A Rising Star in Science

The design and related calculations for the Calais fortifications weren't particularly difficult. Monge had assigned the task to Joseph mostly so he could earn a little extra money. But it wasn't long before Monge realized that Joseph was getting far more than just a little money out of the work.

One day in July, Monge, who was away on business in Nice, suddenly received a letter from Joseph. It was an exceptionally thick, heavy letter. If it hadn't gone through military channels, the postage would surely have cost Joseph a great deal more. Monge opened the envelope and found a thick stack of pages covered in numbers and symbols.

He skimmed through it and realized that the letter discussed the limit problem in calculus. But he was just about to head out and didn't have time to study it closely, so he tucked it into his coat pocket and left.

By the time he finished work, it was already past four in the afternoon. A few colleagues arranged to go out for dinner together. They naturally invited Monge, too, but he politely declined, saying he had some personal matters to take care of. His colleagues didn't press him and went on their own.

According to Christianity, seven sins could send a person's soul plunging into hell: pride, envy, wrath, sloth, greed, gluttony, and lust. If that was true, then in Europe, the French were probably the most likely to end up in hell for gluttony. Much like the Great Eater Nation in the East, the French—especially the French aristocracy—were famous throughout Europe for their "long nights of drinking." And prices in Nice were much lower than in Paris, with all kinds of seafood in abundance. The group ate from afternoon until late at night, until food and wine had not only filled their stomachs but packed their esophagi all the way up to their throats. Only then did they stagger into their carriage and head home. When they returned, they discovered that Monge's room was still lit, even though he always lived a very regular life and, by his usual habits, should have been in bed long ago.

"What's Monge doing?" someone muttered.

"Who cares? That stiff old fellow doesn't seem French at all," another drunken man replied.

But these drunken fellows weren't really interested in finding out what Monge was doing. They merely grumbled a little before going off to bed themselves.

Monge had no idea what the drunks outside his door were saying about him. On his desk lay a thick stack of draft paper, neatly covered in rows upon rows of calculations. Frowning, he worked through them carefully until another candle burned down and went out, and the sky outside his window began to grow faintly bright.

"Joseph's research is quite good. At least, I haven't found any problems so far. Hmm, he was inspired while working on the problem of building the fortifications? How nice to be young. When I was young, my mind was much sharper, too." Monge set down his quill and sighed.

"Joseph must have sent this paper to the Academy of Sciences, too. I wonder what those fellows there made of it." That was Monge's final thought.

Joseph had indeed sent the paper to the Academy of Sciences. But Monge hadn't anticipated one thing: within a week, Joseph sent the Academy another paper, in which he derived an important inequality. In the history he knew, it was called the Cauchy Inequality. Now, though, it seemed it might have to be given a different name.

But that was only the beginning. Six months later, Joseph published a physics paper titled Research on Frictional Heat. In it, he rubbed two pieces of ice together inside a glass box submerged in water until they melted, then compared the result with two pieces of ice of equal mass and temperature that were left to melt on their own. He recorded the changes in the water's temperature in both groups. The water in the group subjected to friction didn't cool more rapidly. In fact, its temperature fell by less, and its cooling curve was smoother. Joseph pointed out that this result was completely at odds with what traditional caloric theory would predict. On that basis, he further inferred that the currently popular caloric theory might be incorrect.

Caloric theory was a scientific hypothesis that emerged after Lavoisier used experiments to overturn the phlogiston theory. It assumed that heat was a substance called "caloric," which had no mass and occupied no space. An object's temperature rose when it absorbed caloric, and caloric flowed from hotter objects to colder ones. It could also pass through the pores of solids and liquids.

