Why does a person need measurements
Measurement is one of the most important things in modern life. But not always
It was like this. When a primitive man killed a bear in an unequal duel, he, of course, was happy if it turned out to be big enough. This promised a well-fed life for him and the entire tribe for long time... But he did not drag the carcass of the bear onto the scales: at that time there were no scales. There was no particular need for measurements when a person made a stone ax: technical conditions on such axes did not exist and everything was determined by the size suitable stone that I managed to find. Everything was done by eye, as the master's instinct suggested.
Later people began to live large groups... The exchange of goods began, which then passed into trade, the first states arose. Then there was a need for measurements. The royal arctic foxes should have known what the area of the field for each peasant was. This determined how much grain he should give to the king. It was necessary to measure the yield from each field, and when selling flaxseed meat, wine and other liquids, the volume of goods sold. When they began to build ships, it was necessary to outline the correct dimensions in advance: otherwise the ship would have sunk. And, of course, the ancient builders of pyramids, palaces and temples could not do without measurements, they still amaze us with their proportionality and beauty.
^ OLD RUSSIAN MEASURES.
The Russian people have created their own system of measures. Monuments of the 10th century speak not only of the existence of a system of measures in Kievan Rus, but also state supervision over their correctness. This supervision was entrusted to the clergy. One of the statutes of Prince Vladimir Svyatoslavovich says:
"... from time immemorial it has been established and entrusted to eat the bishops of the city and everywhere all sorts of measures and scales and scales ... watch without filth, neither multiply, nor diminish ..." . do not allow them to be either diminished or increased ...). This need to supervise the needs of trade both within the country and with the countries of the West (Byzantium, Rome, later Germanic cities) and the East (Central Asia, Persia, India) was prompted. Bazaars took place on the church square, chests were kept in the church for keeping contracts on trade deals, churches had correct scales and measures, goods were stored in the basements of churches. Weighing was carried out in the presence of representatives of the clergy, who received a fee for this in favor of the church.
Measures of length
The oldest of them are the elbow and the fathom. We do not know the exact initial length of either measure; an Englishman who traveled through Russia in 1554 testifies that a Russian cubit was equal to half an English yard. According to the "Trade Book", compiled for Russian merchants at the turn of the 16th and 17th centuries, three cubits were equal to two arshins. The name "arshin" comes from the Persian word "arsh", which means elbow.
The first mention of the sazhen is found in the chronicle of the 11th century, compiled by the Kiev monk Nestor.
In later times, a measure of the distance of verst was established, equated to 500 fathoms. In ancient monuments, a verst is called a field and is sometimes equated to 750 fathoms. This can be explained by the existence of a shorter fathom in antiquity. Finally, a verst to 500 fathoms was established only in the 18th century.
In the era of the fragmentation of Russia, there was no single system of measures. In the 15th and 16th centuries, the unification of the Russian lands around Moscow took place. With the emergence and growth of national trade and with the establishment of fees for the treasury from the entire population of the united country, the question arises of unified system measures for the entire state. The measure of arshin arising from trade with eastern peoples, comes into use.
In the 18th century, the measures were refined. Peter 1 by decree established the equality of three-arshin fathoms to seven English feet. The former Russian system of measures of length, supplemented by new measures, received its final form:
Mile = 7 versts (= 7.47 kilometers);
Verst = 500 fathoms (= 1.07 kilometers);
Fathom = 3 arshins = 7 feet (= 2.13 meters);
Arshin = 16 vershoks = 28 inches (= 71.12 centimeters);
Feet = 12 inches (= 30.48 centimeters);
Inch = 10 lines (2.54 centimeters);
Line = 10 points (2.54 millimeters).
When they talked about a person's height, they only indicated how many vershoks it exceeds 2 arshins. Therefore, the words "a man of 12 inches of height" meant that his height is equal to 2 arshins 12 inches, that is, 196 cm.
Measures of area
In "Russkaya Pravda" - a legislative monument, which refers to the XI-XIII centuries, the land measure is a plow. This was the measure of the land from which tribute was paid. There is some reason to consider the plow equal to 8-9 hectares. As in many countries, the amount of rye needed to sow the area was often taken as a measure of the area. In the 13th-15th centuries, the main unit of the area was the kad-area, for sowing each one needed about 24 poods (that is, 400 kg.) Of rye. Half of this area, called tithes, became the main measure of area in pre-revolutionary Russia. She leveled about 1.1 hectares. Tithing was sometimes called a box.
Another unit for measuring areas equal to half a tithe was called (quarter) chet. Subsequently, the size of the tithe was brought into line not with measures of volume and mass, but with measures of length. In the Book of Sleepy Writing, as a guide for accounting for taxes from the land, a tithe is set equal to 80 * 30 = 2400 square fathoms.
The tax unit of the land was about x a (this is the amount of arable land that one plowman was able to cultivate).
MEASURES OF WEIGHT (MASS) and VOLUME
The oldest Russian weight unit was the hryvnia. It is mentioned in the treaties of the 10th century between the princes of Kiev and the Byzantine emperors. Through complex calculations, scientists learned that the hryvnia weighed 68.22 g. The hryvnia was equal to the Arab unit of weight, the rothl. Then the basic units for weighing were the pound and the pood. A pound equaled 6 hryvnia, and a pood - 40 pounds. For weighing gold, spools were used, which were 1.96 fractions of a pound (hence the proverb "small spool and dear"). The words "pound" and "pood" come from the same Latin word "pondus" meaning heaviness. Officials those who checked the scales were called "pundovschik" or "weights". In one of the stories of Maxim Gorky, in the description of the barn of the kulak, we read: "On one bolt there are two locks - one poodier (heavier) than the other."
