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Mesurements and units. International metric system

Length and distance The history of metric systems of units of measurement is usually told starting from 1790, when the Academy of Revolutionary France decided to revolutionize the national system of units of length - toise-foot-inch-line - and propose it as an international one. However,  ​​developing and adopting a single interstate (global) system of measures (at that stage and level of metrology development, it was measures, not units) had a long history.

The first nationwide (and even partially interstate) systems of measures arose a long time ago. According to the traditional calculation of time intervals, no less than four thousand years "that time ago", in Ancient Babylon (Chaldea). The next "object" was Ancient Egypt. The systems of measures of both civilizations had several identical, even eponymous, measures. I will name the cubit and the foot (which have survived to this day).

For the civilizations mentioned above, unified systems of measures were natural and vital. Without these systems (they also included weight and volume measures), it was impossible to govern the state, record its income, determine the size and collect taxes, trade, customs operations, arm and maintain the army, and much more.

Babylon's and especially Egypt's experiences were adopted by Ancient Republican and Imperial Rome (to a lesser extent by Greece, which was not a monolithic state). It is difficult to say whether the French academics knew about ancient systems of measures. Archaeology was emerging at that time. J. Champollion, a pioneer in reading Egyptian hieroglyphs, was born in 1790. So, most likely, they came to this idea independently.

The situation was more complicated in Europe in the 16th to 18th centuries. Each state (and there were many) had its own monetary system and system of measures, which became an obstacle to trade (including customs duties), the development of crafts and industry, etc. In this situation, the ideas of developing a unified, interstate system of measures began to emerge. Its supporters and promoters were many prominent scientists and industrialists. Among them, we can name D. Watt, who proposed his version of the future metric system in 1783, and P.S. Laplace, whose insistence was that the meter be defined as part of the Earth's meridian.

The motto of the French academicians, which stated that the new system of measures should be based on an unchanging prototype taken from nature, so that all nations could use it, is well known. But how original is it? No one has seriously investigated this question (I will stipulate immediately that there can be no hint of plagiarism). I will give only a few considerations indicating that this idea, as they say, "hung in the air".

Length and distanceEpisode one: an ancient unit for measuring long distances - stadia (stadium). It (or he) was equal to the path a specially trained priest traveled during the time the Sun rolled over the horizon on the days of the equinox, at the latitude of Babylon, close to two minutes. The most reliable size of the stadium is 185 meters. The unit combined an objectively existing astronomical phenomenon independent of man with the subjective length of a human step. That's what's interesting. If in the definition of the stage we replace the priest's speed with the speed of light in a vacuum, 299,792,458 m/s, and instead of the time of the Sun's roll-out we take 1/299,792,458 of a second, we get the modern definition of the meter.

Episode two. The nautical mile is 1852 meters. One angular minute of the length of the Earth's meridian. It appeared, perhaps, with the advent of the Mercator cartographic projection (1512-1594). The measure is very ancient. Very convenient for navigation purposes and is directly related to the size of the Earth, no worse than the meter.

Episode three. The old French league, one twenty-fifth of an angular degree of the Earth's meridian, about 4.44 kilometers. The same idea of ​​formation as the nautical mile; after adopting the metric system, the French hastened to replace the old French league with a metric one, equal to 4 km. In doing so, they did not notice that they had violated the decimal principle of forming multiples and submultiples. Incidentally, Jules Verne, an ardent supporter of the metric system, had in mind the metric league in his famous novel 20,000 Leagues Under the Sea. The existence of the nautical mile and the league indicates that the size of the Earth was known with sufficient accuracy long before 1700.

So the idea of ​​defining the size of the meter as a fraction of the length of the Earth's meridian is no worse or better than the ideas of defining the nautical mile and the old French league. The only difference is in the experiment's accuracy in determining the meter's value. The French academics saw their future brainchild as a system of measures (not yet a system of units), based on one standard measure - the meter. The measure of mass - the kilogram - was also defined through the meter, or rather, through its fraction - the decimeter.


Measures and units of measurement

Measurements It is time to clarify the relationship between these concepts. Metrology began with measures. This simple truth is confirmed by all historical monuments (material and written) related to its history. The Babylonian (Chaldean) system was a system of measures based on material, artificial, concrete measures of length, weight (mass), and volume. The Ancient Egyptian system and all later systems of measures were the same. Apparently, concrete (not abstract) thinking was characteristic of humanity at the early stages of its development.

As human society and metrology, in particular, developed, the concrete concept of a measure was gradually supplemented (and in many cases replaced) by the abstract idea of a "unit of measurement", which was not necessarily rigidly connected with a concrete measure.

For a long time, not only were systems concrete and objective, but also various decrees, regulations, and other orders of emperors, princes, and governments. And nevertheless... If we examine the old systems of measures in more detail, we can find "measures without measures" in them. At all times, there were measures of a foot, an elbow (cubits), and a weighing talent. But nowhere, for example, do we find information about the existence of a measure of a stadium (a measuring rope or chain, about 185 meters long). Judging by Egyptian hieroglyphs, the longest measuring rope contained one hundred cubits (about 50 meters). The absence of a measure equal to a stadium is indirectly evidenced by the large range of its values, approximately 155 to 210 meters, used simultaneously. Such a measure should have existed since the size of a stadium was determined through time and speed, without any connection with a cubit, and did not contain an integer number of cubits.

