1There was a soldier of France named Lazare Carnot, who was also a man of numbers. When the kings of Europe marched against the young republic, he raised fourteen armies to meet them, and the people called him the Organiser of Victory. In quiet hours he wrote about machines. And he loved the old poets of Persia so well that he named his first son after one of them. He named him Sadi.
2So the lamp-keepers of an earlier book had a namesake in Paris, though they could not have known it. One fire, many hands.
3Sadi Carnot was a thin, quiet boy who did not like to be looked at. He was sent to the great school of engineers in Paris when he was sixteen. He was seventeen when the war came to the city gates.
4For the long wars had turned at last. The armies of the kings were in France, a hundred thousand strong, and marching on Paris. The students of the school begged to fight. They were given cannon and sent out along the road to Vincennes, on the east side of the city, boys in school coats serving the guns.
5Sadi served his gun that day. He saw the horsemen come over the fields in a line that did not seem to end. He saw the boy beside him go down. He rammed and loaded and stood clear, and did it again, with his ears ringing, until the order came to fall back. They fell back through the gate. The next day the city was given up.
6That was his one battle, and it was lost. A year later the last battle of all was lost, in a field in Belgium, and the king came back to France. The king did not forgive the Organiser of Victory. Lazare Carnot was sent out of the country and told he would never come home. He went east into the German lands, an old man with a trunk of books, and his younger son Hippolyte went with him.
7Sadi stayed, for he was an officer and under orders. The new masters did not trust the son of such a father. They sent him from one dull fortress to another, to count stones and draw plans that no one would build. He was patient. He did his counting. And in the evenings he asked himself a question that would not leave him alone. Why had France lost?
8It was not for want of courage. He had seen courage on the road to Vincennes. It was not for want of generals. He came to think it was for want of something that no one had put in the histories. England had iron and coal, and she had engines to marry the two. Her engines pumped her mines dry and carried her coal and drove her mills. An engine does not tire, and it does not eat when it is idle. He judged that if you took away England's engines you would take away her iron and her coal with them, and all her strength.
9And yet no one understood the engine. That was the strange part. Men built them by habit and by guessing. One builder used high steam and another low. One swore by a great boiler and another by a small. No one could say what the best engine would be, or whether there was a best at all. There was no law of the engine. There was only a craft.
10In the seventh year of his father's exile, Sadi got leave and went to see him. The old man was living in the town of Magdeburg, on the river Elbe. He was nearly seventy. The three of them walked by the river in the evenings, the father and the two sons, and they talked of what the Carnots always talked of, which was machines.
11A steam engine had lately come to that town, the first it had seen, and the old soldier had gone to look at it like a boy. But what they stood and watched most often were the mills on the river. They were built on boats moored in the stream, and the current turned their wheels.
12"I wrote about that once," said Lazare. "The best wheel is the one that wastes nothing of the water. The water should come onto it without a splash and leave it without any speed. Whatever splashes is lost. Whatever still runs fast when it leaves the wheel is lost. The whole craft is to let the water fall quietly."
13Sadi watched the wheel go round. The water came to it high and left it low. The same water left as came. The wheel did not use up the water. It used the fall.
14"Father," he said. "What if heat is like that?"
15The old man waited.
16"An engine has a hot place, where the fire is. And it has a cold place, where the steam is cooled again. No one thinks about the cold place. They think the fire does the work. But a fire with nothing cold near it does nothing. You could have a sea of hot water, and if everything around it were just as hot, you could not turn one wheel with it. It is like a lake on a plain. There is water enough, and nowhere for it to fall."
17"Go on," said Lazare.
18"So the work does not come from the heat. It comes from the heat falling. From hot to cold. The engine stands in the fall the way your mill stands in the river. And then there are only two things to ask. How much heat? And how far does it fall?"
19Hippolyte, who was twenty and wanted to mend the world by other means, said that it sounded too simple to be new.
20"It may be too simple to be seen," said his father. He put his hand on his elder son's arm. He was a man who had commanded armies, and he knew when a thing had been said that mattered. "Write it down, Sadi. Write it so a man who is no engineer can follow it. I have read a thousand clever books that died because no one could get through them."
21That was the last time Sadi saw him. Lazare Carnot died in Magdeburg two years later, still shut out of France. His son was not allowed to bring him home.
22Sadi took half pay and a small apartment in Paris, and he wrote. He kept his father's rule. When he had finished a part, he read it aloud to Hippolyte, who had come back to France after the burial. Hippolyte was no engineer. Wherever Hippolyte frowned, Sadi stopped and made the place plainer. It is for this that a child can read that book today.
23Now hear what was in it, for it is the first stone of this whole Articles of Heat.