By the end of the 17th century, a system of Russian weight measures had developed in the following form:
Last = 72 pounds (= 1.18 tons);
Berkovets = 10 pounds (= 1.64 centners);
Pounds = 40 large hryvnias (or pounds), or 80 small hryvnias, or 16 steelyards (= 16.38 kg.);
The original ancient measures of the liquid - the barrel and the bucket - remain unclear exactly. There is reason to believe that the bucket held 33 pounds of water and the barrel held 10 buckets. The bucket was divided into 10 shtofs.
Monetary system Russian people
Monetary units for many peoples were pieces of silver or gold of a certain weight. In Kievan Rus such units were silver grivnas. Russkaya Pravda, the oldest set of Russian laws, says that for killing or stealing a horse, a fine of 2 hryvnias is imposed, and for an ox - 1 hryvnia. The hryvnia was divided into 20 legs or 25 kuna, and the kuna - into 2 cut. The name "kuna" (marten) recalls the times when there was no metallic money in Russia, and instead of them furs were used, and later - leather money - quadrangular pieces of leather with brands. Although the hryvnia is like currency unit long gone out of use, but the word "hryvnia" has survived. A 10 kopeck coin was called a dime. But this, of course, is not the same as the old hryvnia.
Minted Russian coins have been known since the time of Prince Vladimir Svyatoslavovich. In times Horde yoke Russian princes were obliged to indicate on the coins issued the name of the khan who ruled in the Golden Horde. But after the Battle of Kulikovo, which brought victory to the troops of Dmitry Donskoy over the hordes of Khan Mamai, the liberation of Russian coins from the khan's names began. At first, these names began to be replaced by illegible script of oriental letters, and then completely disappeared from the coins.
In chronicles dating back to 1381, the word "money" is first encountered. This word comes from the Hindu name for the tanka silver coin, which the Greeks called Danaka, the Tatars - Tenga.
The first use of the word "ruble" refers to XIV century... This word comes from the verb "cut". In the XIV century, the hryvnia began to be cut in half, and a silver bar of half a hryvnia (= 204.76 g) was called the ruble or ruble hryvnia.
In 1535, coins were issued - Novgorodoks with a drawing of a horseman with a spear in his hands, called kopeck money. The chronicle from here produces the word "penny".
Further oversight of measures in Russia.
With the revitalization of the inner and foreign trade oversight of the measures was transferred from the clergy to special bodies of civil power - the order of the big treasury. Under Ivan the Terrible, it was ordered to weigh goods only from the poodists.
In the 16th and 17th centuries, uniform state or customs measures were diligently introduced. In the XVIII and XIX centuries measures were taken to improve the system of measures and weights.
The Weights and Measures Act of 1842 ended over 100 years of government efforts to streamline the system of weights and measures.
DI Mendeleev - metrologist.
In 1892, the genius Russian chemist Dmitry Ivanovich Mendeleev became the head of the Main Chamber of Weights and Measures.
Supervising the work of the Main Chamber of Weights and Measures, D.I. Mendeleev completely transformed the measurement business in Russia, established scientific research work and resolved all questions about the measures that were caused by the growth of science and technology in Russia. In 1899, developed by D.I. Mendeleev a new law on measures and weights.
In the first years after the revolution, the Main Chamber of Weights and Measures, continued the traditions of Mendeleev, carried out colossal work to prepare the introduction of the metric system in the USSR. After some restructuring and renaming, the former Main Chamber of Weights and Measures currently exists as the All-Union Scientific Research Institute of Metrology named after D.I. Mendeleev.
^ French measures
Initially, in France, and throughout cultural Europe, Latin measures of weight and length were used. But feudal fragmentation made her own adjustments. For example, another gentleman had a fantasy to slightly increase the pound. None of his subjects will object, and not to rebel over such trifles. But if you count, in general, all the quitrent grain, then what a benefit! Also with the city workshops of artisans. It was beneficial for someone to reduce the fathom, for someone to increase it. Depending on whether they are selling or buying cloth. A little bit, a little bit, and now you have the Rhine pound, and Amsterdam, and Nuremberg and Paris, etc., etc.
And with fathoms, even that the situation was worse, only in the south of France more than a dozen different units of length rotated.
True, in the glorious city of Paris, in the fortress of Le Grand Chatel, since the time of Julius Caesar, a standard of length was embedded in the fortress wall. It was an iron crooked compass, the legs of which ended in two protrusions with parallel edges, between which all used fathoms must exactly fit. Châtel's fathom remained the official measure of length until 1776.
At first glance, the measures of length looked like this:
Sea Lie - 5, 556 km.
Liege overland = 2 miles = 3.3898 km
Mile (from Lat. Thousand) = 1000 toises.
Tuaz (fathom) = 1.949 meters.
Foot (foot) = 1/6 toise = 12 inches = 32.484 cm.
Inch (finger) = 12 lines = 2.256 mm.
Line = 12 points = 2.256 mm.
Point = 0.188 mm.
In fact, since no one canceled feudal privileges, all this concerned the city of Paris, well, the Dauphine, in extreme cases. Somewhere in the outback, a foot could easily be defined as the size of a senior's foot, or as average length feet of 16 people leaving from Matins on Sunday.
Parisian pound = livre = 16 ounces = 289.41 gr.
Ounce (1/12 lb) = 30.588 gr.
Gran (grain) = 0.053 gr.
But the artillery pound still equaled 491.4144 gr., That is, it simply corresponded to the Nuremberg pound, which was used in the 16th century by Mr. Hartmann, one of the theorists - the masters of the artillery shop. The size of the pound in the provinces also walked in accordance with the traditions.
Measures of liquid and free-flowing bodies, too, did not differ in harmonious uniformity, because France was still a country where the population mainly grew bread and wine.
Wine muid = about 268 liters
Chain - about 156 liters
Mine = 0.5 net = about 78 liters
Mino = 0.5 mines = about 39 liters
Boissot = about 13 liters
^ English measures
English measures, measures applied in the UK, USA. Canada and other countries. Some of these measures in a number of countries differ somewhat in their size, therefore, below are mainly rounded metric equivalents of English measures, convenient for practical calculations.
