At that time, people were infected with a strong desire to understand the earth-to determine the age of the earth, how big it is, which part of the universe it hangs in, and how it formed. The task of the French team is to measure the meridian length of 1 degree (that is, one third of the circumference of the earth) along a straight line from Yalok near Quito to Cuenca, Ecuador, thus helping to solve the circumference problem of this planet.
Things went wrong almost from the beginning, and sometimes it was a big problem that surprised people. In Quito, tourists somehow angered the locals and were stoned out of the city by thugs. Not long after, due to misunderstanding with a woman, a doctor of the survey team was murdered. The botanist in the group is a madman. Others died of fever or falls. The third person on the expedition-a man named Jean Godin-eloped with a girl of 13 years old, but he failed to persuade her to come back.
The investigation team once had to stop work for 8 months; At the same time, Kangdaming rode to Lima to solve the permit problem. He finally stopped talking to Bug and refused to cooperate. Everywhere this shrinking investigation team went, local officials were suspicious. It is hard for them to believe that these French scientists will walk halfway around the world in order to measure the world. It doesn't make any sense. Two and a half centuries later, this still seems to be a very reasonable question. The French don't have to suffer so much when they go to the Andes. Why don't they do an investigation in France?
On the one hand, this is because scientists in the18th century, especially French scientists, rarely do things in simple ways. On the other hand, it is related to a practical problem. This problem originated many years ago-long before Bug and Camming dreamed of going to South America, not to mention there was a reason to go-British astronomer edmund halley.
Harley is an extraordinary person. During his long and productive career, he worked as a captain, a cartographer, a professor of geometry at Oxford University, a deputy director of the Royal Mint, a royal astronomer and the inventor of the deep-sea diving clock. He wrote authoritative articles about magnetism, tides and planetary motion, and naively wrote articles about the influence of opium. He invented weather charts and tables, proposed methods to measure the age of the earth and the distance between the earth and the sun, and even invented a practical method to keep fish fresh until the off-season. The only thing he didn't do was to find the comet with his name engraved on it. He just admitted that the comet he saw at 1682 was the same comet as the comets that others saw at 1456, 153 1 and 1607 respectively. This comet was not named Halley's Comet until 1758, about 16 years after his death.
However, despite his achievements, perhaps his greatest contribution to human knowledge is that he took part in a scientific bet. The stakes are not big, and the other party is two other outstanding figures of that era. One is robert hooke, who may be remembered for describing cells. The other is the great and majestic Sir Christopher Wren, who was actually an astronomer at first, and later became an architect, although people often don't remember this now. 1683, Harley, Hook and Ryan were having dinner in London when suddenly the topic turned to celestial sports. People think that planets often orbit with a special oval line, that is, an ellipse-in richard feynman's words, "a special and precise curve"-but I don't know why. Ryan generously offered to give one of them a bonus worth 40 shillings (equivalent to two weeks' salary) if he could find the answer.
Hook is famous for his ambition, although some ideas are not necessarily his own. He claimed that he had solved the problem, but now he didn't want to tell everyone that his reason was interesting and ingenious, saying that doing so would make others lose the opportunity to find an answer for themselves. Therefore, he wants to "keep the answer secret for a while, so that others will know how to cherish it." There is no indication that he has thought about it again. However, Harley was fascinated and had to find the answer. The following year, he also went to Cambridge University and took the liberty of visiting isaac newton, a professor of mathematics at the university, hoping to get his help.
Newton is definitely an eccentric-he is smart, withdrawn, slow, sensitive and suspicious, and his attention is very unfocused (it is said that after he puts his feet out of bed in the morning, sometimes his thoughts will suddenly surge and sit for hours), and what he does is very interesting and strange. He set up his own laboratory, which was the first laboratory in Cambridge University, but later he engaged in unusual experiments. On one occasion, he inserted a large needle-eye suture needle-a long needle used to sew leather-into the eye socket and rubbed it "as close to the back of the eye as possible between the eye and the bone" just to see what would happen. As a result, strangely, nothing happened-at least there were no lasting consequences. On another occasion, he stared at the sun as long as possible to find out what effect the sun had on his eyesight. Once again, he was not seriously injured, although he had to stay in a dark room for a few days, waiting for his eyes to recover.
