Traveling from the city of Alexandria to the south, to the city of Siena (now Aswan), people noticed that there in the summer on the day when the sun is highest in the sky (day summer solstice- June 21 or 22), at noon it illuminates the bottom of deep wells, that is, it happens just above your head, at the zenith. Vertically standing pillars at this moment do not give a shadow. In Alexandria, even on this day, the sun does not reach its zenith at noon, does not illuminate the bottom of the wells, objects give a shadow.

Eratosthenes measured how far the midday sun in Alexandria deviated from the zenith, and received a value equal to 7 ° 12 ", which is 1/50 of the circle. He managed to do this using an instrument called a scaphis. The scaphis was a bowl in the shape of a hemisphere. In the center she was sheerly strengthened

On the left - determination of the height of the sun with a skafis. In the center - a diagram of the direction of the sun's rays: in Siena they fall vertically, in Alexandria - at an angle of 7 ° 12 ". On the right - the direction of the sun's beam in Siena at the time of the summer solstice.

Skafis - an ancient device for determining the height of the sun above the horizon (in section).

needle. The shadow of the needle fell on inner surface skafis. To measure the deviation of the sun from the zenith (in degrees), circles marked with numbers were drawn on the inner surface of the skafis. If, for example, the shadow reached the circle marked 50, the sun was 50° below the zenith. Having built a drawing, Eratosthenes correctly concluded that Alexandria is 1/50 of the Earth's circumference from Syene. To find out the circumference of the Earth, it remained to measure the distance between Alexandria and Siena and multiply it by 50. This distance was determined by the number of days that camel caravans spent on the transition between cities. In the units of that time, it was equal to 5 thousand stages. If 1/50 of the circumference of the earth is 5,000 stadia, then the whole circumference of the earth is 5,000 x 50 = 250,000 stadia. In terms of our measures, this distance is approximately equal to 39,500 km. Knowing the circumference, you can calculate the radius of the Earth. The radius of any circle is 6.283 times less than its length. So average radius Earth, according to Eratosthenes, turned out to be equal to a round number - 6290 km, and the diameter is 12 580 km. So Eratosthenes found approximately the dimensions of the Earth, close to those determined by precise instruments in our time.

How information about the shape and size of the earth was checked

After Eratosthenes of Cyrene, for many centuries, none of the scientists tried to measure the earth's circumference again. In the 17th century a reliable method for measuring large distances on the surface of the Earth was invented - the method of triangulation (so named from the Latin word "triangulum" - a triangle). This method is convenient because the obstacles encountered on the way - forests, rivers, swamps, etc. - do not interfere with the accurate measurement of large distances. The measurement is made as follows: directly on the surface of the Earth, the distance between two closely spaced points is very accurately measured BUT and AT, from which distant tall objects are visible - hills, towers, bell towers, etc. If from BUT and AT through a telescope, you can see an object located at a point WITH, then it is easy to measure at the point BUT angle between directions AB and AU, and at the point AT- angle between VA and Sun.

After that, on the measured side AB and two corners at the vertices BUT and AT you can build a triangle ABC and hence find the lengths of the sides AC and sun, i.e. distances from BUT before With and from AT before WITH. Such a construction can be performed on paper, reducing all dimensions by several times or using a calculation according to the rules of trigonometry. Knowing the distance from AT before With and pointing from these points the telescope of the measuring instrument (theodolite) at an object in any new point D, measure the distance from AT before D and from With before D. Continuing the measurements, as if covering part of the Earth's surface with a network of triangles: ABC, BCD etc. In each of them, you can consistently determine all the sides and angles (see Fig.). After the side is measured AB the first triangle (basis), the whole thing comes down to measuring the angles between the two directions. Having built a network of triangles, it is possible to calculate, according to the rules of trigonometry, the distance from the vertex of one triangle to the vertex of any other, no matter how far apart they may be. This solves the problem of measuring large distances on the surface of the Earth. The practical application of the triangulation method is far from simple. This work can only be done by experienced observers armed with very precise goniometric instruments. Usually for observations it is necessary to build special towers. Work of this kind is entrusted to special expeditions, which last for several months and even years.

The triangulation method helped scientists refine their knowledge of the shape and size of the Earth. This happened under the following circumstances.

Famous English scientist Newton(1643-1727) expressed the opinion that the Earth cannot be in the form of an exact ball, because it rotates around its own axis. All particles of the Earth are under the influence of centrifugal force (force of inertia), which is especially strong

If we need to measure the distance from A to D (while point B is not visible from point A), then we measure the basis AB and in the triangle ABC we measure the angles adjacent to the basis (a and b). On one side and two corners adjacent to it, we determine the distance AC and BC. Further, from point C, we use the telescope of the measuring instrument to find point D, visible from point C and point B. In the triangle CUB, we know the side CB. It remains to measure the angles adjacent to it, and then determine the distance DB. Knowing the distances DB u AB and the angle between these lines, you can determine the distance from A to D.

Triangulation scheme: AB - basis; BE - measured distance.

at the equator and absent at the poles. The centrifugal force at the equator acts against the force of gravity and weakens it. The balance between gravity and centrifugal force was achieved when the globe at the equator "inflated", and at the poles "flattened" and gradually acquired the shape of a tangerine, or, to put it scientific language, spheroid. Interesting discovery, made at the same time, confirmed Newton's assumption.

In 1672, a French astronomer established that if accurate clock transport from Paris to Cayenne (in South America, near the equator), they begin to lag behind by 2.5 minutes per day. This lag occurs because the clock pendulum swings more slowly near the equator. It became obvious that the force of gravity, which makes the pendulum swing, is less in Cayenne than in Paris. Newton explained this by the fact that at the equator the surface of the Earth is farther from its center than in Paris.

The French Academy of Sciences decided to test the correctness of Newton's reasoning. If the Earth is shaped like a tangerine, then the 1° meridian arc should lengthen as it approaches the poles. It remained to measure the length of an arc of 1 ° using triangulation at different distances from the equator. The director of the Paris Observatory, Giovanni Cassini, was assigned to measure the arc in the north and south of France. However, his southern arc turned out to be longer than the northern one. It seemed that Newton was wrong: the Earth is not flattened like a tangerine, but elongated like a lemon.

But Newton did not abandon his conclusions and assured that Cassini made a mistake in the measurements. Between supporters of the theory of "tangerine" and "lemon" a scientific dispute broke out, which lasted 50 years. After the death of Giovanni Cassini, his son Jacques, also director of the Paris Observatory, wrote a book in order to defend his father's opinion, where he argued that, according to the laws of mechanics, the Earth should be stretched like a lemon. In order to finally resolve this dispute, the French Academy of Sciences equipped in 1735 one expedition to the equator, the other to the Arctic Circle.

The southern expedition carried out measurements in Peru. A meridian arc with a length of about 3° (330 km). She crossed the equator and passed through a series mountain valleys and the highest mountain ranges of America.

The work of the expedition lasted eight years and was fraught with great difficulties and dangers. However, scientists completed their task: the degree of the meridian at the equator was measured with very high accuracy.

The northern expedition worked in Lapland (until the beginning of the 20th century, this was the name given to the northern part of the Scandinavian and the western part of the Kola Peninsula).