Measures of length
Sea mile (UK) = 10 cables = 1.8532 km
Cable (UK) = 185.3182 m
Cable (USA) = 185.3249 m
Charter mile = 8 furlongs = 5280 feet = 1609.344 m
Furlong = 10chains = 201.168m
Chain = 4 genera = 100 links = 20.1168 m
Rod (pol, perch) = 5.5 yards = 5.0292 m
Yard = 3 feet = 0.9144 m
Foot = 3 hands = 12 inches = 0.3048 m
Hand = 4 inches = 10.16 cm
Inch = 12 lines = 72 points = 1000 mils = 2.54 cm
Line = 6 points = 2.1167 mm
Point = 0.353mm
Mil = 0.0254 mm
Area measures
Sq. mile = 640 acres = 2.59 km2
Acre = 4 ores = 4046.86 m2
Ore = 40 sq. childbirth = 1011.71 m2
Sq. genus (pol, perch) = 30.25 sq. yards = 25.293 m2
Sq. yard = 9 sq. ft = 0.83613 m2
Sq. ft = 144 sq. inches = 929.03 cm2
Sq. inch = 6.4516 cm2
Mass measures
Big ton or long = 20 handweights = 1016.05 kg
Small ton, or short (USA, Canada, etc.) = 20 cents = 907.185 kg
Handreadweight = 4 quarters = 50.8 kg
Cental = 100 lbs = 45.3592 kg
Quarter = 2 groans = 12.7 kg
Moan = 14 lbs = 6.35 kg
Pound = 16 ounces = 7000 grains = 453.592 g
Ounce = 16 drachmas = 437.5 grains = 28.35 g
Drachma = 1.772 g
Gran = 64.8 mg
Units of volume, capacity.
Cube yard = 27 cubic meters ft = 0.7646 cubic meters m
Cube ft = 1728 cubic inches = 0.02832 cubic meters m
Cube inch = 16.387 cc cm
Units of volume, capacity
for liquids.
Gallon (English) = 4 quarts = 8 pints = 4.546 liters
Quart (English) = 1.136 L
Pint (English) = 0.568 L
Units of volume, capacity
for bulk solids
Bushel (English) = 8 gallons (English) = 36.37 L
^ The collapse of ancient systems of measures
In I-II AD, the Romans took possession of almost all the then known world and introduced their own system of measures to all the conquered countries. But after several centuries, Rome was conquered by the Germans and the empire created by the Romans fell apart into many small states.
After that, the collapse of the introduced system of measures began. Each king, or even a duke, tried to introduce his own system of measures, and if he succeeded, then monetary units.
The collapse of the system of measures reached its highest point in the 17th and 18th centuries, when Germany was fragmented into as many states as there were days in a year, as a result of which there were 40 different feet and cubits, 30 different centners, 24 different miles.
In France, there were 18 units of length, called leagues, etc.
This caused difficulties in trade, in the collection of taxes, and in the development of industry. After all, the units of measure acting simultaneously were not related to each other, they had different subdivisions into smaller ones. It was difficult for a highly experienced merchant to understand this, but what can we say about an illiterate peasant. Of course, merchants and officials used this to rob the people.
In Russia, in different localities, almost all measures had different meanings, therefore, in the textbooks of arithmetic before the revolution, detailed tables of measures were placed. In one common pre-revolutionary reference book one could find up to 100 different feet, 46 different miles, 120 different pounds, etc.
The needs of practice forced to start looking for a unified system of measures. At the same time, it was clear that it was necessary to abandon the establishment between the units of measurement and the dimensions of the human body. And the step of people is different and the length of the foot is not the same, and their fingers different widths... Therefore, it was necessary to look for new units of measurement in the surrounding nature.
The first attempts to find such units were made in antiquity in China and Egypt. The Egyptians chose the mass of 1000 grains as a unit of mass. But the grains are not the same! Therefore, the idea of one of the Chinese ministers, who proposed long before our era to choose as a unit 100 grains of red sorghum arranged in a row, was also unacceptable.
Scientists have come up with different ideas. Some suggested taking the dimensions associated with the honeycomb as the basis for measures, some the path traveled in the first second by a freely falling body, and the famous scientist of the 17th century Christian Huygens suggested taking a third of the length of the pendulum, which makes one swing per second. This length is very close to twice the length of the Babylonian cubit.
Even before him, the Polish scientist Stanislav Pudlovsky proposed to take the length of the second pendulum itself as a unit of measurement.
^ The birth of the metric system of measures.
It is not surprising that when in the eighties of the XVIII the merchants of several French cities turned to the government with a request to establish a uniform system of measures for the whole country, scientists immediately remembered Huygens' proposal. The adoption of this proposal was hampered by the fact that the length of the second pendulum is different in different places. the globe... It is larger at the North Pole, and less at the equator.
At this time in France there was bourgeois revolution... A National Assembly was convened, which created a commission at the Academy of Sciences, composed of the greatest French scientists of the time. The commission was to carry out work to create a new system of measures.
One of the members of the commission was the famous mathematician and astronomer Pierre Simon Laplace. For his scientific research, it was very important to know the exact length of the earth's meridian. Some of the members of the commission recalled the proposal of the astronomer Mouton to take as a unit of length a part of the meridian equal to one 21600th part of the meridian. Laplace immediately supported this proposal (or, perhaps, he himself prompted the other members of the commission to think about it). Only one measurement was taken. For convenience, we decided to take one forty-millionth part of the earth's meridian as a unit of length. This proposal was submitted to the National Assembly and accepted by it.
All other units were aligned with the new unit called the meter. The unit of area was taken as a square meter, volume - cubic meter, mass - the mass of a cubic centimeter of water under certain conditions.