Compared with his extraordinary genius, these strange beliefs and eccentric characteristics are nothing-even when he works in a conventional way, he often looks very special. When he was a student, he felt that general mathematics was limited and disappointed, so he invented a brand-new form-calculus, but he didn't tell anyone about it for 27 years. He worked in the field of optics in the same way, which changed our understanding of light and laid the foundation of spectroscopy, but it took him 30 years to share his achievements with others.
Clever as he is, real science is only part of his interest. At least half of his working age is spent on alchemy and capricious religious activities. These activities are not dabbling, but devoted. He secretly believes in a dangerous heresy called arius. The main teaching of this religion is that there is no Trinity (which is somewhat ironic because Newton's work unit is Trinity College of Cambridge University). He spent countless hours studying the floor plan of King Solomon's Temple in Jerusalem (in the process, he taught himself to read the original in Hebrew), thinking that the floor plan hides mathematical clues and helps to know the date of the second coming of Christ and the end of the world. He is equally keen on alchemy. 1936, the economist john maynard keynes bought a box of Newton's literature at the auction, and was surprised to find that most of those materials had nothing to do with optics or planetary motion, but some materials about his painstaking exploration of turning lowly metals into precious metals. In 1970s, by analyzing a lock of Newton's hair, it was found that it contained mercury, which was an element that nobody was interested in except alchemists, hat makers and thermometer manufacturers, and its concentration was about 40 times that of ordinary people. Maybe it's not surprising that he got up unexpectedly in the morning.
1684 In August, Harley called on Newton uninvited. We can only guess what help he expected from Newton. However, due to the narrative of Newton's close friend Abraham Di Mover, we have the record of one of the most historic meetings in the scientific community:
1684, Dr. Harley visited Cambridge. After they stayed together for some time, the doctor asked him, if the gravity of the sun is inversely proportional to the square of the distance between the planet and the sun, what does he think the curve of the planet will be like?
What is mentioned here is a mathematical problem called inverse square law. Harley firmly believes that this is the key to explain the problem, although he is not sure about the mystery.
Isaac newton immediately replied that it would be an ellipse. The doctor was pleasantly surprised and asked him how he knew. "Oh," he said, "I have calculated it." Then, Dr. Harley immediately asked for his calculation materials. Sir Isaac rummaged through the material pile for a while, but he still couldn't find it.
This is very surprising-it's like someone saying that he has found a cure for cancer, but he can't remember where the prescription is. At Harley's urging, Newton promised to do another calculation and write a paper. He did as promised, but he did more. For two years, he has been locked indoors, thinking carefully and drawing, and finally took out his masterpiece: the mathematical principle of natural philosophy, which is more often said.
Occasionally, there are only a few times in history. Someone has made such a keen and unexpected observation that people can't be sure which is more amazing-the fact or his idea. The publication of Principles is such a moment. This immediately made Newton famous. In the rest of his life, he will live in praise and honor, especially becoming the first person in Britain to be knighted for his scientific achievements. Even the great German mathematician gottfried leibniz thought that his contribution to mathematics was comparable to the sum of all his previous achievements, although Newton had a long and fierce struggle with him on who invented calculus first. "No mortal is closer to God than Newton." Harley wrote with deep feelings. His contemporaries felt the same way as many people since then.
Principle has always been called "one of the most difficult books to understand" (Newton deliberately wrote it so as not to be entangled by what he called "amateurs" in mathematics), but it is a bright light for those who can understand it. It not only explains the orbit of celestial bodies from a mathematical point of view, but also points out the gravity that makes celestial bodies move-gravity. Suddenly, every movement in the universe makes sense.