After comparing the results of the work of the expeditions, it turned out that the polar degree is longer than the equatorial one. Therefore, Cassini was indeed wrong, and Newton was right when he said that the Earth was shaped like a tangerine. Thus ended this protracted dispute, and scientists recognized the correctness of Newton's statements.

Nowadays there is special science- geodesy, which deals with determining the size of the Earth using the most accurate measurements of its surface. The data of these measurements made it possible to accurately determine the actual figure of the Earth.

Geodetic work on measuring the Earth has been and is being carried out in various countries. Such work has been carried out in our country. Even in the last century, Russian geodesists did very precise work to measure the "Russian-Scandinavian arc of the meridian" with a length of more than 25 °, i.e., a length of almost 3 thousand meters. km. It was called the "Struve arc" in honor of the founder of the Pulkovo Observatory (near Leningrad) Vasily Yakovlevich Struve, who conceived and directed this enormous work.

Degree measurements are of great practical importance, primarily for compiling accurate maps. Both on the map and on the globe, you see a network of meridians - circles going through the poles, and parallels - circles parallel to the plane earth's equator. A map of the Earth could not have been drawn up without a long and painstaking work surveyors, who determined step by step over the years the position of different places on earth's surface and then applying the results to a network of meridians and parallels. To have accurate maps, it was necessary to know the actual shape of the Earth.

The measurement results of Struve and his collaborators turned out to be a very important contribution to this work.

Subsequently, other geodesists measured with great accuracy the lengths of the arcs of the meridians and parallels in different places on the earth's surface. Using these arcs, with the help of calculations, it was possible to determine the length of the Earth's diameters in the equatorial plane (equatorial diameter) and in the direction earth's axis(polar diameter). It turned out that the equatorial diameter is longer than the polar one by about 42.8 km. This once again confirmed that the Earth is compressed from the poles. According to the latest data from Soviet scientists, the polar axis is 1/298.3 shorter than the equatorial one.

Let's say we would like to depict the deviation of the Earth's shape from a sphere on a globe with a diameter of 1 m. If a sphere at the equator has a diameter of exactly 1 m, then its polar axis should be only 3.35 mm shorter! This is such a small value that it cannot be detected by the eye. The shape of the earth, therefore, differs very little from a sphere.

You might think that the unevenness of the earth's surface, and especially the mountain peaks, the highest of which Chomolungma (Everest) reaches almost 9 km, must strongly distort the shape of the Earth. However, it is not. On the scale of a globe with a diameter of 1 m a nine-kilometer mountain will be depicted as a grain of sand adhering to it with a diameter of about 3/4 mm. Is it only by touch, and even then with difficulty, that this protrusion can be detected. And from the height at which our satellite ships fly, it can only be distinguished by the black speck of the shadow cast by it when the Sun is low.

In our time, the dimensions and shape of the Earth are very accurately determined by the scientists F. N. Krasovsky, A. A. Izotov and others. Here are the numbers showing the size the globe according to the measurements of these scientists: the length of the equatorial diameter - 12,756.5 km, length of polar diameter - 12 713.7 km.

The study of the path traveled by artificial satellites of the Earth will make it possible to determine the magnitude of gravity at different places above the surface of the globe with such accuracy that could not be achieved by any other method. This, in turn, will allow us to further refine our knowledge of the size and shape of the Earth.

Gradual change in the shape of the earth

However, as it was possible to find out with the help of all the same space observations and special calculations made on their basis, the geoid has complex view due to the rotation of the Earth and the uneven distribution of masses in earth's crust, but quite well (with an accuracy of several hundred meters) is represented by an ellipsoid of revolution with a polar oblateness of 1:293.3 (Krasovsky's ellipsoid).

Nevertheless, until very recently, it was considered a well-established fact that this small defect is slowly but surely leveled out due to the so-called process of restoring gravitational (isostatic) equilibrium, which began about eighteen thousand years ago. But more recently, the Earth began to flatten again.

Geomagnetic measurements, which since the late 1970s have become an integral attribute of satellite observation research programs, have consistently recorded the alignment of the planet's gravitational field. In general, from the point of view of mainstream geophysical theories, the gravitational dynamics of the Earth seemed quite predictable, although, of course, both within the mainstream and beyond it, there were numerous hypotheses that interpreted the medium and long-term prospects of this process in different ways, as well as what happened in past life our planet. Quite popular today is, say, the so-called pulsation hypothesis, according to which the Earth periodically contracts and expands; There are also supporters of the "contract" hypothesis, which postulates that in the long run the size of the Earth will decrease. There is no unity among geophysicists in terms of what phase the process of post-glacial restoration of gravitational equilibrium is in today: most experts believe that it is quite close to completion, but there are also theories that claim that it is still far from its end or that it has already stopped.

Nevertheless, despite the abundance of discrepancies, until the end of the 90s of the last century, scientists still did not have any good reasons doubt that the process of post-glacial gravitational alignment is alive and well. The end of scientific complacency came rather abruptly: after spending several years checking and rechecking the results obtained from nine different satellites, two American scientists, Christopher Cox of Raytheon and Benjamin Chao, a geophysicist at NASA's Goddard Space Flight Control Center, came to a surprising conclusion: since 1998, the "equatorial coverage" of the Earth (or, as many Western media dubbed this dimension, its "thickness") began to increase again.
The sinister role of ocean currents.

Cox and Chao's paper, which claims "the discovery of a large-scale redistribution of the Earth's mass," was published in the journal Science in early August 2002. As the authors of the study note, "long-term observations of the behavior of the Earth's gravitational field showed that the post-glacial effect that smoothed it out in the past few years suddenly had a more powerful adversary, approximately twice as strong as its gravitational effect." Thanks to this "mysterious adversary", the Earth again, as in the last "epoch of the Great Icing", began to flatten, that is, since 1998, an increase in the mass of matter has been taking place in the equator region, while its outflow has been going on from the polar zones.

Earth geophysicists do not yet have direct measuring methods to detect this phenomenon, so in their work they have to use indirect data, primarily the results of ultra-precise laser measurements of changes in satellite orbit trajectories occurring under the influence of fluctuations in the Earth's gravitational field. Accordingly, speaking of "the observed displacements of the masses of the earth's matter", scientists proceed from the assumption that they are responsible for these local gravitational fluctuations. The first attempts to explain this strange phenomenon were undertaken by Cox and Chao.

The version of any underground phenomena, for example, the flow of matter in the earth's magma or core, looks, according to the authors of the article, rather doubtful: in order for such processes to have any significant gravitational effect, much more long time than a ridiculous four years by scientific standards. As possible reasons for the thickening of the Earth along the equator, they name three main ones: oceanic influence, melting of the polar and high mountain ice and some "processes in the atmosphere." However, they also immediately dismiss the last group of factors - regular measurements of the weight of the atmospheric column do not give any grounds for suspicion of the involvement of certain air phenomena in the occurrence of the discovered gravitational phenomenon.