In 1790, the National Assembly passed a decree reforming the systems of measures. The report presented to the National Assembly noted that there is nothing arbitrary in the draft reform, except for the decimal base, and nothing local. “If the memory of these works was lost and only one result was preserved, then there would be no sign in them by which it was possible to find out which nation started the plan for these works and carried them out,” the report said. As you can see, the commission of the Academy, sought to ensure that new system measures did not give rise to any nation to reject the system as the French. She tried to justify the slogan: "For all times, for all peoples", which was proclaimed later.
Already in April 17956, a law on new measures was approved, a single standard was introduced for the whole Republic: a platinum ruler on which the meter is inscribed.
The Commission of the Paris Academy of Sciences from the very beginning of work on the development of the new system established that the ratio of neighboring units should be equal to 10. For each quantity (length, mass, area, volume) from the main unit of this quantity, other, larger and smaller measures are formed in the same way (for with the exception of the names "micron", "centner", "ton"). To form the names of measures larger than the basic unit, the Greek words are added to the name of the latter from the front: "deca" - "ten", "hecto" - "one hundred", "kilo" - "one thousand", "miria" - "ten thousand" ; to form the names of measures smaller than the basic unit, the particles are also added in front of the: "deci" - "ten", "centi" - "one hundred", "milli" - "thousand".
^ Archival meter.
The 1795 law, establishing a temporary meter, indicates that the commission's work will continue. Measuring work was completed only by the fall of 1798 and gave the final length of a meter of 3 feet 11.296 lines instead of 3 feet 11.44 lines, which was the length of the temporary meter in 1795 (the old French foot was equal to 12 inches, inch-12 lines).
In those years, the outstanding diplomat Talleyrand was the Minister of Foreign Affairs of France, who even earlier was engaged in the reform project; he proposed to convene representatives of allied with France and neutral countries to discuss the new system of measures and make it international. In 1795, delegates gathered for an international convention; it announced the completion of work on checking the determination of the length of the main standards. In the same year, the final prototypes were manufactured in meters and kilograms. They were published in the Archives of the Republic for safekeeping, therefore they were named archival.
The temporary meter was abolished, and instead of it, the units of length were recognized as an archival meter. It had the form of a rod, the cross-section of which resembles the letter X. Archival standards only 90 years later gave way to new ones, called international ones.
^ Reasons obstructing the implementation of
metric system of measures.
The French people greeted the new measures without much enthusiasm. The reason for this attitude was partly the newest units of measures that did not correspond to age-old habits, as well as new names of measures that were incomprehensible to the population.
Napoleon was among those who were not enthusiastic about the new measures. By a decree of 1812, along with the metric system, he introduced the "everyday" system of measures for use in trade.
The restoration of royal power in France in 1815 contributed to the oblivion of the metric system. The revolutionary origin of the metric system prevented its spread in other countries.
Since 1850, progressive scientists have begun vigorous campaigning in favor of the metric system, one of the reasons for this was the international exhibitions, showing all the conveniences of the various national systems of measures that existed. Particularly fruitful in this direction were the activities of the St. Petersburg Academy of Sciences and its member Boris Semenovich Yakobi. In the seventies, this activity culminated in the actual transformation of the metric system into an international one.
^ Metric system of measures in Russia.
In Russia, scientists with early XIX centuries understood the purpose of the metric system and tried to implement it widely in practice.
In the years from 1860 to 1870, after the energetic speeches of D.I. Mendeleev, the campaign in favor of the metric system was led by Academician B.S. Yakobi, Professor of Mathematics A.Yu.Davidov, the author of school textbooks of mathematics that were widespread at the time, and Academician A.V. Gadolin. Russian manufacturers and breeders also joined the scientists. The Russian Technical Society commissioned a special commission chaired by Academician A.V. Gadolin to elaborate this issue. This commission received many proposals from scientists and technical organizations, unanimously supporting the proposal for the transition to the metric system.
The law on measures and weights, published in 1899, was developed by DT Mendeleev and included paragraph 11:
“The international method and the kilogram, their subdivisions, as well as other metric measures are allowed to be applied in Russia, probably with the main Russian measures, in trade and other transactions, contracts, estimates, contracts, and the like - by mutual agreement of the contracting parties, as well as in within the limits of the activities of individual government departments ... by expansion or by order of the subject ministers ... ".
The final solution to the question of the metric system in Russia was received after the Great October socialist revolution... In 1918, the Council People's Commissars under the chairmanship of V. I. Lenin, a resolution was issued, which proposed:
“To put in the basis of all measurements the international metric system of measures and weights with decimal subdivisions and derivatives.
Take the unit of length as a basis - a meter, and as a basis for a unit of weight (mass) - a kilogram. For samples of units of the metric system, accept a copy of the international meter bearing sign No. 28, and a copy of the international kilogram bearing sign No. 12, made of iridium platinum, transferred to Russia by the First international conference weights and measures in Paris in 1889 and are now stored in the Main Chamber of Weights and Measures in Petrograd. "
From January 1, 1927, when the transition of industry and transport to the metric system was prepared, metric system measures became the only system of measures and weights allowed in the USSR.
^ Old Russian measures
in proverbs and sayings.
Arshin and a caftan, and two for patches.
A beard with inches, and words with a bag.
To lie - seven miles to heaven and all in the forest.
We were looking for a mosquito seven miles away, and a mosquito was on our nose.
An arshin of a beard, but an inch of mind.
He sees three arshins in the ground!
I will not give up an inch.
From thought to thought, five thousand miles.
A hunter walks seven miles away to sip jelly.
To write (talk) about other people's sins in arshins, and about their own - in lowercase letters.
You are from the truth (from the service) by a span, and it is from you - by a fathom.
Stretch a mile, but don't be simple.
For this, you can put a pood (ruble) candle.
A grain of pood protects.
It's not bad that the roll is half a meal.
One grain of pood brings.
Your own spool of someone else's pood is more expensive.
