New Star of Science

The design and related calculations for the Calais battery were not particularly difficult; Monge had handed this task to Joseph primarily to help him earn some extra money. However, Monge soon discovered that what Joseph gained from this work was far more than just a little coin.

One day in July, while on a business trip in Nice, Monge suddenly received a letter from Joseph. It was an exceptionally thick, heavy envelope; had it not been sent through military channels, the postage would have cost Joseph a small fortune. Monge tore open the envelope to find a thick stack of paper covered in various numbers and symbols.

Monge glanced over it briefly and realized the letter discussed the limit problems of fluxions. However, he was about to head out and lacked the time to study it in detail, so he stuffed the letter into his coat pocket and left.

By the time he finished his work, it was already past four in the afternoon. Several colleagues invited him to join them for dinner. Monge declined, citing some personal matters he needed to attend to. His colleagues did not press him and went on their way.

According to Christianity, there are seven deadly sins that can cast a soul into hell: pride, envy, wrath, sloth, greed, gluttony, and lust. If this were true, the French would likely have the highest probability of falling into hell for gluttony. Much like the Great Eater Nation of the East, the French—especially the nobility—were famous throughout Europe for their "penchant for long nights of drinking." Compared to Paris, the cost of living in Nice was much lower, and the variety of seafood was incredibly rich. The group ate and drank from the afternoon until deep into the night, until the food and wine not only filled their stomachs but reached their very esophagi and throats. Only then did they wobble toward their carriages to return home. When they arrived, they were surprised to see that the lights were still on in the room of Monge, a man who lived a strictly disciplined life and, by habit, should have been in bed long ago.

"What is Monge doing?" someone muttered.

"Who cares? That rigid fellow doesn't even seem like a Frenchman," another drunken man replied.

However, these intoxicated men were not truly interested in what Monge was doing, so they simply grumbled and went off to sleep.

Monge, naturally, was unaware of what the drunks outside his door were saying about him. At his desk lay a large stack of draft paper, covered neatly and densely with various calculations. He frowned, calculating intently until another candle burned down to nothing and the sky outside his window began to brighten.

"Joseph's research is quite excellent; at least, I haven't found any flaws yet. Hmm, was he inspired by this while working on the construction of the battery? Youth is truly a wonderful thing; when I was young, my mind was much more agile than it is now," Monge sighed, setting down his quill.

Joseph must have sent this paper to the Academy as well, Monge thought to himself. I wonder how those fellows at the Academy will evaluate it.

Joseph had indeed sent the paper to the Academy, but there was one thing Monge had not anticipated: within a week, Joseph had sent yet another paper to the Academy, in which he derived an important inequality. In the original history, this would be known as the Cauchy Inequality, but now, it would likely have to be renamed.

However, this was merely a starting point. Half a year later, Joseph published a physics paper titled Research on Frictional Heat. In this paper, Joseph placed two blocks of ice inside a sealed glass box submerged in water and rubbed them together until they melted. He compared this to a control group of two ice blocks of equal mass and temperature left to melt naturally, recording the temperature changes of the water in both groups. The water in the group subjected to friction did not show a sharper drop in temperature; in fact, the decrease was smaller, and the cooling curve was flatter. Joseph pointed out that this phenomenon was diametrically opposed to the inferences made based on the traditional Caloric Theory. Based on this, he further inferred that the currently popular Caloric Theory might be incorrect.

The "Caloric Theory" was a scientific hypothesis that emerged after Lavoisier used experiments to overturn the "Phlogiston Theory." This hypothesis assumed that heat was a substance called "caloric." Caloric was considered a massless substance that occupied no space; objects would rise in temperature upon absorbing it, and it would flow from hotter objects to colder ones, capable of passing through the pores of solids or liquids.