The core of "principle" is Newton's three laws of motion (the laws clearly point out that the direction of motion of an object is the direction of thrust; It always moves in a straight line until other forces slow it down or change its direction; Every action has an equal reaction) and his law of universal gravitation. This shows that every object in the universe attracts other objects. It seems unlikely, but when you sit here, you are attracting everything around you with your own small (really small) gravitational field-walls, ceilings, lights, pet cats. And these things are also attracting you. It was Newton who realized that the gravity of any two objects, in Feynman's words, "is directly proportional to the mass of each object and inversely proportional to the square of the distance between them". In other words, if you double the distance between two objects, the attraction between them will be weakened by four times. This can be expressed by the following formula:
F=Gmm'R2
This formula is of course of no practical use to most of us, but at least we appreciate its beauty and simplicity. Wherever you go, just do two quick multiplications and a simple division. Hey, you'll know your gravity. This is the first truly universal natural law put forward by human beings, and it is also the reason why Newton is respected by people everywhere.
The emergence of principles is not without drama. To Harley's shock, when the work was about to be finished, Newton and Hook quarreled about who invented inverse square law first. Newton refused to reveal the key third volume, without which the first two volumes would be meaningless. After intense shuttle diplomacy and many kind words, Harley finally managed to get the last volume from this eccentric professor.
Harry's troubles are not over yet. The Royal Society promised to publish this work, but now it has backed out, saying that it is in financial difficulties. The year before last, the Society made a bet on the history of fish, which cost a lot and resulted in the loss of original capital. They are worried that a book about mathematical principles will not sell. Although Harley is not very rich, he published the book at his own expense. As usual, Newton paid nothing. To make matters worse, Harley has just accepted the post of clerk of the society. He was told that the association could no longer give him the promised annual salary of 50 pounds, and he could only pay with a few fish history books.
Newton's law explains many things-the splash and churning of tides in the ocean; The motion of the planets; Why do shells fly along a specific trajectory before landing? Although the planet under our feet is spinning at the speed of hundreds of kilometers per hour, why haven't we been thrown into space-the complete meaning of these laws needs great efforts to understand. However, they revealed a fact that caused controversy almost immediately.
That is, the law holds that the earth is not round, but round. According to Newton's theory, the centrifugal force produced by the earth's rotation makes the poles a little flat and the equator a little bulging. Therefore, the planet is slightly oblate. This means that the length of longitude 1 degree is not equal in Italy and Scotland. To be precise, the farther away from the poles, the shorter the length. This is not good news for those who think that the earth is a round ball and use it to measure the planet. Those people are everyone.
For half a century, people want to calculate the size of the earth, and most of them use very strict measurement methods. The first person to make such an attempt was the British mathematician Richard Norwood. When Norwood was young, he took a diving bell made in Harley style to Bermuda, hoping to get some pearls from the bottom of the sea and make a fortune. The plan didn't succeed, because there were no pearls and the diving bell in Norwood was broken, but Norwood was a man who didn't want to waste an experience. /kloc-At the beginning of the 7th century, Bermuda was famous for its difficulty in determining its position as a captain. The problem is that the ocean is too big and Bermuda is too small, and there is a serious lack of navigation instruments to solve this difference. Even the length of 1 nautical mile is different. With regard to the width of the ocean, the smallest calculation error will also increase, so ships often can't find a target as big as Bermuda with a big error. Norwood likes trigonometry, so he also likes triangles. He wants to use some mathematics in navigation, so he decides to calculate the length of longitude 1.
Norwood set out on the journey with his back against the Tower of London. He walked 450 kilometers north to York in two years, straightening and measuring a chain while walking. In this process, he took into account the ups and downs of the land and the curvature of the road, and always corrected the data meticulously. The last step is to measure the angle of the sun in York on the same day of the year and at the same time of the day. He completed his first measurement in London. According to this measurement, he deduced that the meridian length of the earth 1 degree could be obtained, and the entire circumference of the earth could be calculated. This is almost an ambitious task-if the length of 1 degree is miscalculated, the whole length will differ by many kilometers-but in fact, as Norwood proudly claimed, his calculation is very accurate and the difference is "tiny"-more precisely, the difference is less than 550 meters. Expressed in metric system, he got the figure that the length of each meridian is110.72km..