Caloric theory could explain many physical phenomena quite effectively. For instance, it could explain why hot tea cooled at room temperature: the tea was hotter, which meant its caloric concentration was higher, so caloric naturally flowed into regions with lower concentrations—in other words, into the cooler air around it. Caloric theory could also explain why air expanded when heated: its molecules absorbed caloric, causing its volume to increase. By examining the details of how air molecules absorbed caloric, one could even explain thermal radiation, phase changes in objects at different temperatures, and most gas laws. So, well into the mid-nineteenth century, caloric theory remained the mainstream scientific hypothesis. The molecular motion theory had also been proposed by then, but people generally considered the two theories equivalent.

However, caloric theory had its flaws. It held that "heat" was a substance, and according to Lomonosov's law of the conservation of matter, caloric naturally could neither be created from nothing nor destroyed; it could only be transferred from one object to another. This led to an obvious deduction: if an object's temperature rose, another object's temperature must fall, and the amount of caloric gained by the warming object should equal the amount lost by the cooling one. This made the theory difficult to use in explaining phenomena such as heat generated by friction. In such cases, it was hard to find an object that had lost caloric—or, sometimes, impossible to find one at all. In Joseph's experiment, for example, there was simply nowhere the caloric that melted the ice could have come from.

Unlike Humphry Davy, who had first conducted this experiment in history, Joseph fully understood its significance and subjected it to a rigorous mathematical analysis. Davy himself hadn't entirely understood what lay behind the experiment, nor had he analyzed it rigorously in mathematical terms. In fact, he hadn't thought much of the experiment, so it had been overlooked at the time.

Joseph, however, was different. He had also provided the experiment with a relatively rigorous mathematical analysis, proving that caloric theory and molecular motion theory were not equivalent in this matter.

"To be honest, this paper has practically sentenced caloric theory to death!" Laplace said to Lavoisier, his face contorted with pain. "Joseph really is a headache! There are so many things in this world to study, yet he always seems to take pleasure in tearing down other people's towers. He... he really..."

"Yes, now I understand how much you suffered when he proposed that light was a wave last time," Lavoisier replied with a grimace. "In fact, I've just completed a study based on caloric theory."

"Same here," Laplace replied. "I'd just had an idea. Perhaps by taking changes in caloric into account, I could correct some problems with Newton's formula for the speed of sound. But now, just as the research has gotten started, I can hardly avoid putting it on hold."

"That's not such a big problem," Lavoisier said. "First of all, you haven't been working on it for long. It's not impossible to switch to studying it from the perspective of molecular motion. And according to Joseph's argument, although molecular motion and caloric theory aren't entirely equivalent, in most cases they can still be treated as equivalent. So you should need to change very little. But I've already completed my research..."

"Then, teacher, what do you think of his paper?" Laplace asked.

"What else can I think?" Lavoisier said. "Just like last time, at least for now, I haven't found any problems with his paper. Of course, his view must be wrong. How could caloric theory possibly be wrong? At most, there are parts that need changing and additions that need to be made. Hmm, he admits there may be explanations other than his own. Caloric theory does have flaws when it comes to heat generated by friction, but that doesn't mean it's completely done for. It only means that, if we want to keep it standing, we'll have to patch it up some more... I just haven't found a way to do that yet... That Joseph is always making trouble for us."

Laplace noticed that although Joseph's research had caused Lavoisier so much trouble, and conflicted with his work in many ways, Lavoisier should have had a poor opinion of Joseph under normal circumstances. But whenever Lavoisier spoke of Joseph now, his words were full of complaints, yet his tone and expression seemed to say, "That boy is such a handful." There wasn't a trace of malice in them.

"Teacher is actually this generous? That doesn't seem like him!" Laplace couldn't help thinking. "And the truth is, he doesn't agree with Joseph's views at all. If someone else had put forward such ideas—if it had been me, for instance—perhaps, perhaps teacher would have been furious long ago. So why is he being so gentle this time?"

"That boy really is clever, just too fond of stirring up trouble. Imagine what he could do if he put all that cleverness to useful work instead of making trouble for us. Hmm, when he gets back, I'll have a good talk with him." Lavoisier, unaware of Laplace's thoughts, continued speaking with a smile.