The design and related calculations for the Calais Fortress weren't really particularly difficult, and Monge had given the job to Joseph more so that he could actually get more money. But soon, Monge realizes that Joseph is getting more than just a little money out of this job.
One day in July, Monge, who was traveling to Nice on business, suddenly received a letter from Joseph. It was a very thick, heavy letter that would surely have cost Joseph more in postage if it hadn't gone through army channels. Monge opened the envelope containing a thick stack of letterheads filled with various numbers and symbols.
Monge skimmed through the letter and realized that the letter was discussing the limit of the flux number. But he was on his way out the door at that moment and had no time to study the letter in detail, so Monge slipped it into his coat pocket and went out the door.
It was after four o'clock in the afternoon when he finished his work. A few coworkers then met to go out to dinner together. Naturally, they invited Monge as well. Monge, however, excuses himself on the grounds that he has some personal business to attend to. Those coworkers went off on their own without much persuasion.
According to Christianity, there are seven sins that will cause a person's soul to fall into hell: pride, envy, anger, sloth, greed, gluttony, and lust. If this is true, the French should have the highest chance of falling into hell because of gluttony in Europe. Like the great eating nations of the East, the French, and especially the French aristocracy, were famous throughout Europe for their "All-night feasting". And compared to Paris, the price of goods in Nice is much cheaper, all kinds of seafood is also extremely abundant, a few people eat from the afternoon until late at night, until the food and wine not only stuffed their intestines, and even all stuffed their esophagus, all the way up to their throats, they wobbled into the carriage and returned to their own accommodation. And when they came back, they realized that the light was still on in the room of Monge, who had been living a very regular life and who, according to custom, should have gone to bed long ago.
"What's Monge doing?" Someone muttered.
"Whatever, that deadbeat guy, just doesn't seem French." Another drunken fellow replied.
But these drunken guys weren't really looking into the question of what Monge was doing. So they just mouthed off and went back to bed themselves.
Naturally, Monge didn't know what the drunks were saying about him outside his door. In front of his desk was a large stack of draft paper, which was neatly and densely packed with all kinds of calculations. He frowned, calculating carefully until another candle burned out and went out, and the sky outside his window began to glow faintly.
"This research by Joseph is quite good, at least I don't see anything wrong with it right now. Well, he was inspired when he was dealing with the issue of the construction of the fort? It's really good to be young, and when I was young, my thoughts were much quicker than they are now." Monge put down his quill and sighed.
"Joseph should have sent this paper to the Academy of Sciences as well. I wonder what those guys in the Academy of Sciences say about it." Monge thought this at last.
Joseph did send this paper to the Academy of Sciences. However, one thing that Monge still did not anticipate was that Joseph sent a new paper to the Academy within a week, in which he also derived an important inequality. This inequality was called Cauchy Inequality in its original history, but nowadays, it is also subject to a name change.
This was just a starting point, though. Six months later, Joseph published another physics paper, "A Study of Heat by Friction," in which Joseph used two pieces of ice enclosed in a glass box submerged in water to melt by friction against each other, and a comparison group of two pieces of ice of equal mass and temperature to melt naturally, and recorded the change in temperature of the water in the two groups. The water temperature didn't drop more drastically with the use of the friction set. Instead, its decline is smaller, and the decline curve is flatter. Joseph points out that this phenomenon is diametrically opposed to the inferences that can be made on the basis of the traditional caloric theory. Accordingly, he further deduced that today's popular thermal mass theory may not be correct.
The "Caloric Theory" is a scientific hypothesis that appeared after Lavoisier experimentally disproved the "Phlogiston Theory". This explanation assumes that heat is a substance called caloric, which is a massless substance that does not occupy space, that the temperature of an object rises when it absorbs caloric, and that caloric flows from a warmer object to a cooler one, and can also pass through the pores of a solid or liquid.
