Volume 4: Gathering of Sages Chapter 672 Density
Zhang Shou always asks a lot of whys, and students at Jiuzhang Hall and Banshan Hall have experienced this. Sometimes when you are listening to difficult content and are already confused, he will suddenly throw out a bunch of whys, leaving you unprepared and confused for a long time. And the most annoying thing is that after asking whys, Zhang Shou usually does not answer them, but asks you to go back and think about it yourself!
Sometimes, Zhang Shou would mercifully answer their questions in class after they had been thinking for days but still could not get the point. But more often, he would just continue to guide and instruct them, asking them to continue thinking and pondering. As Zhang Shou often said, the magic and mystery of the world cannot be solved by others, but by asking why when you have nothing to do, and then pondering and understanding.
But, in an occasion like today, Zhang Shou wouldn't play tricks on us in such a bad way, right?
Lu Sanlang was in a state of uncertainty, and could only hope that the Third and Fourth Princes would be more helpful and not let the people below continue to think about it. Sure enough, the Third Prince, as a diligent and studious prince, was really trying to figure out why, but the Fourth Prince, this naughty kid, asked directly without any scruples.
"Then teacher, do you know why this is happening?"
Seeing that the audience had completely lost interest and many of the scholars looked either dumbfounded or confused, Principal Yue had intended to start the conversation himself, but he did not expect the Fourth Prince to take the lead again, so he sat down leisurely. You know, as the Principal of Zhaoming Academy, he had dabbled in a lot of subjects, but although he had noticed many phenomena, he was still unable to explain the reasons.
If Zhang Shou really had many teachers as he said, then he would have dared to start with such a topic in front of so many talented astronomical figures and candidates from all over the country, and he would definitely be able to give a reasonable answer. Otherwise, wouldn't that be a joke?
Zhang Shou did not answer the Fourth Prince's question immediately, but continued to ask: "Why do gold, iron and stone sink to the bottom of the water? Why do some wood float on the water surface, but some wood sinks to the bottom? Why are both liquids, oil floats on the water surface, but mercury sinks to the bottom?"
After asking three more whys, he saw that the people below were already making a commotion, as if someone was saying that this was all common sense and there was nothing to explore. He said calmly, "Don't think that these phenomena, which are seen everywhere and have always been considered commonplace, are nothing surprising. The truth of the world is actually all hidden in what we see in daily life."
"You know, when I solved the Nine Chapter Hall plaque that contained the Emperor Taizu's scroll in public, the principle behind it was similar to this one."
"Whether an object floats or sinks in water or other liquids depends on the density of the object and liquid, and liquids such as pure water, salt water, and oil also have their own density. Therefore, objects with high density will sink to the bottom in liquids with low density, while objects or liquids with low density will float on the surface in liquids with high density."
"And if the density of the object and the liquid is almost the same, then it is very likely that the object will be completely submerged in the water, but will not sink to the bottom, but will float in the middle of the water. Of course, if anyone still thinks this is a sorcery, then you can verify it after you go back. Just add salt little by little and dissolve it, and you should be able to verify not only suspension but also floating."
After dropping another bombshell, Zhang Shou saw that many people were eager to try it out. It was obvious that they really intended to verify this extremely simple experiment after returning. He smiled and continued, "Now, let's continue to talk about density. What is density? The mass of an object per unit volume is density. And is density useful in real life?"
"The answer is simple. Of course it is useful. When minting coins, the copper ratio is often too low, which makes the coins too light and difficult for the people to trust. But if the copper ratio is too high, the court will be burdened and the miners will have a greater workload. If the density is controlled well, not only copper coins can be minted, but also silver coins and even gold coins."
"Of course, money is the most important thing in a country. Today we are not going to talk about that. Let's talk about something else, which is measuring tools."
As Zhang Shou spoke, he glanced at the Third Prince who was listening very attentively beside him, and then continued calmly.
"Our ancestors invented measuring tools for weighing rice, flour, millet, sorghum and other grain crops, such as hu, dou, sheng, he, shao, etc. To this day, these measuring tools are still used by the court to collect taxes, landlords to collect rent, and civilians to buy grain. Are these measuring tools used to weigh the weight of rice and flour? No, these measuring tools actually measure the volume of various grains."