Ate half a meal - as long as he is full.
Find out how much a pood is dashing.
He does not have a creeper of the brain (mind) in his head.
The thin ones fall in poods, and the good ones come with spools.
^ MEASURES COMPARISON TABLE
Measures of length
1 verst = 1.06679 kilometers
1 fathom = 2.1335808 meters
1 arshin = 0.7111936 meters
1 vershok = 0.0444496 meters
1 foot = 0.304797264 meters
1 inch = 0.025399772 meters
1 kilometer = 0.9373912 versts
1 meter = 0.4686956 fathoms
1 meter = 1.40609 arshins
1 meter = 22.4974 inches
1 meter = 3.2808693 ft
1 meter = 39.3704320 inches
1 fathom = 7 feet
1 fathom = 3 arshins
1 fathom = 48 vershoks
1 mile = 7 versts
1 verst = 1.06679 kilometers
^ Measures of volume and area
1 quad = 26.2384491 liters
1 quarter = 209.90759 liters
1 bucket = 12.299273 liters
1 tithe = 1.09252014 hectares
1 liter = 0.03811201 quadruple
1 liter = 0.00952800 quarters
1 liter = 0.08130562 buckets
1 hectare = 0.91531493 tithes
1 barrel = 40 buckets
1 barrel = 400 damask
1 barrel = 4000 charms
1 quarter = 8 quads
1 quarter = 64 garnets
Weights
1 pood = 16.3811229 kilograms
1 pound = 0.409528 kilograms
1 spool = 4.2659174 grams
1 share = 44.436640 milligrams
1 kilogram = 0.9373912 versts
1 kilogram = 2.44183504 pounds
1 gram = 0.23441616 spool
1 milligram = 0.02250395 shares
1 pood = 40 pounds
1 pood = 1280 lots
1 berks = 10 poods
1 last = 2025 and 4/9 kilograms
Monetary measures
Ruble = 2 fifty
half a dollar = 50 kopecks
five dollars = 15 kopecks
altyn = 3 kopecks
dime = 10 kopecks
2 money = 1 kopeck
penny = 0.5 kopeck
half a half = 0.25 kopecks
The meaning of the above is in one phrase: "You cannot control what cannot be measured."
Here are some of the most important points about measurement. "What I measured is what I got." This means that, as a rule, it is precisely those areas of work where monitoring and measurements were carried out that first of all receive attention, resources are sought for them; "Measurements determine behavior." This means that taking measurements often leads to changes in the system, to its adaptation to new benchmarks.
As noted earlier, companies are usually divided into functional departments. The dominant direction of monitoring indicators is the assessment of financial parameters, which, as a rule, are taken directly from accounting statements... The problem is that such monitoring methods often come into direct conflict with the improvement process and interfere with the implementation of relevant activities. The point is that many improvement efforts can be very difficult to adequately assess with conventional investment analysis. As a rule, costs are needed both for training and for the actual implementation of the project. But the results of improvement are largely operational in nature. For example, this is a reduction in time, a decrease in the proportion of defects, etc. It can be very difficult to assess these indicators in financial terms, since the result of such improvements does not appear immediately, but after some time, i.e. in future. Therefore, it can be difficult to achieve allocation of resources and time for improvement projects.
V last years developments were aimed at creating more operational systems for measuring indicators. but general issues measuring indicators and intensifying these processes are beyond the scope of this book. To support the improvement approach discussed in this book, you need to create a system with the following elements: Continuous measurement of relevant aspects of key business process indicators, approximately 15-30 processes. What is meant by “relevant aspects” is discussed later in this chapter. All of these measurable metrics together should form a complete and coherent dashboard that can be used to continuously monitor metrics. Unlike the antediluvian "knife switch" finance department, which with a great delay then turns on and off the red light, warning of profit or loss, the new dashboard will contain a set of measuring instruments, which can be used to assess the real state of affairs (see Fig. 4.1). This dashboard will point out any emerging negative trends, show developments over time, and help determine the prerequisites for specific improvement efforts.
However, you need to be careful not to overdo it with measurements.
Rice. 4.1. Various measuring systems
Example.
Xerox (USA) and Rank Xerox in Europe, each in its own country, have been at the forefront of developing a system for operational measurement of indicators. However, their efforts were so great that in these companies even a joke arose: "If something moves, measure it!" This, of course, led to the emergence of redundancy of information that no one ever uses, and not because it is not interesting, but because there is no time to look through it. For this reason, they began to treat any information with disdain, even information that is really important. All measures to measure indicators have lost their relevance.
In conclusion of this section, I would like to cite a few "common amateurish rules" for taking measurements: Measurement is not a good thing for a long time, especially since the Taylor era, with his study of timing and movements, measurements were often aimed at monitoring employees. The measurement methods offered in this book have a very different focus. They are conducted not in order to look for a scapegoat, but in order to understand how well the processes work. It is very important to separate the measurement and the assessment that is made on its basis. The measurement itself never harmed anyone. This is only an interpretation of the measurement results and its use could have Negative consequences... The more accurate the better1. An all-round increase in measurement accuracy may be relevant for technical systems or for accounting, but not for measuring indicators. Often, the purpose of performance measurement is to establish whether an improvement has been made or not, rather than to determine the exact level of performance. Investing heavily in the development of overly accurate measuring systems can actually slow down and slow down the practical implementation of these systems. So it needs more practical approach.
Everything is decided only by money1. The traditional view of the world around us through the prism of money, the assertion that only money is a reliable indicator of everything, turned out to be the main obstacle to the development of softer directions in measurement systems. Indicators such as the quality of the work situation, the ability of the product to meet the customer's needs, etc. also deliver valuable information. They should not be discarded just because there is no corresponding cash equivalent for them. Everything should be strictly according to the standards! Quite the opposite. Standards are often viewed as an upper bound on performance. A good standard means that as long as you work with it, you don't need to improve.