24He asked the reader to think of the best engine there could be. Not one that was ever built, but one imagined, with no leaks and no rubbing and no heat creeping where it was not sent. In such an engine heat would never jump from a hot thing to a cold thing for nothing, with a hiss and a splash, as water jumps over a ledge. It would be let down gently, doing work all the way.
25Then he showed a strange thing about that best engine. You could run it backward. Feed it work, and it would carry the heat back up from the cold place to the hot, as a wheel driven by hand can lift water back to the millpond. And from that he drew his law, with nothing but plain reasoning. No engine can do better than that one. For if any engine could, you could set the better one to drive the best one backward, and have work left over for nothing, for ever. And work for nothing is a thing the world has never once given.
26So there was a wall. Matthew Reay had been right to look for it. And the wall did not care what the engine was made of. Steam, or air, or anything a builder could dream of: it made no difference. The most work a fire can give depends on two things only. How hot is the hot place, and how cold is the cold. The further the fall, the more of the heat can be turned to work. And never all of it. Not in the best engine that could ever be.
27He was wrong in one thing, and you should know it. He thought of heat as a kind of fine water, a stuff that ran through the engine and all came out the other side. That was the belief of his time, and he reasoned from it. Later, in his private notes, he began to doubt it. He wrote that heat might be nothing but motion, the hidden shaking of the small parts of things. He was nearly at a second great truth. He did not live to print it.
28The book was small, a hundred and some pages. He called it Reflections on the Motive Power of Fire. He paid for the printing himself. Six hundred copies were made. He was twenty-eight years old.
29A kind old engineer spoke well of it once, at a meeting of learned men. Then there was silence. The builders of engines did not read it, for it had no drawings of valves. The men of numbers did not read it, for it was about engines. The copies sat in the bookseller's back room and gathered dust. Sadi did not complain. He was not a man who knew how to push himself forward. He went on thinking, and filling loose sheets with notes, and playing his violin in the evenings.
30Eight years went by like that.
31Then a sickness came to Paris out of the east. It was the cholera, and the city had never seen it before. It killed in a day. A man would be well at breakfast and cold by dark. The carts went through the streets at night. Eighteen thousand died in the city that year, and no one knew the cause, and so everyone feared everything: the air, the water, the touch of a hand, the clothes of the dead.
32Sadi had been ill already that summer with a fever that left him weak and troubled in his mind. He was resting in a house of healing outside the city when the cholera found him. It took him between one morning and the next. He was thirty-six years old.
33There was a rule in that season, made in terror. Whatever a cholera victim had owned was to be burned. So they carried out his clothes and his bedding, and his books, and his papers. Years of thinking, written small on loose sheets, went onto the fire in a yard. It burned as any paper burns. In a quarter of an hour it was warm ash, and then it was cold ash, and the heat that had been in it had gone off into the grey air above Paris, where no one could ever gather it again.
34Hippolyte stood and watched. He had been allowed to keep only what was already in his own hands: one thin bundle of his brother's notes. He kept that bundle for forty-six years. When he was an old man he gave it to the world. In it were the pages where Sadi had seen that heat is motion.
35And the book? The book was nearly lost as well. But there was a man named Clapeyron who had been at the same school. Two years after Sadi's death he found the Reflections and understood it. He set its argument out again in a journal, with a drawing that made it clear. Very few had read the book. A good many read the journal.
36One who read it was a young Scot named William Thomson. He was twenty-one and already feared for his cleverness, and he was in Paris for a season to learn the craft of measuring. He read Clapeyron and knew he must have the book itself. So he went to look for it.
37He walked to every bookseller he could find. He asked for the work of Carnot on the motive power of fire. Some had never heard the name. Some brightened and said yes, certainly, and brought out a book on the troubles of society by Hippolyte Carnot, who was by then a man of politics and well known. No, said Thomson, the other Carnot. They shook their heads. There was no other Carnot.
38He went home without it. It was three years more before a friend put a copy in his hand.
39Think of it, you who work and are not seen. A man found the law that rules every engine that ever ran or ever will. He wrote it down so plainly a child could follow. Then his own city could not find one copy of it, thirteen years after he was in the ground.
40And still it was not lost. A brother had frowned at the hard places, so the book was clear. A schoolfellow had copied its argument, so the argument travelled. A stranger went hunting for it through the streets, so the hunt became a story, and the story sent others looking. An ember does not need a great fire around it. It needs one hand, and then another.
41Sadi Carnot never knew what he had begun. He thought he had written a small book about engines, to help France. He had opened a door onto the way of all heat, in the stars and in the blood. Others would walk through it. A pastor's son in Germany would walk furthest, and he would find something on the other side that frightened the whole century.
42But first you must hear of a girl with a hammer, on a cold shore, who was reading a much older book than his.