"That is to say, using measuring utensils to weigh grain is completely different from using scales to weigh pork, mutton, etc. at the market."
"Your Highness once asked a question about farming in the examination of the East Palace attendants. I think the news should have spread by now. At this moment, there should be no one asking what hu, dou, sheng, he, and shao are, and how these measuring tools are used to weigh grain, right?"
He paused and saw that some people smiled knowingly, but some were hiding the confusion on their faces. He knew that among these scholars who were devoted to reading the books of sages, there were probably many who had never seen even a small amount of money. He couldn't help but smile.
"The measuring tools were originally government-made, but when they got into the hands of some wicked people, they would often come up with their own set of things, for example, the big and small buckets. They bought the big buckets and sold the small buckets to make a profit. Today I won't talk about this, but only about another method, which is the so-called "leaning the tip and kicking the bucket". I want to ask, does anyone know what these four words mean?"
The Third Prince frowned, but he couldn't think of anything. He wasn't even sure what the four words were. There was a buzz of discussion below. Although most people tried their best to keep calm, their erratic eyes showed that some people, like him, had heard of these four words for the first time, and some people might know the trick.
Thinking of this, he immediately asked, not intending to be a mere observer today, "Teacher asked about the 'Lin Jian Ki Hu'. Is there really no one who knows what it means?"
Seeing that no one responded, he simply laughed at himself and said, "It seems that you would rather let me be an ignorant person?"
As soon as the Third Prince finished speaking, a young man stood up and said loudly, "Reporting to His Royal Highness, the so-called "涼尖踢橛" is a malpractice of the tax collectors when they collect grain! When the people carry their grain to hand it in, the government does not use shengdou to weigh it, but hu. The so-called hu is a measuring tool that can hold five dou of grain!"
The fourth prince found that he actually recognized the person. He had once questioned his third brother's solution in the Jiuzhang Hall of the Imperial College, and was later kept in Zhang Garden by Zhang Shou. He didn't care that this was in public, and hurriedly whispered in the third prince's ear to remind him again. The third prince immediately laughed. Do you need to explain? It's not like I don't know him!
Fang Qing stood up in indignation and revealed the matter. Although he had noticed that Mr. Song was desperately pulling at his clothes, he ignored it. After all, when he was still a scholar, his family was exploited like this. Later, when he was a scholar, he paid less taxes.
"In theory, one hu, or five dou of grain, should be filled until the mouth of the hu is level. However, in order to save more, the clerks often require the people to continue to fill the hu with grain until the mouth of the hu is level. This is called linjian."
"But if it is just pouring water like this, even if it is a bad policy, it can be regarded as storing grain for the country. However, these clerks often have a more powerful trick, which is to kick the bucket. You know, the bucket is placed flat on the ground. Once it is poured with water, a lot of grain will naturally fall down when kicked. This can be blatantly regarded as loss and they can fill their own pockets!"
"There are some who are even more evil-minded. In order to collect more grain, they not only weigh the grain by the pound, but also make the people drink the grain again. After the grain is stored in the warehouse, they will weigh it again according to the pound..."
As Fang Qing described this vividly, the Third Prince's expression finally changed. He could never have imagined that collecting taxes would have so many tricks. Seeing Fang Qing sitting down, he couldn't help but ask Zhang Shou, " Is this what the teacher just said about the Linjian Kihuo?"
"Yes, but not entirely. What I just wanted to say is that there is another point hidden in the Linjiantihuo."
Zhang Shou smiled nonchalantly, then clapped his hands. Not long after, Ah Liu came over with a hu in one hand and two rice bags in the other. He then placed the things next to Zhang Shou. However, when a muffled sound was heard, everyone below realized that the two things were surprisingly heavy.
"Both bags have been measured with the official measure. Five dou is half a stone of millet. Now, Ah Liu, put it in the official measure and show it to everyone."
Ah Liu was a person who always did what Zhang Shou said, so he untied the string of the bag and lifted it up easily with one hand, then controlled the mouth of the bag and poured it into the large jar.