Why does a person need measurements
Measurement is one of the most important things in modern life. But not always
it was like this. When a primitive man killed a bear in an unequal duel, he, of course, was happy if it turned out to be big enough. This promised a well-fed life for him and the entire tribe for a long time. But he did not drag the carcass of the bear onto the scales: at that time there were no scales. There was no particular need for measurements when a person made a stone ax: there were no technical conditions for such axes and everything was determined by the size of a suitable stone that could be found. Everything was done by eye, as the master's instinct suggested.
Later people began to live in large groups. The exchange of goods began, which then passed into trade, the first states arose. Then there was a need for measurements. The royal arctic foxes should have known what the area of the field for each peasant was. This determined how much grain he should give to the king. It was necessary to measure the yield from each field, and when selling flaxseed meat, wine and other liquids, the volume of goods sold. When they began to build ships, it was necessary to outline the correct dimensions in advance: otherwise the ship would have sunk. And, of course, the ancient builders of pyramids, palaces and temples could not do without measurements, they still amaze us with their proportionality and beauty.
OLD RUSSIAN MEASURES.
The Russian people have created their own system of measures. Monuments of the 10th century speak not only of the existence of a system of measures in Kievan Rus, but also of state supervision over their correctness. This supervision was entrusted to the clergy. One of the statutes of Prince Vladimir Svyatoslavovich says:
"... from time immemorial it has been established and entrusted to eat the bishops of the city and everywhere all sorts of measures and scales and scales ... watch without filth, neither multiply, nor diminish ..." . do not allow them to be either diminished or increased ...). This need to supervise the needs of trade both within the country and with the countries of the West (Byzantium, Rome, later Germanic cities) and the East (Central Asia, Persia, India) was prompted. Bazaars took place on the church square, chests were kept in the church for keeping contracts on trade deals, churches had correct scales and measures, goods were stored in the basements of churches. Weighing was carried out in the presence of representatives of the clergy, who received a fee for this in favor of the church.
Measures of length
The oldest of them are the elbow and the fathom. We do not know the exact initial length of either measure; an Englishman who traveled through Russia in 1554 testifies that a Russian cubit was equal to half an English yard. According to the "Trade Book", compiled for Russian merchants at the turn of the 16th and 17th centuries, three cubits were equal to two arshins. The name "arshin" comes from the Persian word "arsh", which means elbow.
The first mention of the sazhen is found in the chronicle of the 11th century, compiled by the Kiev monk Nestor.
In later times, a measure of the distance of verst was established, equated to 500 fathoms. In ancient monuments, a verst is called a field and is sometimes equated to 750 fathoms. This can be explained by the existence of a shorter fathom in antiquity. Finally, a verst to 500 fathoms was established only in the 18th century.
In the era of the fragmentation of Russia, there was no single system of measures. In the 15th and 16th centuries, the unification of the Russian lands around Moscow took place. With the emergence and growth of national trade and with the establishment of fees for the treasury from the entire population of the united country, the question arises of a single system of measures for the entire state. The measure of arshin, which arose during trade with the eastern peoples, comes into use.
In the 18th century, the measures were refined. Peter 1 by decree established the equality of three-arshin fathoms to seven English feet. The former Russian system of measures of length, supplemented by new measures, received its final form:
Mile = 7 versts (= 7.47 kilometers);
Verst = 500 fathoms (= 1.07 kilometers);
Fathom = 3 arshins = 7 feet (= 2.13 meters);
Arshin = 16 vershoks = 28 inches (= 71.12 centimeters);
Feet = 12 inches (= 30.48 centimeters);
Inch = 10 lines (2.54 centimeters);
Line = 10 points (2.54 millimeters).
When they talked about a person's height, they only indicated how many vershoks it exceeds 2 arshins. Therefore, the words "a man of 12 inches of height" meant that his height is equal to 2 arshins 12 inches, that is, 196 cm.
Measures squares
In "Russkaya Pravda" - a legislative monument, which refers to the XI-XIII centuries, the land measure is a plow. This was the measure of the land from which tribute was paid. There is some reason to consider the plow equal to 8-9 hectares. As in many countries, the amount of rye needed to sow the area was often taken as a measure of the area. In the 13th-15th centuries, the main unit of the area was the kad-area, for sowing each one needed about 24 poods (that is, 400 kg.) Of rye. Half of this square, called tithes became the main measure of area in pre-revolutionary Russia. She leveled about 1.1 hectares. Tithing was sometimes called box.
Another unit for measuring areas equal to half a tithe was called (quarter) chet. Subsequently, the size of the tithe was brought into line not with measures of volume and mass, but with measures of length. In the Book of Sleepy Writing, as a guide for accounting for taxes from the land, a tithe is set equal to 80 * 30 = 2400 square fathoms.
The tax unit of the land was about x a (this is the amount of arable land that one plowman was able to cultivate).
MEASURES OF WEIGHT (MASS) and VOLUME
The oldest Russian weight unit was the hryvnia. It is mentioned in the treaties of the 10th century between the princes of Kiev and the Byzantine emperors. Through complex calculations, scientists learned that the hryvnia weighed 68.22 g. The hryvnia was equal to the Arab unit of weight rothl... Then the main units for weighing steel pound and pood... A pound equaled 6 hryvnia, and a pood - 40 pounds. For weighing gold, spools were used, which were 1.96 fractions of a pound (hence the proverb "small spool and dear"). The words "pound" and "pood" come from the same Latin word "pondus" meaning heaviness. The officials who checked the scales were called "pundovschiki" or "weights". In one of the stories of Maxim Gorky, in the description of the barn of the kulak, we read: "On one bolt there are two locks - one poodier (heavier) than the other."