The "Caloric Theory" explains many physical phenomena quite effectively. For example, hot tea cooling at room temperature can be explained by the caloric theory: The high temperature of hot tea indicates a higher concentration of caloric, so the caloric will automatically flow to the area with a lower concentration of caloric, i.e., the colder surrounding air. The caloric theory also explains the expansion of air when it is heated, as the molecules of the air absorb the caloric, making it larger. Suppose one goes further and analyzes the details in the process of absorption of caloric by air molecules. In that case, one can also explain thermal radiation, object phase changes at different temperatures, and even to most gas laws. That is why the "caloric theory" was the dominant scientific hypothesis until the middle of the nineteenth century. The theory of molecular motion had already been proposed at that time, but in this era, the two doctrines were generally considered equivalent.
However, the "Caloric Theory" is also flawed. Because the "Caloric Theory" considers "heat" to be a substance, and according to Lomonosov's "Law of Conservation of Mass", "caloric" naturally can neither be created nor destroyed out of thin air but can only be transferred between one object and another. From this follows the natural inference that if the temperature of some object rises, there must be a fall in the temperature of another object, and the total amount of heat mass gained by the object that rises should be equal to the total amount of heat mass lost by the object that cools. This makes it difficult to use this hypothesis to explain phenomena such as friction-generated heat. This is because it is difficult, if not impossible, to find objects that have lost their "caloric" in such phenomena.
Not unlike Humphry Davy, who historically first accomplished this experiment. Humphry Davy was not fully aware of the significance behind this experiment, nor did he analyze this experiment mathematically and rigorously. In fact, he himself paid so little attention to this experiment that it was ignored at the time.
But unlike Joseph, he also paired this experiment with more rigorous mathematical analysis, demonstrating that the caloric theory and the molecular motion theory were not equivalent in this matter.
"Honestly, this paper is pretty much a death sentence for caloric theory!" Laplace said to Lavoisier with a face full of pain, "This guy, Joseph, is a real pain in the ass! There are obviously so many things to study in this world, but he always seems to take pleasure in going and destroying people's mansions. He ... he this is really ..."
"Yeah, I'm also feeling the pain you guys felt the last time he brought up light as a wave." Lavoisier replied bitterly, "As a matter of fact I've just finished a study based on the caloric theory."
"Me too." Laplace replied, "I've just had an idea that perhaps some of the problems with Newton's formula for the speed of sound can be corrected after taking changes in caloric into account. Now, however, the study has barely gotten off the ground before it almost had to be temporarily discontinued."
"That's not such a big deal." Lavoisier said, "First of all your research hasn't been going on for long, and it's not impossible to change it now to study it from the point of view of molecular motion. And following Joseph's argument, molecular motion, while not exactly equivalent to the caloric theory, can actually be considered equivalent in most cases. So there should be very little you have to change. But all my research is done ..."
"So, teacher, what do you think of this paper of his?" Laplace asked.
"What else is there to look at?" Lavoisier said, "Like last time, at least for the moment, I haven't identified any problems in his paper. Surely there must be something wrong with this view of his, how can caloric theory be wrong? At best, there are changes that need to be made and additions that need to be made. Well, he also admits that perhaps there are other explanations than his. The current caloric theory is indeed flawed on the issue of frictional heat generation, but that doesn't mean that the caloric theory is completely finished, it just means that in order for it to continue to hold true, we have to tinker with it more ... It's just that, at the moment, I haven't found a thought to fix it ... This Joseph, he's always messing us up."
Laplace noticed that despite all the trouble Lavoisier had gotten into with Joseph's research, much of it conflicted with Lavoisier's. Under normal circumstances, Lavoisier would not have had a favorable impression of Joseph. Still, when Lavoisier mentioned Joseph, although he was complaining on his lips, he spoke with a tone that seemed to say, "This child is really naughty," and did not contain any malice.
'Teacher is actually such a generous person? It's not like that!' Laplace couldn't help thinking, 'And he does not, in fact, agree with Joseph at all. If it had been someone else making such a point, like me for example, maybe, maybe the teacher would have exploded into a rage, but why is it that this time, his attitude is so mild?'
"That kid, yeah, he's really smart, just too much of a troublemaker. You say how nice it would be if he would use all his smarts in a more useful way, instead of specializing in messing us up. Well, I'll have to have a good talk with him when he gets back." Lavoisier didn't notice those thoughts of Laplace, still smiling and saying so.