Although the people below could not see the specific situation, they could still hear the sound of the grain pouring down. The Fourth Prince, who was watching intently at the side, could not help but shout, "Sixth brother, be careful, it's almost full, don't spill it!"
As Ah Liu watched the grain pouring down, he looked at the Fourth Prince with disdain. He wanted to say that when he was in Rongshui Village, he didn't rely on that unreliable guy Old Liu to collect rent, but on him. He was an old hand at pouring grain into the bucket, so did he need to be reminded?
Sure enough, when it was almost at the mouth of the jar, he quietly closed the mouth of the bag, and the grains fell much slower. He skillfully adjusted his wrist and the direction of the mouth of the bag, and soon all the grains in the bag were poured out, and then he smoothed it out with his hand. At this time, the third and fourth princes beside him saw that the grains were exactly level with the mouth of the jar.
The Fourth Prince was not as reserved as the Third Prince. Upon seeing this, he immediately shouted, "Sixth Brother, what a trick! It's even!"
Seeing the brothers' testimony, Zhang Shou said with a smile, "This is a real hu, or half a stone of grain. Now, I won't be so harsh. Ah Liu, kick it. Be gentle, don't knock it over, don't let the grains spill, and don't break this official hu!"
As soon as these words came out, Lu Sanlang, who had been planning to fill in the gaps but had never found an opportunity, broke out in a sweat, and the Fourth Prince couldn't help but think of the suffering he had suffered in the past. For a moment, he thought that the official was himself, and hurriedly dodged behind his third brother. As for the other lecturers and those who came to listen to the lecture, they were stunned or dazed.
They have listened to countless lectures since they were young, but have they ever experienced such a unique lecture?
Although countless eyes were on him, Ah Liu remained calm. He did not do much preparation like the tax collectors in the government, and did not even take a step back. Instead, he casually raised his foot and kicked Guan Hu. The Fourth Prince even found that Guan Hu did not move at all, and could not help but widen his eyes and said: "Sixth brother, your kick is too light..." Could it be because he did not eat enough today?
Before he could finish his words, he was interrupted by the Third Prince: "Fourth brother, if you don't understand, don't make a fuss! With his kick, not a single grain of millet that was level with the mouth of the bucket just now fell out. And most importantly, look at the millet in this official bucket now!" The Fourth Prince was slightly stunned, and when he looked inside again, his eyes widened: "Really, it seems to be less all of a sudden!"
Although all the people who came to attend the lecture today with invitations were scholars, few people knew about the trick of Lin Jian Ki Hu - otherwise, it might not be Fang Qing's turn to be in the limelight in front of His Royal Highness the Crown Prince. Even if some people would worry about being hated after the news spread, there has never been a shortage of gamblers who dare to take a chance in this world. However, for this situation, it is not that no one has anticipated it.
At this moment, someone below immediately shouted, “Isn’t it the same when you use boxes to store things? They’re obviously full, but if you knock and pat them, they can be filled again!”
"That's right, that's the truth!" Zhang Shou praised him as he slapped the podium. But after praising him, he changed his tone and asked, "But has anyone ever thought about why this is the case?"
Hearing the word "why" again, Lu Sanlang's scalp was numb, and even the Fourth Prince was confused. The Third Prince had been trying to keep up with Zhang Shou's pace, and didn't notice that most of the others looked dumbfounded. Instead, he thought to himself, "Is it because after the kick, it was like being pressed by hand, and the grains were more compact in the bucket?"
"That's about the same principle. Millets are irregular objects, so when they are poured into the hu, there are often gaps between them, so the volume they occupy is actually relatively large. And with such a strong kick, the millets in the hu are hit hard, and the arrangement between them will change. The originally larger gaps will be filled. Since the gaps between them are reduced, the millets that were originally flush with the mouth of the hu will naturally appear less full."
"So, the same hu of millet has different weights. To measure the approximate density of non-lump objects such as grains, you can do it like kicking the hu with a tip, kicking it repeatedly and finally smoothing it out, or you can just calculate it after filling it up. Then, weigh the weight of the grain and divide it by the volume of the official hu. This is the density, but most of the time we can call it bulk density."