1637, Norwood's masterpiece "The Practice of Sailors" was published, which immediately won a group of readers. Reprinted 17 times, still printing 25 years after his death. Norwood returned to Bermuda with his family and became a successful planter. In his spare time, he used his favorite trigonometry as a pastime. He lived there for 38 years. If you tell everyone that he has been very happy and admired for 38 years, everyone will be very happy. However, this is not the case. On the voyage after leaving England, his two young sons shared a cabin with the pastor Nathaniel White, which somehow made the young pastor deeply traumatized and tried to pick on Norwood many times in the rest of his life.
Norwood's two daughters' marriages were not satisfactory, which brought extra pain to their father. A son-in-law may be instigated by a priest to sue Norwood in court for trivial matters, which makes him very angry and often has to go to Bermuda to defend himself. Finally, in the 1950s of 17, interrogation wizards became popular in Bermuda, and Norwood spent his last few years in fear. His trigonometry thesis with mysterious symbols will be regarded as communicating with the devil, and he will be horribly sentenced to death. We know very little about Norwood. Anyway, he spent his old age in an unpleasant environment, but he probably deserved it. This is how he spent his old age, which is of course true.
At the same time, the momentum of measuring the circumference of the earth also spread to France. There, astronomer Jean piccard invented an extremely complicated triangulation method, which used a sector plate, a pendulum clock, a zenith quadrant and an astronomical telescope (to observe the movement of Saturn's satellites). It took him two years to travel all over France and measure by triangulation. Later, he announced a more accurate measurement result: longitude 1 degree is 1 10.46 km. The French are very proud of this, but this result is based on the assumption that the earth is a sphere-and now Newton says that the earth is not this shape.
To make matters more complicated, after Picard's death, Giovanni and Jacques Cassini repeated Picard's experiment in a larger area. Their results show that the earth does not bulge at the equator, but at the poles-in other words, Newton was completely wrong. Because of this, the Academy of Sciences sent Bouguer and Kangdamin to South America for re-measurement.
They chose the Andes, because they need to measure the place near the equator to determine whether there is really a difference in roundness there, and because they think the mountain area has a wider view. In fact, the mountainous areas in Peru are often covered with dark clouds, and teams often have to wait for several weeks before they can wait for an hour of sunny days to take measurements. Not only that, they chose the most difficult terrain on earth. Peruvians call this kind of terrain "very rare"-this is absolutely true. These two Frenchmen not only have to climb some of the most challenging mountains in the world-mountains that even their mules can't cross-but also have to wade through several fast-flowing rivers, drill through dense jungles and cross cobblestone deserts several kilometers high, which are hardly marked on the map and far from the supply sources. However, Bug and Kangdaming are both persevering people. They persevered, were not afraid of the wind and the sun, and persisted in carrying out their tasks for nine and a half years. When the project was about to be completed, they suddenly got the news that another French expedition was measuring in the northern Scandinavia (facing its own difficulties, from impassable swamps to dangerous ice floes) and found that the meridian of 1 degree was indeed longer near the poles, as Newton asserted. The earth's measurements in the equatorial region are 43 kilometers thicker than those around the poles from top to bottom.
So, it took Bouguer and Kangdamin nearly 10 years to reach a result they didn't want, and found that this result was not the first one they got. They ended the investigation listlessly, just to prove that the French first team was right. Then, they silently returned to the seaside and set foot on the way home by boat.
Another conjecture made by Newton in "Principles" is that the vertical line hanging near the mountain will be slightly inclined to the mountain due to the gravitational mass of the mountain and the earth. This speculation is very interesting. If you accurately measure this deviation and calculate the mass of the mountain, you can calculate the gravity constant-the basic value of gravity, called G-and also calculate the mass of the earth.