Volume measures were made and used over a fairly wide range. But with area measures, things were completely different. They did not exist, so to speak, "due to lack of need."

The history of metric systems is quite indicative in this regard. The metric systems of 1791 and 1875 are, without a doubt, still systems of measures, the meter and kilogram. Of great interest in this regard are the Gauss (millimeter, milligram, second) and CGS (centimeter, gram, second) systems. Firstly, what is a "measure of a second"? The size of a second can and should certainly be reproduced. But what about storing it? The well-known incantation: "moment, you are beautiful, stop, wait", unfortunately, is not feasible as a technical device. And no one thought of making standard millimeters and milligrams for the Gauss system, or centimeters and grams for the CGS. These systems quietly continued to rely on measures of a completely different system – the meter and kilogram. In the process of further expansion of metric systems, which led to the formation of the modern international system of units - SI, they "acquired" a large set of derived units of measurement. Namely, units, and not measures, since it is impossible for many of these units to develop and implement measures. And not all, and not always, the basic units of the SI are based on measures. For example, there is no measure of the kelvin. No one has ever created a measure of the ampere (although one can imagine it).

So, as metrology developed, in addition to the concept of "measure", the idea of "unit of measurement" appeared, abstracted from material embodiment, and the designation "system of measures" was replaced by "system of units of measurement".


Adoption of the metric system by France

MeasurementsOn the threshold of the 19th century a significant event in the history of metrology took place: by decree of the French revolutionary government of December 10, 1799, the metric system of measures was legalized and introduced in France as mandatory, intended, according to the idea of ​​its creators, for all times, for all peoples (á tous les temps, pour tous les peuples). However, this system was not immediately introduced despite its major advantages, not even in France.

Napoleon Bonaparte, by decree of February 12, 1812, linked the meter with the toise, thereby violating the decimal principle of division. In the 1930s, two measures were used in France: one based on the toise and one based on the meter. "In France," wrote E.E. Lenz in 1839, "two measures are accepted: the Parisian foot…, 6 feet make up a toise (toise); meter (métre)." Only by the law of July 4, 1837, was the metric system of measures in its original form declared mandatory for use in France from January 1, 1840. Only after this did the spread of the system beyond France become realistic.

Based on the results of the measurements of the meridian arc from Dunkirk to Barcelona, ​​the size of the meter was determined to be 0.513074 toises and an end measure was made of forged platinum (it was not yet possible to melt it) - a ruler with a length between the ends of 1 m and a cross-section of 25'4 mm, the so-called "archival meter", since this standard was sent for storage to the archives of the French Republic. At the same time, a kilogram standard was made - the "archival kilogram", a weight also made of platinum.

 The meter ruler was not a purely end measure. Along one of its edges, there were divisions every one dm. Because the definition of the kilogram was associated with the decimeter. On the front surface of the ruler, there was engraved (in French) the word "meter" and the motto "for all times, for all peoples". The archival kilogram repeated the shape of an ordinary trade weight and was supplied with a rather primitive case. In addition, a special vessel with a capacity of 1 dm3 was made (and, apparently, also transferred to the archive). Its further fate is unknown to me. It is not mentioned in any book on metrology in Russian. The meter turned out to be a legally and practically successful measure. Firstly, it was "nobody's" by origin, and did not affect any state's national traditions and ambitions. Secondly, it was quite proportionate to a person and did not differ much from a yard, an arshin, and half a toise.

Euphoria and disappointment

MeasurementsThe euphoria over adopting the metric system lasted about forty years. It ended in 1837, when the famous astronomer, mathematician, and metrologist F. Bessel repeated the measurement of the length of a quarter of the Paris meridian and found that it was not 10,000,000, but 10,000,856 m. The meter was shorter than the 1799 meter by almost 0.1 mm. This is a lot for precise linear measurements. Subsequent measurements continued to give different results each time. Finally, in 1872, an international commission convened on the initiative of the St. Petersburg Academy of Sciences made a forced, but the only possible decision: from now on, the meter is not connected with the length of the earth's meridian, but is simply equal to the archive meter, a platinum end measure made back in 1799. To appreciate the non-triviality of the decision, let us recall once again the formulation of the basic principles that the metric system had to correspond to. It had to be "based on an unchanging prototype taken from nature, so that all nations could use it." The decision of 1872 meant the rejection of the prototype (standard) taken from nature, and its replacement with a "man-made" product.

Around 1870, metrologists became convinced that each new definition of the kilogram, as the mass of 1 dm3 of water at the temperature of its maximum density, also gives a different result. The traditional path – tightening the measurement conditions, taking into account more and more new sources of error, clearly led to a dead end (and at that time, they did not yet suspect, for example, that "different" water has a different isotopic composition). Again, a non-standard solution was needed.

In 1872, the same international commission adopted a new definition: the kilogram became equal to the mass of the archive kilogram (weights made back in 1799) and lost its connection with the meter. It was necessary to abandon the second basic principle formulated in 1791, constructing a system of units based on one prototype, on one single basic unit - the meter. Now there were two of them. And nothing remained from the main idea of ​​the creators of the metric system.
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