Far from being so unambiguous seems to Cox and Chao the hypothesis of the possible influence on the equatorial swelling of the process of ice melting in the Arctic and Antarctic zones. This process is like essential element of the notorious global warming of the world climate, of course, to one degree or another can be responsible for the transfer of significant masses of matter (primarily water) from the poles to the equator, but theoretical calculations made by American researchers show that in order for it to be the determining factor (in particular, , "blocked" the consequences of the thousand-year "growth of the positive relief"), the dimension of the "virtual block of ice" annually melted since 1997 should have been 10x10x5 kilometers! There is no empirical evidence that the process of ice melting in the Arctic and Antarctic last years could take on such a scale, geophysicists and meteorologists do not have. According to the most optimistic estimates, the total volume of melted ice floes is at least an order of magnitude smaller than this "super iceberg", therefore, even if it had some effect on the increase in the Earth's equatorial mass, this effect could hardly be so significant.

As the most probable reason for the sudden change in the Earth's gravitational field, Cox and Chao consider today the oceanic impact, that is, the same transfer of large volumes of the World Ocean's water mass from the poles to the equator, which, however, is associated not so much with the rapid melting of ice, how much with some not quite explainable sharp fluctuations in ocean currents that have occurred in recent years. Moreover, as experts believe, the main candidate for the role of a disturber of gravitational calm is the Pacific Ocean, more precisely, the cyclic movements of huge water masses from its northern regions to its southern regions.

If this hypothesis turns out to be correct, humanity in the very near future may face very serious changes in the global climate: the sinister role of ocean currents is well known to everyone who is more or less familiar with the basics of modern meteorology (which is worth one El Niño). True, the assumption that the sudden swelling of the Earth along the equator is a consequence of the climate revolution already in full swing looks quite logical. But, by and large, it is still hardly possible to really understand this tangle of cause-and-effect relationships on the basis of fresh traces.

The obvious lack of understanding of the ongoing "gravitational outrages" is perfectly illustrated by a small fragment of the interview of Christopher Cox himself to the correspondent of the Nature magazine news service Tom Clark: one thing: Our planet's "weight problems" are likely temporary and not a direct result of human activity." However, continuing this verbal balancing act, the American scientist immediately once again prudently stipulates: "It seems that sooner or later everything will return" to normal ", but perhaps we are mistaken on this score."



ERATOSPHENES - THE FATHER OF GEOGRAPHY.

We have every reason to celebrate June 19 as the Day of Geography - in 240 BC. On the day of the summer solstice (then it fell on June 19), the Greek, or rather, Hellenistic scientist Eratosthenes conducted a successful experiment to measure the circumference of the earth. Moreover, it was Eratosthenes who coined the term "GEOGRAPHY".

Glory to Eratosthenes!

So what do we know about him and his experiment? Let's take a look at what we've collected...

Eratosthenes - Eratosthenes of Cyrene, ( OK. 276-194 BC e.),., Greek writer and scholar. Possibly a student of his compatriot Callimachus; He also studied in Athens with Zeno of Kytheon, Arcesilaus and the Peripatetic Ariston from Chios. Managed the Library of Alexandria and was an educator heir to the throne, later Ptolemy IV Philopatra. Unusually versatile, he studied philology, chronology, mathematics, astronomy, geography, he wrote poetry himself.

Among the mathematical writings of Eratosthenes, one should mention the work of Platonik (Platonikos), which is a kind of commentary on Plato's Timaeus, which dealt with issues from the field of mathematics and music. The starting point was the so-called Delhi question, that is, the doubling of the cube. The geometric content was the work "On average values ​​(Peri mesotenon)" in 2 parts. In the famous treatise Sieve (Koskinon), Eratosthenes outlined a simplified method for determining the first numbers (the so-called "sieve of Eratosthenes"). Preserved under the name of Eratosthenes, the work "Transformation of the Stars" (Katasterismoi), being probably a synopsis of a larger work, linked together philological and astronomical studies, weaving stories and myths about the origin of the constellations into them.

In "Geography" (Geographika) in 3 books, Eratosthenes presented the first systematic scientific presentation of geography. He began by reviewing what had been achieved by Greek science in this area up to that point. Eratosthenes understood that Homer was a poet, so he opposed the interpretation of the Iliad and the Odyssey as a storehouse geographical information. But he managed to appreciate the information of Pytheas. Created mathematical and physical geography. He also suggested that if you sail from Gibraltar to the west, you can swim to India (this is the position of Eratosthenes indirectly reached Columbus and gave him the idea of ​​his journey). Eratosthenes supplied his work with a geographical map of the world, which, according to Strabo, was criticized by Hipparchus of Nicaea. In the treatise "On the Measurement of the Earth" (Peri tes anametreseos tes ges; possibly part of "Geography"), based on the known distance between Alexandria and Syene (the modern city of Aswan), as well as the difference in the angle of incidence of the sun's rays in both areas, Eratosthenes calculated the length of the Equator (total: 252,000 stadia, or about 39,690 km, a calculation with minimal error, since the true length of the equator is 40,120 km).

In the voluminous work "Chronography" (Chronographiai) in 9 books, Eratosthenes laid the foundations of scientific chronology. It covered the period from the destruction of Troy (dated E. 1184/83 BC) to the death of Alexander (323 BC). Eratosthenes relied on the list of Olympic winners he compiled and developed an accurate chronological table, in which he dated all political and cultural events known to him according to the Olympiads (that is, four-year periods between games). The "Chronography" of Eratosthenes became the basis for the later chronological studies of Apollodorus of Athens.

The work "On Ancient Comedy" (Peri tes archiaas komodias) in 12 books was literary, linguistic and historical research and solved the problems of authenticity and dating of works. As a poet, Eratosthenes was the author of the learned epilions. "Hermes" (fr.), probably representing the Alexandrian version of the Homeric hymn, told about the birth of the god, his childhood and entry to Olympus. "Revenge, or Hesiod" (Anterinys or Hesiodos) narrated the death of Hesiod and the punishment of his murderers. In Erigone, written in elegiac distich, Eratosthenes presented the Attic legend of Icarus and his daughter Erigone. It was probably the best poetic work of Eratosthenes, which Anonymus praises in his treatise On the Sublime. Eratosthenes was the first scientist who called himself a "philologist" (philologos - loving science, just as philosophos - loving wisdom).

Eratosthenes' measurement experiment circumference of the earth:

1. Eratosthenes knew that in the city of Siena at noon on June 21 or 22, at the time of the summer solstice, the sun's rays illuminate the bottom of the most deep wells. That is, at this time the sun is located strictly vertically over Siena, and not at an angle. (Now the city of Siena is called Aswan).

2. Eratosthenes knew that Alexandria was north of Aswan at about the same longitude.

3. On the day of the summer solstice, while in Alexandria, he established from the length of the shadows that the angle of incidence of the sun's rays is 7.2 °, that is, the Sun is separated from the zenith by this amount. In a circle 360°. Eratosthenes divided 360 by 7.2 and got 50. Thus, he established that the distance between Syene and Alexandria is equal to one fiftieth of the circumference of the Earth.

4. Eratosthenes then determined the actual distance between Syene and Alexandria. At the time, this was not easy to do. Then people traveled on camels. The distance traveled was measured in stages. The camel caravan used to travel about 100 stadia a day. The journey from Syene to Alexandria took 50 days. So, the distance between two cities can be determined as follows:

100 stages x 50 days = 5,000 stages.

5. Since a distance of 5,000 stadia is, as Eratosthenes concluded, one fiftieth of the circumference of the earth, therefore, the length of the entire circumference can be calculated as follows:

5,000 stages x 50 = 250,000 stages.