Bug and Condamine did this experiment in Chimborazo Mountain in Peru, but it didn't succeed, on the one hand, because of the great technical difficulty, and on the other hand, because they quarreled with each other. Therefore, the matter was put on hold for some time, and it was not until 30 years later that Neville Maskelyne, a royal astronomer, restarted it in Britain. In her best-selling book Meridian, dava sobel described Maskelyne as a fool and a bad guy, who would not appreciate the outstanding talent of the watchmaker john harrison. This may be true. However, we should thank Maskelyne for other aspects that she didn't mention in her book, especially his successful plan to weigh the earth.
Maskelyne realized that the key to the problem was to find a mountain with regular shape and evaluate its quality. At his urging, the Royal Society agreed to hire a reliable person to the British Isles to see if such a mountain could be found. Maskelyne happened to know such a person-astronomer and surveyor Charles Mei Sen muskie Lin and Mason became friends 1 1 years ago. Together, they undertook a project to measure major astronomical events: transit of venus phenomenon. A few years ago, the tireless Edmund halley suggested that if this phenomenon is measured at a selected position on the earth, the distance from the earth to the sun can be calculated by using the law of trigonometry, and then the distance to all other celestial bodies in the solar system can be calculated.
Unfortunately, the so-called transit of venus is an irregular thing. This phenomenon appears in pairs, eight years apart, and then it will not appear once in a century or even longer. Harley will never do this in his life. However, this idea has always existed. 176 1 year, nearly 20 years after Harley's death, when the next transit arrives on time, the scientific community is ready-more than any astronomical phenomenon observed in the past.
With the instinct of suffering-a characteristic of that era-scientists went to more than 65,438+000 places around the world-including the jungles of Siberia, China, South Africa, Indonesia and Wisconsin. France sent 32 observers, Britain 18, Sweden, Russia, Italy, Germany, Iceland and other countries.
This is the first international cooperative scientific activity in history, but it is full of difficulties almost everywhere. Many observers met with war, disease or shipwreck. Some arrived at the destination, only to find that the instrument had been damaged or bent by the tropical sun when they opened the box. It seems that the French are doomed to bad luck again. It took Jean Sharpay several months to reach Siberia by carriage, boat and sleigh, and every bump had to be carefully guarded by fragile instruments. In the end, there was only one crucial trip left, but it was blocked by the rising river. It turned out that just before he arrived, there was a rare spring rain in the local area. The locals immediately blamed him because they saw him pointing the strange instrument at the sky. Sharpay managed to escape, but did not make any meaningful measurements.
What's even more unfortunate is Jishoum Jeanty, whose experience Timothy Ferris gave a wonderful and brief description in the book Growing up in the Galaxy. Jean-Marie set out from France one year in advance and planned to observe the transit in India, but she was still at sea on the day of the transit-this is almost the worst place, because the measurement needs to be stable and can't be done on a bumpy ship.
Undaunted, Janet went on to India, waiting for the next transit phenomenon in 1769. He had eight years to prepare, so he set up a first-class observatory. He tested his instrument again and again, making the preparation perfect. June 4th 1769 is the day of the second transit phenomenon. When he woke up in the morning, he saw a sunny day; However, just as Venus passed the surface of the sun, a dark cloud blocked the sun and stayed there for 3 hours 14 minutes and 7 seconds, almost exactly the time of transit of venus.
Letty packed her tools in disappointment and went to the nearest port. On the way, she suffered from dysentery and stayed in bed for nearly a year. In spite of his weak body, he finally boarded a ship. The ship was almost killed in a hurricane off the coast of Africa. After leaving for eleven and a half years, he finally went home. He found nothing, only to find that his relatives had declared him dead and robbed him of his property.