By the end of the 17th century, a system of Russian weight measures had developed in the following form:
Last = 72 pounds (= 1.18 tons);
Berkovets = 10 pounds (= 1.64 centners);
Pounds = 40 large hryvnias (or pounds), or 80 small hryvnias, or 16 steelyards (= 16.38 kg.);
The original ancient measures of the liquid - the barrel and the bucket - remain unclear exactly. There is reason to believe that the bucket held 33 pounds of water and the barrel held 10 buckets. The bucket was divided into 10 shtofs.
Monetary system of the Russian people
Monetary units for many peoples were pieces of silver or gold of a certain weight. In Kievan Rus such units were hryvnia of silver... Russkaya Pravda, the oldest set of Russian laws, says that for killing or stealing a horse, a fine of 2 hryvnias is imposed, and for an ox - 1 hryvnia. The hryvnia was divided into 20 legs or 25 kuna, and the kuna - into 2 cut. The name "kuna" (marten) recalls the times when there was no metallic money in Russia, and instead of them furs were used, and later - leather money - quadrangular pieces of leather with brands. Although the hryvnia as a monetary unit has long gone out of use, the word "hryvnia" has survived. A coin in denomination of 10 kopecks was called dime. But this, of course, is not the same as the old hryvnia.
Minted Russian coins have been known since the time of Prince Vladimir Svyatoslavovich. During the Horde yoke, Russian princes were obliged to indicate on the coins issued the name of the khan who ruled in the Golden Horde. But after the Battle of Kulikovo, which brought victory to the troops of Dmitry Donskoy over the hordes of Khan Mamai, the liberation of Russian coins from the khan's names began. At first, these names began to be replaced by illegible script of oriental letters, and then completely disappeared from the coins.
In chronicles dating back to 1381, the word "money" is first encountered. This word comes from the Hindu name for a silver coin tank, which the Greeks called Danaka, Tatars - tenga.
The first use of the word "ruble" refers to the XIV century. This word comes from the verb "cut". In the XIV century, the hryvnia began to be cut in half, and a silver bar in half a hryvnia (= 204.76 g) received the name ruble or ruble hryvnia.
In 1535, coins were issued - Novgorodoks with a drawing of a horseman with a spear in his hands, which received the name kopeck money... The chronicle from here produces the word "penny".
Further oversight of measures in Russia.
In 1892, the genius Russian chemist Dmitry Ivanovich Mendeleev became the head of the Main Chamber of Weights and Measures.
Supervising the work of the Main Chamber of Weights and Measures, he completely transformed the business of measurements in Russia, established research work and solved all questions about the measures that were caused by the growth of science and technology in Russia. In 1899, a new law on measures and weights was developed.
In the first years after the revolution, the Main Chamber of Weights and Measures, continued the traditions of Mendeleev, carried out colossal work to prepare the introduction of the metric system in the USSR. After some restructuring and renaming, the former Main Chamber of Weights and Measures now exists as the All-Union Scientific Research Institute of Metrology named after.
French measures
Initially, in France, and throughout cultural Europe, Latin measures of weight and length were used. But feudal fragmentation made its own adjustments. For example, another gentleman had a fantasy to slightly increase the pound. None of his subjects will object, and not to rebel over such trifles. But if you count, in general, all the quitrent grain, then what a benefit! Also with the city workshops of artisans. It was beneficial for someone to reduce the fathom, for someone to increase it. Depending on whether they are selling or buying cloth. A little bit, a little bit, and now you have the Rhine pound, and Amsterdam, and Nuremberg and Paris, etc., etc.
And with fathoms, even that the situation was worse, only in the south of France more than a dozen different units of length rotated.
True, in the glorious city of Paris, in the fortress of Le Grand Chatel, since the time of Julius Caesar, a standard of length was embedded in the fortress wall. It was an iron crooked compass, the legs of which ended in two protrusions with parallel edges, between which all used fathoms must exactly fit. Châtel's fathom remained the official measure of length until 1776.
At first glance, the measures of length looked like this:
Sea Lie - 5, 556 km.
Liege overland = 2 miles = 3.3898 km
Mile (from Lat. Thousand) = 1000 toises.
Tuaz (fathom) = 1.949 meters.
Foot (foot) = 1/6 toise = 12 inches = 32.484 cm.
Inch (finger) = 12 lines = 2.256 mm.
Line = 12 points = 2.256 mm.
Point = 0.188 mm.
In fact, since no one canceled feudal privileges, all this concerned the city of Paris, well, the Dauphine, in extreme cases. Somewhere in the outback, a foot could easily be defined as the size of a senior's foot, or as the average length of the feet of 16 people leaving from Matins on Sunday.
Parisian pound = livre = 16 ounces = 289.41 gr.
Ounce (1/12 lb) = 30.588 gr.
Gran (grain) = 0.053 gr.
But the artillery pound still equaled 491.4144 gr., That is, it simply corresponded to the Nuremberg pound, which was used in the 16th century by Mr. Hartmann, one of the theorists - the masters of the artillery shop. The size of the pound in the provinces also walked in accordance with the traditions.
Measures of liquid and free-flowing bodies, too, did not differ in harmonious uniformity, because France was still a country where the population mainly grew bread and wine.
Wine muid = about 268 liters
Chain - about 156 liters
Mine = 0.5 net = about 78 liters
Mino = 0.5 mines = about 39 liters
Boissot = about 13 liters
English measures
English measures, measures applied in the UK, USA. Canada and other countries. Some of these measures in a number of countries differ somewhat in their size, therefore, below are mainly rounded metric equivalents of English measures, convenient for practical calculations.
Measures of length
Sea mile (UK) = 10 cables = 1.8532 km
Even before him, the Polish scientist Stanislav Pudlovsky proposed to take the length of the second pendulum itself as a unit of measurement.
Birth metric system of measures.
The bourgeoisie "href =" / text / category / burzhuaziya / "rel =" bookmark "> bourgeois revolution. A National Assembly was convened, which created a commission at the Academy of Sciences, composed of the greatest French scientists of the time. The commission was to carry out the work to create a new system measures.