6. Stage length is now defined in various ways; according to one version, the stage is 157 m. Thus, the circumference of the Earth is

250,000 stadia x 157 m = 39,250,000 m.

To convert meters to kilometers, you need to divide the resulting value by 1,000. The final answer is 39,250 km
According to modern calculations, the circumference of the globe is 40,008 km.

Eratosthenes was an extremely inquisitive person. He became a mathematician, poet, philosopher, historian and librarian of one of the first libraries in the world, the Library of Alexandria in Egypt. Books at that time were not books in our sense of the word, but papyrus scrolls.
The famous library contained more than 700,000 scrolls, which contained all the information about the world, known to people of that era. With the assistance of his assistants, Eratosthenes was the first to sort the scrolls into themes. Eratosthenes lived to a ripe old age. When he became blind from old age, he stopped eating and starved to death. He could not imagine life without the opportunity to work with his favorite books.

For the first time, measurements of the size of the Earth were performed by the Alexandrian scientist Eratosthenes back in the 3rd century BC, and he managed to get surprisingly accurate results. How was it done?

Eratosthenes knew that on the day of the summer solstice in the city of Siena, the Sun at noon is exactly at its zenith, illuminating the bottom of deep wells. Indeed, this city is located on the line of the northern tropic. On this day, Eratosthenes measured the height of the Sun in Alexandria and found that it was 1/50 of the circumference from the zenith. The distance between these cities was known and amounted to 5000 stadia. Therefore, the entire circumference of the globe has a length of 50 times greater - 250,000 stadia or 39,600 kilometers. Perhaps the actual measurement accuracy was somewhat lower and the result only accidentally turned out to be so close to reality, but the fact remains that a more accurate value could only be obtained in the 18th century ...

(This value is 40,000 km. And one should not be surprised at such a round figure - the fact is that it was precisely on the basis of the results of these measurements that the definition of a kilometer was adopted, as 1/40,000 of the length of the meridian. Later, the value of the meridian length was refined more than once, but the length of the standard meters have not been changed, so now the numbers are not so "beautiful")

We can repeat this experience of the great scientist. In general, we do not need the Sun to be at the zenith at one of the observation points, we do not even need to take measurements on the same day - we only need to calculate the difference in latitudes determined from the height of the Sun. Another issue is that if we determine the declination of the Sun approximately, as described earlier, this will introduce additional errors. Therefore, if, out of the desire for purity of the experiment, one does not use modern astronomical tables and computer technology, it is really better to make measurements near the solstice day - at this time, its declination changes very little over several days. So if we're traveling from June 20th to 25th, we can get away with comparing the heights of the Sun.

Δφ/360 = L/2πR 0

R 0 \u003d L * 360 / 2πΔφ, where

R 0 - radius of the Earth

Δφ \u003d (z 1 -z 2) - difference geographical latitudes observation points or the difference in the heights of the Sun

L - distance between observation points

(By the way, the same Eratosthenes also determined the declination of the Sun on the day of the solstice as 11/166 of the circle, or 23.855 ° - also a very decent accuracy!)

The second condition for obtaining a more or less accurate result is a sufficiently large and accurately known distance between observation points located approximately at the same longitude. Of course, it makes no sense to measure this distance on the map - in this case, we are already implicitly using the value that we are just going to determine, but measuring the car's odometer will be a completely honest way.

I once tried to do this experiment, determining the heights of the Sun in Minsk and located 100 km south of Slutsk, but such a distance between cities is too small to get at least some acceptable result - after all, the heights of the Sun differed by less than 1 degree, which is comparable with the accuracy of measurements using the gnomon. It would be much better to use pairs Kyiv-Odessa or even Vitebsk-Odessa, Moscow-Yelets or Moscow-Rostov-on-Don.

I wonder if someone else considers the gnomon a frivolous instrument?

ERATOSPHENES
Kirensky
(c.276-194 BC)

ancient Greek scholar. Born in Cyrene ( North Africa). Educated in Alexandria and Athens. Served as an educator crown prince at the court of Ptolemy III Euergetes, about 225 BC. e. began to manage the Alexandria Library. He laid the foundations of mathematical geography, for the first time measured the arc of the meridian. He determined the tilt of the ecliptic with great accuracy, compiled a catalog of 675 fixed stars. He laid the foundations of scientific chronology, proposed to introduce an extra day into the calendar every 4 years. Works on mathematics (number theory), astronomy, philology, philosophy, music. Only fragments have survived.

Jean Effel, Creation of the World
-And how slim! If you count in millions of centimeters, her waist is 40!

Now you know that in the fabulous Universe of our distant ancestors, the Earth did not even resemble a ball. Inhabitants Ancient Babylon imagined it as an island in the ocean. The Egyptians saw it as a valley stretched from north to south, in the center of which was Egypt. And the ancient Chinese at one time depicted the Earth as a rectangle ... You smile, imagining such an Earth, but how often have you thought about how people guessed that the Earth is not an unlimited plane or a disk floating in the ocean? When I asked the guys about this, some said that people learned about the sphericity of the Earth after the first trips around the world, while others recalled that when a ship appears from behind the horizon, we first see the masts, and then the deck. Do such and some similar examples prove that the Earth is a sphere? Unlikely. After all, you can go around and around ... a suitcase, and the upper parts of the ship would appear even if the Earth had the shape of a hemisphere or looked like, say, a ... log. Think about it and try to depict what is said in your drawings. Then you will understand: the examples given show only that The earth is isolated in space and possibly spherical.

How did you know that the Earth is a sphere? It helped, as I already told you, the Moon, or rather, lunar eclipses, during which the round shadow of the Earth is always visible on the Moon. Arrange a small "shadow theater": illuminate objects in a dark room different shapes(triangle, plate, potato, ball, etc.) and notice what kind of shadow they get on the screen or just on the wall. Make sure only the ball always casts a circle shadow on the screen. So, the Moon helped people to know that the Earth is a sphere. To this conclusion, scientists Ancient Greece(for example, the great Aristotle) ​​came as early as the 4th century BC. But for a very long time common sense"A person could not come to terms with the fact that people live on the ball. They could not even imagine how it was possible to live on the" other side "of the ball, because the" antipodes " located there would have to walk upside down all the time ... But no matter where there was a person on the globe, everywhere a stone thrown up will fall down under the influence of the force of gravity of the Earth, that is, on the earth's surface, and if it were possible, then to the center of the Earth.In fact, people, of course, nowhere, except for circuses and gyms, you don't have to walk upside down and upside down.They walk normally anywhere on the Earth: the earth's surface is under their feet, and the sky is above their heads.

