Chapter 4 Section 3 Early Measurement Techniques

After all, the area of ​​the tripod is limited. It can be imagined that the figures cast on it are quite simple, and the geographical location they can express is naturally very rough.Because in the absence of measurement technology, people's feeling and expression of geographical location can only be purely intuitive. According to legend, when Dayu controlled the water, he "left the guideline and right the rules"; that is to say, he held the guideline in his left hand and the gauge and moment in his right hand. "Zhun" and "rope" are instruments for measuring the flatness and straightness of objects, "gauge" is a tool for correcting circles, and "moment" is a curved ruler for drawing squares.It is also said that Dayu once sent his two assistants, Da Zhang and Shu Hai, to measure the size of the world.Although these measuring tools were not necessarily invented in Dayu's era, and it was difficult for Dayu's assistants to measure the size of the world, it shows that in ancient times, people had mastered these tools in production practice, and it also shows that at the latest in the late Warring States period or In the early Han Dynasty, there were already specialized surveyors. The invention of "moment" is even more significant, because "moment" can form a right angle, and only when it forms a right angle can it be used for measurement.

There is an article "Gong Liu" in "The Book of Songs Daya", which is said to have been written by Duke Zhao Kang, a minister of King Cheng of Zhou.Among them is a sentence that calls Gong Liu "Jijing Naigang", which means standing on a hill to measure the shadow to determine the direction.Gong Liu was around the end of the 15th century BC. "Zhou Li · Kao Gong Ji" says that craftsmen "use water and land to counties" (use level and plumb line to determine whether the ground is level), "set to county" (use plumb line to determine whether the pole is vertical).According to Zheng Xuan's explanation, "Shuidi Yixian" means "stand upright at the four corners and the county is surrounded by water, look at its height, the height is fixed, it is the position and the ground is flat" (hang four straight lines on the four corners of the instrument respectively. Hanging on the surface of the water, the measurer observes the height of each line. After measuring the height of each line, you can know whether the ground is level.) From this record, it can be seen that the method of measuring the level of the line with heavy objects was mastered at that time . "Zhou Li" was written no later than the Warring States period, and some of its contents can certainly be traced back to the Western Zhou Dynasty. "Zhou Bi [bi coin] Suan Jing" and "Nine Chapters of Math" prove that at the latest in the Western Han Dynasty, people had been able to use multiple methods to measure mountain heights, valley depths, distances, or simultaneously measure mountain heights and distances.Guide car (no matter which direction the car is driving, the indicator on the car is always pointing to the south) and meter drum car (measure the distance traveled during the driving process of the car, and when a specified distance is reached, the wooden man on the car will beat the drum once ) appeared at the latest in the Han Dynasty, which provided favorable conditions for large-scale and long-distance measurement.

The well-developed astronomy in ancient my country also provided people with the conditions to use astronomical phenomena for positioning.In "Xiaoya·Dadong" in "Xiaoya Dadong", the poems such as "Weinan has a Ji" (ah, there is a star in the south!), "Weibei has a bucket" (ah, there is a dipper in the north!), this poem was roughly written in Before 684 BC, it proved that people at that time knew to use the position of the constellation to determine the direction. There are four directions recorded in "Shangshu·Yao Dian": east, west, south, and north, and "Shangshu·Yugong" has increased to eight. In 1977, on the Liuren-style plate of the early Western Han Dynasty unearthed from the tomb of Ruyinhou in Fuyang, Anhui, there are 12 orientations composed of eight stems and four dimensions.In the "Tian Wen Xun", which was written in the book "Huainanzi" in the early Western Han Dynasty (between the first and second centuries BC), 24 directions have appeared (Figure 1).Combining the type plate and the compass can become an instrument for measuring azimuth, which can measure the specific position of mountains, rivers and city walls, and express it on the plan more accurately.

These theories, technologies and tools all provide conditions for the emergence and progress of maps. The "cross" or rangefinder was once the most important measuring tool in the Middle Ages in Europe. It is generally believed that it was first mentioned by Levi Ben Gerson, a Jewish scholar in Provence in 1321.In its simplest form it is a graduated rectangular rod about four feet long, with a cross-bar always at right angles to it, which slides back and forth with the rectangular rod.This range finder can be used to measure the length of those unreachable or walkable line segments.However, Shen Kuo, a scientist in the Northern Song Dynasty, discovered that as early as the end of the 2nd century AD, the principle of measuring distance with cross-hair grids had been used in our country.

At the end of the Eastern Han Dynasty, the world was in turmoil, but Chen Wang and Liu Chong relied on his magical shooting skills to keep one side safe for the time being. There is such a record in Volume 50 of "Hou Han Shu": "Chong is good at crossbow shooting, ten shots and ten hits, all of them are in the same place." ( Liu Chong is good at archery with a crossbow. He can hit the target ten times, and the position of the shot is exactly the same.) "Chong has thousands of crossbows." The secret of Liu Chong's "ten shots and ten hits" is According to Hua Qiao's explanation, "It is strange to see the sky and the earth, and it is connected. There are three micros and three smalls. The three micros are the warp, and the three smalls are the latitude. The longitude and latitude are intertwined. The formula of all victories must be in Jiya." .Because these few sentences are quite cryptic, they have not attracted people's attention.

When Shen Kuo was in Haizhou, someone dug a crossbow in the ground. When Shen Kuo saw it, he felt very strange: when using it to observe the entire width of the mountain, the distance on the crossbow is very long, and a small distance on the crossbow is used to observe the mountainside. Partially, the distance on the crossbow is very short (because the crosspiece must be pushed farther away from the eye, and the scale is counted from the far end).The crossbow stand looks like a ruler with minute and inch scales.Shen Kuo believes that the intention of the original designer is that when the crossbowman puts the arrows at different points and aligns his eyes with the two ends of the arrowhead [zu foot], he can measure the degree of the mountain on the crossbow machine, so that The height of the mountain can be calculated, just like the similar triangle calculation method used by mathematicians.

At this time, Shen Kuo understood the mystery of Chen Chong's divine shooting: the so-called "overwhelming heaven and earth" refers to the posture of holding the crossbow with both hands, one hand in front and the other behind; The relative position on the scale, which depends on the distance of the target, can determine the appropriate elevation angle of the crossbow.This principle is exactly the same as using similar right triangles to calculate height and depth. The "three longitudes and three latitudes" (three horizontal lines and three vertical lines, that is, the grid or crosshairs for aiming) are set on a frame, and the shooter can use them to aim at the target up, down, left, and right.

In order to prove this principle, Shen Kuo also conducted an experiment himself. He set three horizontal lines and three vertical lines on the crossbow, and aimed at the target with an arrow with a crossbow, and the result was seven out of ten.He believes that if a scale can be added to the crossbow, the accuracy will definitely be further improved. Shen Kuo may not have noticed this sentence in "Book of the Later Han Dynasty": "Chong has thousands of crossbows." Obviously Liu Chong alone can't use thousands of crossbows anyway. Use such a strong crossbow, that is, the special crossbow used by Liu Chong.This also shows that Liu Chong's marksmanship is mainly due to this special crossbow, not just his technique.The mass production of this kind of crossbow is enough to prove that Liu Chong and the others fully understood the special functions of the crossbow at that time, rather than accidentally using the crossbow sight by accident.

Therefore, it is likely that the cross was first invented in China and then introduced to Europe.