The Shadow of Great Britain

Chapter 880: Chapter 12 The Issue of Beyond and Within the Scope of the College Entrance Examination_2

Coriolis said: “I have not yet reached that stage; recently, I have been conducting experiments using rotating systems such as waterwheels. Based on the experimental results, this hypothesis is most likely correct. If you don’t mind, I would like to invite you to join me in researching the energy transformation and conservation relations in similar rotating systems. After all, as you know, not everyone is Euler, Fourier, Poisson, or Cauchy. For most researchers, understanding mathematical expressions might take many years to grasp.”

Navier also felt somewhat helpless: “You’re right. If Mr. Cauchy were still in Paris, as long as your hypothesis is correct, he could find the mathematical expression’s rules in just a few months. When I was researching the Euler equations, I thought that the reason the Euler equations didn’t align with the real fluid motion was that the Euler equations consider fluids as molecular aggregates, which only applies to completely uniform flow. However, in reality, fluid motion is usually non-uniform.

From practical experience, pressure does not have a significant effect on the resistance generated by molecular interactions between different parts of the moving fluid. Instead, this resistance mainly comes from the differences in velocity magnitude or direction between adjacent molecules. So, based on this premise, I further derived classification expressions for the forces acting on molecules from the movement of adjacent molecules on the basis of the Euler equations.

Just after I completed this work, the next day, I eagerly took my latest research findings to Cauchy for review. He happened to be interested in this area as well and immediately identified a flaw in the formula—this was merely a set of equations describing the dynamic balance and motion of incompressible fluids, evidently insufficient to describe the macroscopic fluid motion laws. I was aware of this flaw, but with my abilities, deriving to this point was already my limit.

I thought the research on the Euler equations would end there, but to my surprise, a few months later, Cauchy suddenly walked into my office with a stack of papers. He said that under the given premises, he introduced the concept of a stress tensor for a fluid microelement into the Euler equations and thus, accidentally found a set of formulas that can accurately reflect the differences between fluid motion and solid motion.

Later, in a conversation, Cauchy told Mr. Poisson about my new findings. As a result, Poisson also took only a few months to derive, under the same conditions, an equation describing the motion of compressible fluids from the Euler equations.”

At this point, Navier felt both happy and a bit of a headache, and he said: “The greatest fortune for the French Academy of Sciences is having Cauchy and Poisson, these two mathematical monsters. In many research problems, they have inadvertently saved us a lot of trouble. If it weren’t for the two of them, I believe the current research at the Academy would still be stuck at the hypothesis and derivation stage. The greatest misfortune for the French Academy of Sciences, however, is that one of these mathematical monsters left last year. Rather than insisting on my return to the bridge construction committee, I think the government should first find a way to get Cauchy back.”

Hearing this, Coriolis said helplessly: “Mr. Navier, you know that’s impossible. You and Mr. Cauchy are old friends, and Mr. Cauchy is my mentor. Both of us understand his temperament and stance: he is a staunch supporter of the Legitimate Dynasty, dedicating his life to supporting the Bourbon Dynasty. Although Napoleon also won his willingness to serve, our current King is Louis Philippe, who obviously does not have the same allure for Mr. Cauchy as Napoleon did. Therefore, it is impossible for Mr. Cauchy to ever pledge allegiance to the July Monarchy.”

Navier was equally helpless but out of concern for his old friend, he inquired about Cauchy’s recent situation from Coriolis: “Is Cauchy still in Prague? Is he still working as the tutor for the Duke of Bordeaux, the Bourbon Dynasty’s Crown Prince?”

Coriolis shook his head: “No, he recently went to Graz with the Bourbon Royal Family. Metternich of the Austrian Empire ordered all Legitimate Dynasty exiles in the territory to be relocated there.”

“Is he still doing research?”

“Recently, he should be doing less, at least not as intensely as he did in Paris. Now, he mostly focuses on the education of the Duke of Bordeaux.”

“This might actually be a good thing. After all, using his brain so intensely and producing papers, his body couldn’t handle it for long. You don’t know how it was when he was young; he would write papers as if he were a printing press. Because he wrote so many thick papers, they almost filled up the entire journal’s pages by himself, forcing the Academy to pass a special resolution limiting the length of future papers to no more than four pages each. For him to rest a bit is a good thing for those young scholars eager to make their mark.”

Hearing this, Coriolis couldn’t help but chuckle: “You’re right. Mr. Cauchy’s temporary departure is a misfortune for the entire French scientific community but a blessing for all French scientists. When he was at the Academy, he was like the Alps pressing down on everyone’s heads. Perhaps only a genius of the same level as Mr. Poisson could be completely indifferent to him.”