"Teacher, don't you think it's inconvenient to not have a precision timekeeping tool all these days, hourglasses, and water leaks, and so on, and they're too rough. ”

That afternoon, Kaichi found Im, and the beginning was a question about clocks, or rather, timekeeping tools.

"Is there anything you have to do?" Im knew as soon as he heard Kaichi's words that he needed his help for something he wanted to do.

Jia Yi said: "Teacher, I read the paper on the three laws of motion in the collection of essays you brought back, and I found something. ”

"Oh, what's the matter?"

"If we tie a small ball on a thin wire, then the time for the ball to swing is equal, especially at a small angle, which I calculated by the three laws of motion and the acceleration of gravity, that the swing time is theoretically equal. Jia began to explain the pendulum to Imu.

"How do you prove it?" asked Imu, if there is no detailed process of proof, then the theory you have invented is basically not absolutely wrong, at least it cannot be considered correct.

"We start with an idealized pendulum and a cycloid, which is provided by a thin, non-scalable line of incalculable mass, and the pendulum is denser and the radius of the ball is much smaller than the length of the cycloid, so that the pendulum can be seen as a mass... In this way, when the angle of the line pendulum is particularly small, we can consider it to be a simple harmonic motion..."

Jia took out a pen and paper and drew a diagram while demonstrating the calculation process to Imu.

Finally, he concludes: "In this way, the time of the pendulum is only related to the length of the cycloid, and has nothing to do with other factors. If we choose a suitable cycloid length, we will be able to time it according to this. ”

After reading the process and method of Kaichi's proof, Imu had to be impressed by his keen insight, and theoretically, Kaichi's method was very feasible.

He was persuaded by Kaichi and began to design and make pendulum clocks with Kaichi.

Now that we have decided to start making a pendulum clock, the first thing we need to define is the most basic unit, the second. The whole day here is divided into 12 hours, and in order to facilitate himself, according to the division method of his previous life, he persuaded Yimu to divide 1 hour into a 24-hour system. Then, from the easy division of the disc, there was also a 60 base system in ancient times, etc., so that Im received the setting of one hour and 60 minutes, and one minute and 60 seconds.

This is very necessary, and if you can't confirm the basic time unit, you can't continue the rest of the work. Originally, the magicians were clocking through the standard magic hourglass, and a standard magic hourglass was leaked for about 24 minutes, but they didn't continue to subdivide it, only talking about a few hourglasses, and a few tenths of an hourglass.

After determining the basic unit of the second, the chia began to calculate how long the pendulum rope needed for a second of swing according to the formula. The gravitational acceleration here is not the same as that of the Earth, but is faster, and each revolution takes a little longer. As a result, one second here is longer than the time on Earth in Jia Yi's previous life, and one second here is about 1.25 seconds.

Of course, we don't discuss any of this, just know that the day is now 24 hours, 3600 seconds per hour, and it would be a waste to redefine time.

It doesn't matter how long a second is!

In fact, the principle of a single pendulum is easy to understand, and the length of a single pendulum is easy to calculate.

Speaking of how to open the square, Jia Yi learned it in this world. Because when Jia Yi went to school in his last life, the school no longer taught how to prescribe prescriptions manually, and when he used a calculator, even if he didn't use a calculator, he would give an approximate value after the numerical prescription. So after Jia Yi arrived in this world, he was a little blind about Kaifang.

At first, he could only rely on the correct value step by step, for example, 3 open square, he first used 1.5 to calculate, small, added to 1.6, still small, added to 1.8, large reduced to 1.7, now get between 1.7 and 1.8, then use 1.75 to calculate, has been like this, it is very cumbersome, not scientific.

Fortunately, after learning from Yimu, I made up this piece, in fact, it is also simple, the large value can be divided into two sections, thousands and tens are calculated separately, in the merger, if the value is relatively small, there is a formula, through repeated calculations step by step to approximate the correct value, although it can not be done in one step, but compared to the original method is much more trouble-free.

With these foundations, Jia Yi calculated the pendulum length of one second according to Newton's three laws, although it was not very accurate.

After determining this basic information, Ka began to design the drawings, a step that was done with Imu, but the work of drawing was given to Kaichi. Who is called Jiayi sketching already has some skills, and it is just right to use it for drawing.

These can be solved calculatingly, but it is more difficult to get to the design part. After all, he had never built a clock, and he was not familiar with the internal structure. In my previous life, when my family was poor, I couldn't afford to buy a grandfather clock, and when I could afford it, the grandfather clock had been eliminated and became a small alarm clock, and then there was an electronic clock.

But Jia Yi knew the structure of the pendulum clock, and he once went to Baidu to check the principle of the table clock because of curiosity. The time of the pendulum is indeed fixed, but because of the resistance, the pendulum will become slower and slower and eventually stop. He had never understood why the grandfather clock could keep moving after it had been wound, until he had watched a video of how the grandfather clock worked.

In addition to the pendulum control time standard, the most important thing left in the pendulum is the escape wheel and the pallet fork, which constitute the escapement system, through which the swing of the pendulum controls the movement of the second hand, and at the same time, the escape wheel and the pallet fork have a subtle angle, which gives the pendulum a weak force while controlling the movement of the hands, so that it can overcome the resistance in the swing process.

Of course, these are all theoretical, and it is not as simple as it sounds, as both the escape wheel and the pallet fork need to be carefully designed to ensure that only one gear passes at a time and that the second hand only goes one step. There is also power, Jia Yi did not use the clockwork directly at first, he wound a wire around the axle of the gear, tied a heavy object under the line, and used gravity as power.

Of course, this is only a stopgap measure, but the production of the spring is not simple, in addition to the right steel, it also needs to be cut thin enough, able to be rolled up, elastic enough, etc., etc. Jia Yi felt that this was still too troublesome, so he decided to make do with the power first, and then put it on later.

In fact, what Kaichi wanted to make most was a pocket watch, because there was magic, although industrial mass production was not as good as modern craftsmanship on earth - not even the level of the early 20th century. But with the help of magic, the fine work by hand can be very delicate. But he didn't know the principle of the chronograph mechanism of the pocket watch, he had only heard of the quartz watch or something, but he didn't know the vibration principle of the quartz, even if he took it apart himself, he couldn't see the principle.

Let's take it step by step, you can't eat a fat man in one bite. Kaichi believes that although he doesn't know how to do it (mainly because the author doesn't know), when the pendulum clock is introduced and the mages understand the principle of the pendulum clock, they will definitely be able to make pocket watches, watches, and so on.