Around 250 BC, a Greek scholar Eratosthenes first accurately measured the globe. Eratosthenes lived in Egypt in the city of Alexandria. He guessed to compare the height of the Sun (or its angular distance from a point overhead, zenith, which is called - zenith distance) at the same time in two cities - Alexandria (in northern Egypt) and Syene (now Aswan, in southern Egypt). Eratosthenes knew that on the day of the summer solstice (June 22) the Sun was at noon illuminates the bottom of deep wells. Therefore, at this time the Sun is at its zenith. But in Alexandria at this moment the Sun is not at its zenith, but is separated from it by 7.2 °. Eratosthenes obtained this result by changing the zenith distance of the Sun with the help of his simple goniometric tool - the scaphis. This is just a vertical pole - a gnomon, fixed at the bottom of a bowl (hemisphere). The skafis is installed in such a way that the gnomon takes a strictly vertical position (directed to the zenith). The pole illuminated by the sun casts a shadow on the inner surface of the skafis divided into degrees. So, at noon on June 22 in Siena, the gnomon does not cast a shadow (the Sun is at its zenith, its zenith distance is 0 °), and in Alexandria, the shadow from the gnomon, as can be seen on the scale of the skafis, marked a division of 7.2 °. At the time of Eratosthenes, the distance from Alexandria to Syene was considered equal to 5000 Greek stadia (about 800 km). Knowing all this, Eratosthenes compared an arc of 7.2 ° with the entire circle of 360 ° degrees, and a distance of 5000 stadia - with the entire circumference of the globe (we denote it by the letter X) in kilometers. Then from the proportion

it turned out that X = 250,000 stages, or about 40,000 km (imagine this is true!).

If you know that the circumference of a circle is 2πR, where R is the radius of the circle (and π ~ 3.14), knowing the circumference of the globe, it is easy to find its radius (R):

It is remarkable that Eratosthenes was able to measure the Earth very accurately (after all, even today it is believed that the average radius of the Earth 6371 km!).

But why is it mentioned here average radius of the earth, Aren't all spheres the same radius? The fact is that the figure of the Earth is different from the ball. Scientists began to guess about this back in the 18th century, but what the Earth really is - is it compressed at the poles or at the equator - it was difficult to find out. To understand this, the French Academy of Sciences had to equip two expeditions. In 1735, one of them went to carry out astronomical and geodetic work in Peru and did this in the equatorial region of the Earth for about 10 years, and the other, Lapland, worked in 1736-1737 near the North polar circle. As a result, it turned out that the length of the arc of one degree of the meridian is not the same at the poles of the Earth and at its equator. The meridian degree turned out to be longer at the equator than at high latitudes (111.9 km and 110.6 km). This can only happen if the Earth is compressed at the poles and is not a ball, but a body close in shape to spheroid. At the spheroid polar radius less equatorial(for the terrestrial spheroid, the polar radius is shorter than the equatorial one by almost 21 km).

It's good to know that great Isaac Newton (1643-1727) anticipated the results of the expeditions: he correctly concluded that the Earth is compressed, because our planet rotates around its axis. In general, the faster the planet rotates, the greater must be its compression. Therefore, for example, the compression of Jupiter is greater than that of the Earth (Jupiter manages to make a revolution around the axis with respect to the stars in 9 hours and 50 minutes, and the Earth only in 23 hours and 56 minutes).

And further. The true figure of the Earth is very complex and differs not only from a ball, but also from a spheroid. rotation. True, in this case we are talking about the difference not in kilometers, but ... meters! Scientists are engaged in such a thorough refinement of the figure of the Earth to this day, using for this purpose specially carried out observations with artificial satellites Earth. So it is quite possible that someday you will have to take part in solving the problem that Eratosthenes took up a long time ago. This is very what people need case.

What is the best way to remember the figure of our planet? I think that for now it is enough if you imagine the Earth as a ball with an "additional belt" put on it, a kind of "slap" on the equator region. Such a distortion of the figure of the Earth, turning it from a sphere into a spheroid, has considerable consequences. In particular, due to the attraction of the "additional belt" by the Moon, the earth's axis describes a cone in space in about 26,000 years. This movement of the earth's axis is called precessional. As a result, the role polar star, which now belongs to α Ursa Minor, some other stars alternately play (in the future it will become, for example, α Lyra - Vega). In addition, because of this precessional) movements of the earth's axis Zodiac signs more and more do not coincide with the corresponding constellations. In other words, 2000 years after the era of Ptolemy, the "sign of Cancer", for example, no longer coincides with the "constellation of Cancer", etc. However, modern astrologers try not to pay attention to this ...

A.V. Klymenko The earliest determinations of the size of the earth / Development of methods astronomical research. Issue 8, Moscow-Leningrad, 1979

A.V. Klymenko

Ancient definitions of the size of the earth

One of the most complex and little studied problems in the history of astronomy and geodesy is the establishment of the origin and accuracy of the results of the most ancient determinations of the dimensions of the Earth. The oldest surviving source, which gives the result of determining the size of the Earth, is the work of the ancient Greek scientist Aristotle (384-322 BC) “On the Sky”. “Mathematicians,” wrote Aristotle, “trying to calculate the circumference of the earth, give a figure of about 400,000 stadia.” Some researchers believe that "Aristotle rather carelessly takes this figure from" mathematicians ", without explaining how it was derived" . However, it is more likely that Aristotle did not know how this result was obtained.

A.B. Dietmar writes that “when calculating the size of the Earth, clearly overestimated results were obtained: even if we start from the usual stage of 157.5 m, then a circle of 400,000 stadia will be equal to 63,000 km (instead of 40,009 km along the meridian); if we take stages of 176 m, then we get a circle of 70,400 km.

Why did the ancient scientists, reporting the third result of the determination in the III century. BC e. circumference of the Earth in 250,000 stadia, never forgot to note that it was obtained by Eratosthenes, and the names of the authors of earlier definitions were hushed up? Obviously, because these measurements were made not by Greek, but by Eastern, that is, Egyptian, or Babylonian scientists.

The tradition of belittling the merits of Egyptian and Babylonian scientists in the development scientific knowledge goes into the distant past. So, for example, one of the ancient writers, created by ancient Egyptian scientists, calls the Heliopolis astronomical observatory near Cairo, without any reason, "Eudoxian". However, it is known that this observatory, in which Eudoxus only “studied astronomy” and “determined the movements of some luminaries”, was created by ancient Egyptian scientists. This is evidenced by the following words of Strabo: “In Heliopolis we saw large houses in which priests lived, because, as they say, this city was in ancient times the main seat of priests, philosophers and astronomers.”

Greek scientists, as a rule, did not indicate the source of their scientific knowledge. The main reason for this silence should be sought, first of all, in the fact that for the Greeks any foreigner, even a free representative of an independent country, was a "barbarian", that is, a potential slave. For results acquired in other countries scientific papers looked upon as their own property. In a society affected by slave-owning psychology, it was not customary to refer to the works of "barbarians".

It is known that by 747 BC. e. refers to the beginning of the so-called "astronomical era of Nabonassar", during which very intensive astronomical observations. Greek scientists highly appreciated the results of astronomical observations of the Babylonian priests. Hypsicles (3rd century BC), Hipparchus (2nd century BC) and other Greek astronomers made extensive use of the results of Babylonian observations. Even Claudius Ptolemy in the II century. n. e. used them, essentially, without any amendments.

Diogenes Laertius, Strabo, Pliny and other ancient authors wrote that many Greek scientists owe their knowledge to the Babylonian and Egyptian priests.

Plutarch argued that the scientific views of Thales and other Greek scientists were based on the achievements of the Babylonians and Egyptians. So, for example, according to the information that has come down to us, Thales predicted solar eclipse May 28, 585 B.C. e. Since the Greeks at that time were not yet engaged in theoretical research in the field of astronomy and did not systematic observations celestial bodies, we can conclude that Thales could predict a solar eclipse only on the basis of the scientific achievements of the scientists of Babylonia and Egypt. Chaloyan V.K. rightly notes that "Thales transferred from Egypt to Hellas not only the materialistic principle of philosophy - the idea of ​​water as the beginning of all things, but also knowledge of geometry and astronomy".

