing to note is the writing style. His usual first-person, conversational, sans-culottes style is still present. The [todo]

[todo: talk about how odd this way of writing is. Or maybe not.]]

Every one knows that gunpowder can produce motion. That it possesses vast motive-power for both shells and people no one can doubt, in these days when the story of the Revolution is everywhere so well known.

These thoughts are based on conversations with Charles Dupin and Émile Clapeyron discussing to what extent, if any, the actions of peoples can be put on solid philosophical foundations.

Myself and my contemporaries feel awe and envy of Newton. His calculus of bodies in motion was a great gift to all students of philosophy. Taking after his example, everyone now wants a calculus of fluids. Father wants a calculus of money and economies. Generals want a calculus of tactics. But these are too narrow, splitting up our lives into pieces that can be reasoned. No one seems to want a calculus of people in their entirety.

The National Assembly saw the spontaneous physical separation of republicans and royalists. What mechanism can cause this?

The manuscripts in their hands are a sieve, a sort of reverse osmosis, a one-way barrier for people and minds. It couldn't have been more effective if they had printed their enlightenment thoughts on cheesecloth. The delegates there understood this too, for they then wrote the Declaration of the Rights of Man: a sieve that, with the right pressure applied, could separate an entire nation.

[todo]

People move independently inside their group, but as a whole will flow down streets, will fit the shape of a building they are in. They will bunch closer and flow slower when calm, but will spread and run out when agitated. Newton wrote of Man's mind as alchemical mercury. Fitting, as people in this way act like a mercury thermometer, measuring their own temperature. Perhaps Newton is ahead of us still.

[todo]

Let me engage in a little suasoria. Gaius Pontius, meddix of Samnium, you've defeated the Romans at Caudine Forks.

Cornering them in the valley, containing them, that was good. A drop of oil in water will contain itself and not disperse, but that doesn't work with Romans and Samnites. You're both descendants from the Umbrians, and so not very different from them. If you want to them contained, and eventually removed in an irreversible way, you need an impermeable membrane. Preferably made of spears.

You can transport the Roman army, contained in their spear bubble, back across the Apennines. This translation requires 0 work, because the bubble doesn't change volume. Make sure to keep them separate!

Alternatively they can be killed. Applying constant pressure to the enemy, the enthalpy decreases by approximately $\Delta G = \Delta U - T \Delta S + P \Delta V$. Each soldier occupies [todo].

The worst option would be to create a valve at the border, increase pressure, and squeeze the Romans through it. The army that exits the other side will have a very high temperature, and will raise the temperature of the Romans on the other side. Living next to hot Romans is a bad idea.

[todo: comment on reversible processes?]

[todo: this is different from the paris example because there the people are all diffused, but here they're all contained]

[todo]

In Paris all the little particle people moved more rapidly then. By what mechanism were they able to pass their own heightened state to their neighbor? Particles can bounce off each other and share their velocities. What about people, what do they pass around? Currency is a reasonable contender, as the amount of assignat traded each day rose in proportion with peoples' fervor. But all places have currency, and did not experience this.

No, rather it is revolutionary manuscripts passed from hand to hand, the people's caloric, that is the answer. As one man explains to another his ideas, he feels righteous satisfaction that is balanced perfectly with an increase in righteous anger in the other.

Streets are flooded each morning with these manuscripts, and Paris grows hotter. No amount of work can push the Seine one centimeter, so the volume remains constant. $PV \propto NT$, so the only way to keep the pressure from reaching criticality is to reduce the number of particles in Paris.

The obvious first choices for removal are the largest particles, as weighed in the minds of men, since their mass grants them the greatest energy. This is why the King and Queen lost their heads.

But it wasn't enough. The pressure kept growing and more and more people kept dying to keep the pressure under critical. (what is the critical pressure?).

Eventually even the leaders of this regime died in an effort to reduce the pressure.

[todo: maybe here place the aside about what caused this rise in energy and pressure and temperature]

The new leaders opted for a different strategy: increase volume. "Increasing the volume must decrease pressure, right?" Poor guys, it was an isobaric process, which increases volume while keeping the same pressure, and also raising temperature, lol. Those expansions were too slow.

It isn't until some generals show up that make large, adiabatic expansions that the pressure and temperature let up.

In the northern front of the battle of Leipzig, Blücher's main force, under command of Langeron, squared off against Ney's Polish regiments, under command of Dabrowski, in the twin cities of Wiederitzsch north of Leipzig. But while that was going on the real action was taking place a couple kilometers to the west.

There, von Yorck's Prussian army squared up against Marmont's French army. Marmont's troops were pushed out of Lindenthal, and then Wahren, before digging in in Möckern.

[todo: steps of first battle in Mockern]

Von Yorck pushed Marmont's position several more times, taking heavy damage. In a last ditch effort, von Yorck snuck some hussars and uhlans close to the french infantry and charged.

[todo: steps of this battle. french forming into squares and getting crushed. over and over. Some of them just got flanked. Many guns and prisoners taken. calculations too.]

[todo: Can a heat engine be placed between two nations to generate work?]

To finish the story, 2 days after Marmont's defeat, Blücher was focused the rest of Ney's forces. The fighting was inconclusive until a Saxon unit (?) on the French side defected and turned the tides. Also, Bernadotte and his Swedish army arrived, but mostly just played the positioning game. With Ney's troops defeated, everyone fell back to Leipzig, and started the retreat.

On the fourth and final day of the battle, Bernadotte's troops stormed the city through the Grimmisches Gate.

This last encounter reminds me of a chess match recorded to have been played by Napoleon and Bernadotte, back when Bernadotte was a French Marshal. The game was played, with the emperor as white:

Napoleon Bonaparte v. Jean-Baptiste Bernadotte (later King Charles John), Paris 1808

1.e4 e5 2.Nf3 Nc6 3.d4 Nxd4 4.Nxd4 exd4 5.Bc4 Bc5 6.c3 Qe7 &.O-O Qe5 8.f4 dxc3+ 9.Kh1 cxb2 10.Bxf7+ Kd8 11.fxe5 bxa1=Q 12.Bxg8 Be7 13.Qb3 a5 14.Rf8+ Bxf8 15.Bg5+ Be7 16.Bxe7 Kxe7 17.Qf7+ Kd8 18.Qf8#

[todo: actual game]

[todo: board]

Or maybe that's not correct, because [todo] should be on [todo], but the emperor was a notorious cheater, so who can know?

That same events play out on the board: a stronghold taken after several volleys, and a piercing of the back rank by an idle piece once the rest has fallen. How curious.

Can chess be analyzed in the same way? A two dimensional map of fluctuating temperatures and pressures, with each side trying to perform their preferred thermodynamic transformation.

[todo: word order example, from like the declaration of rights or something]

This week's Sunday mass read [todo], which of course means the same as [todo]! The energy imparted on people via God's word, like light shining down on us from heaven, takes the form of discrete corpuscles, landing with their full energy one at a time, with nothing in-betweeen, just as Newton predicted.

What must the protestants think about this? Were that line read in a protestant church, most of the energy would exist in the continuum between the words, to be able to distiguish [todo] and [todo]. If Lord Huygens were a protestant, he would be pleased I think.

• something about military tactics. Long lines leard to high volume and low pressure.
• something about Marie Carnot, president, & assasination
• the banging of guns, The Model 1777, caused by gas expansion. Both to accelerate and to cause sound.