Comparatively speaking, the disappointment experienced by 18 British observers sent to various places is nothing. Mei Sen got along well with the young surveyor Jeremiah Dixon, and they also established a lasting partnership. They were ordered to go to Sumatra and draw a transit map there. But their ship was attacked by a French frigate on the second night of sailing. Although scientists are in the mentality of international cooperation, countries are not. ) Mei Sen and Dixon sent a short message to the Royal Society, saying that it seems that the high seas are very dangerous, and I don't know whether we should cancel the whole plan. They quickly received a chilling reply, in which they were scolded first, and then said that they had taken the money. The state and the scientific community had placed hope on them, and they would lose face if they didn't implement the plan. They changed their mind and went on, but news came from the road that Sumatra had fallen into the hands of the French. So they finally observed the transit phenomenon at the Cape of Good Hope, and the effect was very bad. On their way home, they came to St. Helena, an island in the Atlantic Ocean, and made a short stop, where they met Maskelyne. Due to the overcast clouds, the observation work in Maskelyne could not be carried out. Mei Sen and muskie Lin have established a strong friendship. Together, they have drawn a trend chart and spent several happy and even meaningful days.
Shortly thereafter, Maskelyne returned to England and became a royal astronomer, while Mei Sen and Dixon-obviously more mature at this time-set off for America for a long and often dangerous four years. They crossed 393 kilometers of dangerous wasteland, doing surveying work along the way, in order to solve the border disputes between william penn and Lord Baltimore manor and between their respective colonies-Pennsylvania and Maryland. The result is the famous Mei Sen-Dixon Line. Later, this line was symbolically regarded as the dividing line between slave States and free States in the United States. This line is their main task, but they also made several astronomical observations. Once, they made the most accurate measurement of the meridian length of 65438 0 degrees at that time. Because of this achievement, they won much more praise in Britain than solving the border dispute between two spoiled nobles. )
After returning to Europe, Maskelyne and his German and French colleagues had to conclude that the transit observation of 176 1 basically failed. Ironically, one of the problems is too many observations. When the observation results are put together, they often prove to be contradictory and cannot be unified. Transit of venus was successfully drawn by an unknown Yorkshire-born captain named james cook. He watched the transit of 1769 on a sunny hilltop in Tahiti, then drew a map of Australia and declared it a British royal colony. As soon as he returned to China, he heard that the French astronomer Joseph Lalander calculated that the average distance between the earth and the sun was slightly greater than1.500 million kilometers. (/kloc-there were two transits of the sun in the 0/9th century, and the distance obtained by astronomy was 654.38+49.59 million kilometers, which has been maintained until now. Now, we know that the exact distance should be1.38+0 million kilometers. ) The earth finally has a place in space.
Mei Sen and Dixon returned to England and became heroes in science. However, for some unknown reason, their cooperative relationship broke down. Considering that they often appear in major scientific activities in the18th century, it is remarkable that they know so little about these two people. There are no photos and little written information. As for Dixon, the Dictionary of British Names skillfully mentioned that he was "said to have been born in a coal mine", and then let readers use their imagination to provide a reasonable explanation. The dictionary goes on to say that he died in Durham on 1777. I know nothing except his name and his long-term cooperative relationship with Mei Sen.
There is a little more information about Mei Sen. We know that in 1772, at the request of Maskelyne, he was ordered to find a mountain to measure gravity deviation. Finally, he sent back a report that the mountain they needed was located in the middle of the Scottish Highlands, just beside Taihu Lake. It was called Shihalin Mountain. However, he refused to spend a summer measuring it. He never returned to the scene. It is known that his next activity will be at 1786. He suddenly and mysteriously appeared in Philadelphia, with his wife and eight children, obviously down and out. He has never been back to the United States since he completed his survey in the United States 18 years ago. There is no obvious reason for coming back this time, and there is no friend or patron to meet him. He died a few weeks later.
As Mei Sen was unwilling to survey the mountain, the work fell to Maskelyne. In the summer of 1774, Maskelyne commanded a group of surveyors in a tent in a remote Scottish canyon for four months. They made hundreds of measurements from every possible location. It takes a lot of boring calculations to get the quality of that mountain from such a pile of data. The mathematician who is engaged in this work is Charles Hutton. Surveyors wrote dozens of data on the map, each representing the height of a certain position on the mountain or on the side of the mountain. These figures are really numerous and chaotic. However, Hutton noticed that everything would be very orderly as long as the points of equal height were connected with pencils. In fact, you can immediately know the overall shape and slope of the mountain. So he invented the contour line.
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