There is a legend that Pythagoras was the first of the Greek scientists to express the idea of ​​the sphericity of the Earth. It is not known, however, whether he himself came up with this idea, or, more likely, borrowed it from his teachers, the Babylonian and Egyptian priests. It is known that during his stay in Heliopolis, Pythagoras studied for a long time with the Egyptian astronomer Oniouphis. “Differing in terms of knowledge of celestial phenomena,” Strabo wrote, “the priests kept it a secret, reluctantly entered into communication with people, so it took time and obsequiousness on the part of those who wanted to learn something from them; however most barbarians concealed information. By the way, they taught to replenish the year with the remaining parts of the day and night beyond 365 days. Nevertheless, the length of the year, like many other things, remained unknown to the Hellenes until later astronomers received this information from persons who translated the writings of the priests into Greek language; and up to the present time the Hellenes borrow much from the Egyptian priests and from the Chaldeans.

The fact that in the Nile Valley in the XXIX century. BC e. conducted instrumental astronomical observations, the results of a survey of the ancient Egyptian pyramids testify. High-precision verification geodetic methods showed that true bearing the western side of the pyramid of Cheops is currently 359 ° 57 "30". Approximately with the same accuracy, other Egyptian pyramids. It is obvious that the concept of the "noon line" (meridian) was known to the priests, who fixed the corners of this structure on the ground.

Yu. Frantsov provides evidence that the Egyptians came to the idea of ​​the sphericity of the Earth much earlier than the Greeks. Thus, in the Leiden Demotic Papyrus, the Goddess of the Sun says: “Look, the Earth is like a box in front of me; this means that the lands of God are in front of me, like a round ball. But if the Egyptians knew that the Earth has spherical shape, then for enough high level their development of astronomy and geometry, they could, like the Greeks later, come to determine its size. In ancient Egyptian texts, it is really stated that Thoth (Hermes) is “the god who measured this Earth”, “counted the Earth”, “counted the stars”, etc. .

It is possible that Pythagoras knew the results of determining the size of the Earth by Eastern scientists. But since the very idea of ​​the sphericity of the Earth at that time might seem absurd, there was no point in giving the length of its circumference. Ancient scientists usually gave the values ​​​​of the circumference of the Earth known to them in stages. However, in Arabic sources of the IX-XI centuries. n. e. the results of ancient determinations of the size of the Earth, expressed in the Babylonian, Syrian and other systems of measures of length, have been preserved. Some of these results are given in the works of al-Battani (c. 852-926), al-Masudi (late 9th century - 957) and other Eastern scholars. The outstanding scientist of the Middle Ages Abu Raykhan Beruni (973-1048), who paid much attention to the history of geodesy and astronomy, could not determine the size of the Earth on the basis of information from earlier sources, since, according to him, “the meaning of the concept of“ stages ”is unknown in the quantities we use." Beruni gives the result of determining the circumference of the Earth, which Arab scientists "according to tradition" attributed to the legendary ancient Egyptian sage Hermes. This result, according to Beruni, was equal to "9,000 farsakhs, despite the fact that farsas are 12,000 cubits." It is most likely that the "farce" used by "Hermes" was based on the "elbow" of 37.0413 cm:

0.370413 X 12,000 = 4444.96 m.

In this case, the circumference of the Earth, corresponding to 9,000 farsakhs, in terms of the metric system of measures will be equal to

4.44496 X 9000 = 40,005 km.

Further, Beruni writes: “In accordance with the words of Hermes (one degree will be equal to) 25 farsakhs, which is 75 miles, each of which is equal to four thousand cubits.” The Arab scholars Yaqut and al-Idrisi also accepted the "opinion of the best authors" according to which an earthly degree contains 25 farsakhs, counting a farsah as 3 miles or 12,000 cubits. An analysis of these data shows that Arab scholars, not knowing the actual length of the Hermes farsakh, considered that it was a system of measures inherited by the Arabs from the Persians. In this system of measures, the length of the cubit corresponded to 49.3884 cm, the "ordinary" farce was 5926.61 m (0.493884X 12,000), and the mile was 1975.54 m. Therefore, the circumference of the Earth, translated into the metric system of measures, they got equal to 53,339 km (5.9261 X 9,000).

In the works of Arab scientists of the Middle Ages, there are some other results attributed to Hermes to determine the circumference of the Earth. So, Idrisi (1100-1165) wrote that Hermes set 100 miles in the degree of the equator, which corresponds to the circumference of the Earth at 36,000 miles. Beruni also reports that "a certain scientist" determined each degree in 100 miles, due to which the circumference of the Earth turned out to be 12,000 farsakhs.

Undoubtedly, these figures represent not some independent definitions the circumference of the Earth, but only an interpretation of the result, equal to 9,000 farsakhs. If the result of 36,000 miles is expressed in Roman miles, then we get the circumference of the Earth, equal to 53,340 km. Taking a "short" farce, we find:

4.44496 X 12,000=53,339 km.

Since the length of the degree of the meridian, according to Beruni, was 75 miles, the length of the entire circumference of the Earth is 27,000 miles. If this value was expressed in Roman miles, then we get

1.48165 X 27,000=40,005 km,

which corresponds to the Hermes result of 9,000 farsakhs. If, however, the calculation of the circumference of the Earth was based on the Persian mile, equal to 1.97554 km, then in this case the value of the circumference of the Earth, corresponding to 27,000 miles, will also be equal to 53,339 km.

8 ancient farces were equated with 3 or 4 miles. Therefore, the results of 27,000 and 36,000 miles could have arisen as follows:

9,000 X 3=27,000 miles;

9,000 X 4=36,000 miles.

The results of determining the circumference of the Earth, obtained by Eastern scientists, Aristotle could take from trophy works. Taking the ratio of 1:45 known in antiquity between the "barbarian" schen ("hennub") and the Greek stage, Aristotle considered that

9,000 X 45 = 405,000 stages,

or, as he noted in his writings, "about 400,000 stadia."

If Aristotle proceeded from the result of determining the circumference of the Earth, equal to 12,000 farsakhs, then taking the ratio known in antiquity between the farsakh and the Greek stage as 1:3373. he could get:

12,000 x 33 1/3 = 400,000 stages.

The second time result of determining the circumference of the Earth is given in the writings of Archimedes: "... some have tried to prove that it is approximately 300,000 stadia ...". This message causes a variety of assumptions about the source used by Archimedes.

There is no doubt that this could not have been the result of Eratosthenes (250,000 stadia). Most likely, Archimedes used the same source of information as Aristotle, expressing the result obtained by Eastern scientists in 9,000 "farsakhs" in a different metrological system. The most likely explanation for the origin of the 300,000 stadia result is as follows.

Taking the known antique period the ratio of 1:33 1/3 between "farsakh" and a stage, Archimedes found the value of the circumference of the Earth, which is given in his writings: 9,000 X 33 1/3 = 300,000 stages.

There is no consensus among researchers in assessing the accuracy of determining the size of the Earth by the ancient Greek scientist Eratosthenes (c. 276-194 BC). Suffice it to note that researchers take the length of the "stage of Eratosthenes" in the range from 148 to 210 m. Most authors believe that when determining the circumference of the Earth, Eratosthenes took a stage equal to) 157.5 m.