The Caloric Theory could quite effectively explain many physical phenomena. For example, the cooling of hot tea at room temperature could be explained by the theory: the high temperature of the tea indicated a higher concentration of caloric, which would automatically flow to areas of lower concentration—the surrounding cooler air. The Caloric Theory could also explain the expansion of air when heated, as air molecules absorbed caloric, causing their volume to increase. If one analyzed the details of the process by which air molecules absorbed caloric, one could even explain thermal radiation, phase changes at different temperatures, and even most gas laws. Thus, until the mid-nineteenth century, the Caloric Theory remained the mainstream scientific hypothesis. By then, the Kinetic Molecular Theory had already been proposed, but in that era, people generally considered the two theories to be equivalent.

However, the Caloric Theory had its loopholes. Because it posited that "heat" was a substance, and according to Lomonosov's "Law of Conservation of Matter," caloric could neither be created from nothing nor destroyed; it could only be transferred between objects. From this came a natural inference: if the temperature of one object rose, the temperature of another must necessarily fall, and the total amount of caloric gained by the heating object should equal the total amount lost by the cooling object. This made the hypothesis difficult to use to explain phenomena like frictional heat, as in such cases, it was difficult—or even impossible—to find an object that had lost "caloric." For instance, in Joseph's experiment, there was simply no source of caloric to be found that could have melted the ice into water.

Unlike Humphry Davy, who first completed this experiment in history, Joseph was different. Davy did not fully grasp the significance behind the experiment and did not perform a rigorous mathematical analysis of it. In fact, he did not place much importance on the experiment himself, which is why it was overlooked at the time.

But Joseph was different; he provided the experiment with a relatively rigorous mathematical analysis, proving that on this issue, the Caloric Theory and the Kinetic Molecular Theory were not equivalent.

"Honestly, this paper has all but passed a death sentence on the Caloric Theory!" Laplace said to Lavoisier with a pained expression. "That fellow Joseph is truly a headache! There are so many things in this world that could be studied, yet he seems to take pleasure in tearing down other people's edifices. He... he is truly..."

"Indeed, I felt your pain when he proposed that light was a wave," Lavoisier replied with a wry smile. "In fact, I just finished a piece of research based on the Caloric Theory."

"Same here," Laplace replied. "I just had an idea that perhaps by accounting for the changes in caloric, I could correct some issues in Newton's formula for the speed of sound. Yet now, just as the research has begun, it has to be interrupted."

"That is not a major problem," Lavoisier said. "First of all, your research hasn't been going on for long; it's not impossible to switch to a molecular motion perspective. And according to Joseph's argument, while molecular motion is not entirely equivalent to the Caloric Theory, in most cases, they can be treated as such. So, the parts you need to change should be very limited. But my research is already finished..."

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

"What else is there to think?" Lavoisier said. "Just like last time, at least for now, I haven't found any flaws in his paper. Of course, his viewpoint must be wrong; how could the Caloric Theory be incorrect? At most, it needs some adjustments or additions. Hmm, he even admits that perhaps there are other explanations besides his own. The current Caloric Theory does indeed have flaws regarding frictional heat, but that doesn't mean it's completely finished; it just means that to keep it valid, we must patch it up... It's just that, for now, I haven't found a way to patch it... This Joseph is always causing trouble for us."

Laplace noticed that although Joseph's research had caused Lavoisier so much trouble and conflicted with his work in many areas—under normal circumstances, Lavoisier shouldn't have a very good impression of Joseph—whenever Lavoisier mentioned him now, despite the complaints, his tone and demeanor were as if he were talking about a "naughty child," devoid of any malice.

Is the Teacher actually such a magnanimous person? That doesn't seem right! Laplace couldn't help but think. And in fact, he doesn't agree with Joseph's views at all. If someone else had proposed such a view—say, me—perhaps the Teacher would have been furious. Why is his attitude so gentle this time?

"That brat is truly clever, just too fond of causing trouble. If only he could use his intelligence for something useful instead of specifically making trouble for us, how wonderful that would be. Hmm, when he returns, I must have a good talk with him." Lavoisier did not notice Laplace's thoughts and continued to speak with a smile.