In order to establish the value of the circumference of the Earth obtained by Eratosthenes, it is important to find out what the stages with which he measured the distance from Alexandria to Syene were.

The ancient Greek historian Herodotus, who traveled in the 5th century. BC e. in Egypt, wrote that the distance from the mouth of the Nile to Elephantine is 136 schens or 8160 stadia. During his journey through Egypt, Herodotus did not measure the length of the path traveled, but received it from local residents. Then, when processing travel notes, the distances obtained in Egyptian schenes, he translated into Greek stages.

The Egyptian skhen, according to Herodotus, consisted of 60 stages. However, Strabo, Artemidorus and other ancient scholars wrote that in various parts Nile schen was equated with 30, 40, 60, and even 120 stages.

An analysis of the distances given by Herodotus shows that the Egyptian schen he mentioned was 40, and not 60 Greek stadia. If we assume that the length of the schen was 40 stages (185.207 X 40 \u003d 7408.26 meters), then the distance between the mouth of the Nile and Elephantine will be very close to the actual one:

136 X 40 = 5440 stages;

7.40826 X 136 = 0.185207 X 5440 = 1008 km.

The distances between the settlements of the Nile Valley were known to the Egyptians in ancient times. These distances have been repeatedly measured by land surveyors and bematists for many centuries. Found in ancient sources various meanings such distances is obvious and express the results of multiple measurements. For example, Pliny the Elder wrote that "the island of Elephantine ... is 585,000 paces from Alexandria." Since the geometric step was 1.4817 m, the indicated distance would be 867 km. Referring to Yuba, Pliny reports that from Alexandria to Elephantine there are 562,000 steps, which corresponds to 833 km.

Artemidor believed that from Alexandria to Elephantine, 762,000 steps (about 1129 km), and Aristocreon - 750,000 steps, which corresponds to 1111 km.

Eratosthenes, as you know, believed that from Alexandria to Syene there were 5,000 stadia. According to Strabo, this distance is 5,300 stadia. If we take into account that Elephantine was 16,000 paces (about 130 stadia) upstream from Syene, it is clear that the distance indicated by Strabo from the mouth of this river to Syene is very close to the value obtained from the analysis of Herodotus' messages. With a stage length of 185.207 m, we find:

5,000 X 0.185207 = 926 km;

5,300 X 0.185207 = 981 km.

In fact, the indicated distance (along the Nile Valley) is 980 km.

The Roman architect Vitruvius (1st century BC) wrote: “Eratosthenes of Cyrene, on the path of the Sun, the equinoctial shadows of the gnomon and the declination of the sky, determined, on the basis of mathematical and geometric calculations, that the circumference of the Earth is 252,000 stadia, which is 31,500,000 steps". Considering that the ancient Greek (“Olympic”) stadia was 185.207 m, and the step (Roman “geometric pass”) was 1.48165 m, we find the circumference of the Earth, corresponding in the metric system of measures, 252,000 stadia or 31,500,000 steps:

252,000 X 0.185207 = 46,672 km;

31,500,000 X 0.001481652 = 46,672 km.

Another famous Roman scientist Pliny the Elder wrote that the circumference of the Earth obtained by Eratosthenes is 252,000 stadia or 31,5000 Roman miles. There is reason to believe that a more accurate figure given by al-Battani of the length of a degree of the great circle of the Earth should be 65 °.1. From here we get the length of the entire circumference of the Earth:

65.1 X 360 = 23,436 miles.

Since the Babylonian (Persian) mile with a length of 1.97554 km was used in the Arab Caliphate, the circumference of the Earth according to these data will be 46299 km; (23436 X 1.97554), which practically does not differ from the various interpretations of the result obtained by Eratosthenes in 250,000 stadia given in the works of ancient and Arab scientists.

Based on the testimonies of Vitruvius, Pliny the Elder, al-Kashi, Barbaro and other authors, as well as research data in the field of the history of metrology, we can conclude that the results of Eratosthenes' determination of the circumference of the Earth were based on the ancient Greek stage of 185.2 m.

From ancient sources, the result of determining the size of the Earth, equal to 180,000 stadia, is also known. For the first time this value was given in Strabo's "Geography" (1st century BC - 1st century AD). “Of the new measurements of the Earth,” Strabo wrote, “... the smallest dimensions are the measurements of Posidonius, who considers the circumference of the Earth to be about 180,000 stadia.” According to Claudius Ptolemy (c. 90-169), Marin of Tire "calculated that 1/360 of a large circle is equal to 500 stages on the surface of the Earth - a figure that corresponds to undoubted measurements" (1, p. 298).

In the work of Cleomedes, another result of determining the circumference of the Earth, attributed to Posidonius, is mentioned - 240,000 stadia. M. Lefranc believes that the figures of 180,000 and 240,000 stages are the same linear value, but expressed by stages of different lengths of 210 and 157.5 m. The idea expressed by Lefranc about the linear equality of values ​​​​of 180,000 and 240,000 stages seems as will be shown below, very reasonable, although studies of the history of linear measures give reason to assert that the stage is 157.5 m long in antique time didn't exist.

According to Cleomedes, Posidonius, observing the star Canopus on Rhodes and Alexandria, established that the length of the arc on the earth's surface between these cities is 1/48 of the great circle of the Earth. Assuming that the distance between Rhodes and Alexandria corresponds to 5,000 stadia, Posidonius obtained the length (5,000 X 48) of the circumference of the Earth, equal to 240,000 stadia.

However, 1/48 of the circle corresponds to an angle equal to 7 ° 30 ". The actual difference in the latitudes of Rhodes and Alexandria is 5 ° 14", i.e., about 769 of the Earth's circumference. Pliny also wrote that "for people looking at Canopus from Alexandria, it appears about a quarter of one sign above the horizon, and at Rhodes it somehow comes into contact with the Earth." Since the sign of the zodiac (360 °: 12) is 30 °, then its fourth part is equal to 7 ° 30 ". Apparently Posidonius and Pliny used the same source of information about the difference in the latitudes of Rhodes and Alexandria. If Posidonius really produced astronomical observations on Rhodes, he could hardly have drawn any conclusions about the height of the star Canopus, which, according to the opinion of ancient authors, did not even appear above the horizon there.

All this suggests that Posidonius did not make instrumental observations of the Canopic star in Rhodes and Alexandria, but used literary sources for his conclusions.

It is known from the writings of Eratosthenes that in his time the distance between Rhodes and Alexandria was taken to be 5,000, 4,000, or 3,750 stadia.

Apparently everything indicated figures are the same linear quantity expressed in stages of different lengths:

5000 X 0.148165 = 740.83 km;

4000X0.185207=740.83 km;

3750X0.197554=740.83 km.

Adhering to the data of Posidonius, we find the value of the circumference of the Earth calculated by him, expressed in the metric system of measures:

740.83 X 48 = 35560 km.

If we take the Ionian stadia, then the distance between Rhodes and Alexandria will be 5000 x 0.197554 = 987.77 km, and the circumference of the Earth - 987.77 X 48 = 47,413 km.

The distance between Rhodes and Alexandria is 600 km. Consequently, Posidonius in his calculations operated not only with an exaggerated difference in the latitudes of Rhodes and Alexandria, but also with a significantly overestimated distance between the indicated points. It should also be taken into account that the results of these determinations, undoubtedly, should have been reflected in a significant difference in longitudes (about 1 ° 43 ") of Alexandria and Rhodes.

In order to establish the origin of the results of measuring the length of the meridian arc between Alexandria and Rhodes attributed to Posidonius, let us consider some other sources in which fragments of the results of works known to ancient authors on determining the size of the Earth have been preserved.

So, some Arab scientists, referring to ancient sources, wrote that the circumference of the Earth is equal to 8,000 farsakhs.

Based on these data, we calculate the circumference of the Earth corresponding to 8,000 farsakhs:

8,000 X 5.92661 = 47,413 km.

Beruni wrote in one of his works: “They transmit in books (in the form of tradition) that ancient scientists found the cities of Rakka and Tadmor on the same line from the noon, and between them - 90 miles. From this they deduced that the magnitude of one degree is 662/3 miles. The circumference of the earth according to these data is 24,000 miles.

I.Yu. Krachkovsky, referring to the medieval Arab scholar Iakut, writes that the determination of the length of an arc of one degree of the meridian at 66 2/3 miles was carried out "... by Ptolemy on the basis of measurements in Upper Mesopotamia between Harran and the mountains of Amida" . It is quite possible that in this area work was ever carried out to determine the length of the arc of a degree of the meridian, but not by Ptolemy. In his writings, Ptolemy refers to only one figure - 180,000 stadia, and repeatedly emphasizes that it was obtained by Marina of Tire (c. 1st century AD) as a result of "calculations" and not "measurements".

The performance of work on measuring the length of the arc of the degree of the meridian between Tadmor (Palmyra) and Rakka Krachkovsky refers to the year 827. He writes: “The steppe between Palmyra and Rakka on the Euphrates and the valley in Upper Mesopotamia near Sinjar between 35° and 36° north latitude were chosen for measurement. The commission, assembled at the central point, divided into two parties: one went south along the meridian line for a distance of a degree, and the other for the same distance to the north. Upon returning to their starting point, they verified the results and established the final conclusion ... The astronomer of the late tenth century, Ibn Yunus, reports that one party determined the magnitude of the degree at 57, and the other at 56 1 / 4 miles; when the results were presented to al-Ma'mun, he decided to settle for middle figure at 56 2/3 miles".

Here we should pay attention to some contradictions in the coverage of this event by the specified source. Firstly, the city of Raqqa is located 250 km west of the Sinjar valley, where astronomers and geodesists of al-Mamun measured the length of the arc of a meridian degree. Since both parties, as is known, began measurements from a common point, it is clear that they had nothing to do with degree measurements in the region of Tadmor and Raqqa. The fact that both parties began the measurement from one, common point, located south of Sinjar, is also reported by Beruni.

Secondly, both geodetic parties of al-Mamun, as can be seen from the surviving sources, measured the arc of the meridian, equal to one degree. The difference between the latitudes of Rakka and Tadmor is 1°22".

Since a mile long 1975.54 m was in use in the Arab Caliphate, the value of the arc degree of the meridian obtained as a result of measurements in 827 corresponds to 111,947 m.

The result, equal to 66 2/3 miles, does not belong to the famous Arab scholar al-Battani (c. 858-929), who in 877-918. conducted regular astronomical observations in Raqqa. Al-Battani believed that the length of the arc of a degree of the meridian is 75 miles, and the circumference of the Earth is: 27,000 miles.

It is important to note that the error in determining the difference between the latitudes of Raqqa and Tadmor by ancient scientists, as Beruni established, did not exceed 1 ". However, the scientists who determined the length of the meridian degree arc here were mistaken, believing that Raqqa and Tadmor are on the same meridian. In fact, the difference in longitude these points is about 45".

Since the line connecting Tadmor and Raqqa deviates from the direction of the meridian by about 24°, it is clear that no instrumental measurements of the distance were made here. Otherwise, the difference between the longitudes of Rakka and Tadmor would have been noticed. Apparently, the distance between Tadmor and Rakka was established, as was usually done in antiquity, according to the time of the movement of the caravan. This may explain why instead of the actual distance between Tadmor and Raqqa, equal to 84 miles, 90 miles were obtained.

According to the Tadmor measurements, the length of the arc of a degree of the meridian, in terms of the metric system of measures, was determined to be 131.7 km (66 2/3 X 1.97554), and the circumference of the Earth - 24,000 X 1.97554 = 47,413 km.

Since the farsah consisted of 3 Babylonian miles (1975.54 x 3 = 5926.61 m), we can conclude that the values ​​\u200b\u200bof the circumference of the Earth, equal to 8,000 farsakhs and 24,000 miles, represent the same linear value(8,000 x 3 = 24,000) corresponding to 47,413 km and are therefore the result of the same degree measurements.

The result obtained from the Tadmorian degree measurements, .. equal to 24,000 miles, could be expressed by Posidonius with a more familiar measure of length for ancient scientists - a stage. It is known from various sources that a mile consisted of 7 1/2, 8, 8 1/3 and 10 stadia, i.e.

197.554 X 7 1/2 = 1481.65 m;

185.207 X 8 = 1481.65 m;

177.798 X 8 1/3 = 1481.65 m;

148.165 X 10 = 1481.65 m;

197.554 X 10 = 1975.54 m.

Based on the fact that the results of the Tadmor measurements are expressed in Roman miles, Posidonius could calculate two values ​​​​of the circumference of the Earth - in the Ionian (24,000 X 7 1/2 \u003d 180,000 stadia) and Roman (24,000 X 10 \u003d 240,000 stadia) metrological systems . Thus, both results attributed to Posidonius -180,000 and 240,000 stadia, as M. Lefranc suggested, can be the same linear value:

180,000 X 0.197554 = 240,000 X 0.148165 = 35,560 km.

The fact that the values ​​of 180,000 and 240,000 stadia are of precisely this origin is also evidenced by some other, later sources containing information about measurements of the circumference of the Earth in ancient times. So, for example, Nallino conveys the message of the Arab geographer Yaqut that the circumference of the Earth of 24,000 miles corresponds to 180,000 stadia of ancient authors.

From this analysis it follows that neither Posidonius nor Marin: Tyre did not themselves measure the circumference of the Earth. The data attributed to them (180,000 and 240,000 stadia) are an interpretation of the results of degree measurements made in the region of Tadmor and Raqqa.

It is possible that information about the methods and results of determining the size of the Earth by Eastern scientists became known to Eratosthenes from the numerous works of Eastern scientists stored in the Library of Alexandria. It is no coincidence that Eratosthenes wrote the poem "Hermes" that has not come down to us, where he included extensive astronomical and geographical material. Notice what Aristotle says about "mathematicians" trying to "calculate" rather than "measure" the circumference of the earth. However, when determining the circumference of the Earth, Greek scientists could not do without the appropriate astronomical and geodetic measurements. Since none of the ancient authors mentions such measurements made before Eratosthenes, it is obvious that the Greeks did not make them, but used the results of determining the size of the Earth by scientists of the East.

Establishing the origin and accuracy of the oldest determinations of the size of the Earth will help reveal the directions and scales scientific relations between the centers of ancient civilizations, to highlight another page in the history of astronomy and geodesy.

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