One of the members of the commission was the famous mathematician and astronomer Pierre Simon Laplace. For his scientific research, it was very important to know the exact length of the earth's meridian. Some of the members of the commission recalled the proposal of the astronomer Mouton to take as a unit of length a part of the meridian equal to one 21600th part of the meridian. Laplace immediately supported this proposal (or, perhaps, he himself prompted the other members of the commission to think about it). Only one measurement was taken. For convenience, we decided to take one forty-millionth part of the earth's meridian as a unit of length. This proposal was submitted to the National Assembly and accepted by it.
All other units were aligned with the new unit called meters... For a unit of area was taken square meter, volume - cubic meter, masses - cubic centimeter mass water under certain conditions.
In 1790, the National Assembly passed a decree reforming the systems of measures. The report presented to the National Assembly noted that there is nothing arbitrary in the draft reform, except for the decimal base, and nothing local. “If the memory of these works was lost and only one result was preserved, then there would be no sign in them by which it was possible to find out which nation started the plan for these works and carried them out,” the report said. As you can see, the Commission of the Academy strove to ensure that the new system of measures did not give rise to any nation to reject the system, like the French one. She tried to justify the slogan: "For all times, for all peoples", which was proclaimed later.
Already in April 17956, a law on new measures was approved, a single standard was introduced for the whole Republic: a platinum ruler on which the meter is inscribed.
The Commission of the Paris Academy of Sciences from the very beginning of work on the development of the new system established that the ratio of neighboring units should be equal to 10. For each quantity (length, mass, area, volume) from the main unit of this quantity, other, larger and smaller measures are formed in the same way (for with the exception of the names "micron", "centner", "ton"). To form the names of measures larger than the basic unit, the Greek words are added to the name of the latter from the front: "deca" - "ten", "hecto" - "one hundred", "kilo" - "one thousand", "miria" - "ten thousand" ; to form the names of measures smaller than the basic unit, the particles are also added in front of the: "deci" - "ten", "centi" - "one hundred", "milli" - "thousand".
Archive meter.
International exhibitions "href =" / text / category / mezhdunarodnie_vistavki / "rel =" bookmark "> international exhibitions that showed all the conveniences of the various national systems of measures. in the seventies, this activity culminated in the actual transformation of the metric system into an international one.
Metric system of measures in Russia.
In Russia, scientists from the beginning of the 19th century understood the purpose of the metric system and tried to widely implement it in practice.
In the years from 1860 to 1870, after energetic speeches, the campaign in favor of the metric system was led by an academician, a professor of mathematics, the author of school mathematics textbooks that were widespread at the time, and an academician. Russian manufacturers and breeders also joined the scientists. The Russian Technical Society instructed a special commission chaired by the academician to work out this issue. This commission received many proposals from scientists and technical organizations, unanimously supporting the proposals for the transition to the metric system.
The law on measures and weights, issued in 1899, included paragraph 11:
“The international method and the kilogram, their subdivisions, as well as other metric measures are allowed to be applied in Russia, probably with the main Russian measures, in trade and other transactions, contracts, estimates, contracts, and the like - by mutual agreement of the contracting parties, as well as in within the limits of the activities of individual government departments ... by expansion or by order of the subject ministers ... ".
The final solution to the question of the metric system in Russia was received after the Great October Socialist Revolution. In 1918, a decree was issued by the Council of People's Commissars, chaired by it, proposing:
“To put in the basis of all measurements the international metric system of measures and weights with decimal subdivisions and derivatives.
Take the unit of length as a basis - a meter, and as a basis for a unit of weight (mass) - a kilogram. For samples of units of the metric system, take a copy of the international meter bearing sign number 28, and a copy of the international kilogram bearing sign number 12, made of iridescent platinum, transferred to Russia by the First International Conference of Weights and Measures in Paris in 1889 and now stored in the Main Chamber of Measures and scales in Petrograd ".
Since January 1, 1927, when the transition of industry and transport to the metric system was prepared, the metric system of measures became the only system of measures and weights allowed in the USSR.
Old Russian measures
in proverbs and sayings.
Arshin and a caftan, and two for patches.
A beard with inches, and words with a bag.
To lie - seven miles to heaven and all in the forest.
We were looking for a mosquito seven miles away, and a mosquito was on our nose.
An arshin of a beard, but an inch of mind.
He sees three arshins in the ground!
I will not give up an inch.
From thought to thought, five thousand miles.
A hunter walks seven miles away to sip jelly.
To write (talk) about other people's sins in arshins, and about their own - in lowercase letters.
You are from the truth (from the service) by a span, and it is from you - by a fathom.
Stretch a mile, but don't be simple.
For this, you can put a pood (ruble) candle.
A grain of pood protects.
It's not bad that the roll is half a meal.
One grain of pood brings.
Your own spool of someone else's pood is more expensive.
Ate half a meal - as long as he is full.
Find out how much a pood is dashing.
He does not have a creeper of the brain (mind) in his head.
The thin ones fall in poods, and the good ones come with spools.
MEASURES COMPARISON TABLE
n Measures of length
1 verst = 1.06679 kilometers
1 fathom = 2.1335808 meters
1 arshin = 0.7111936 meters
1 vershok = 0.0444496 meters
1 foot = 0, meters
1 inch = 0 meters
1 kilometer = 0.9373912 versts
1 meter = 0.4686956 fathoms
1 meter = 1.40609 arshins
1 meter = 22.4974 inches
1 meter = 3.2808693 ft
1 meter = 39.3704320 inches
n 1 fathom = 7 feet
1 fathom = 3 arshins
1 fathom = 48 vershoks
1 mile = 7 versts
1 verst = 1.06679 kilometers
n Volume and area measures
1 quad = 26.2384491 liters
1 quarter = 209.90759 liters
1 bucket = 12.299273 liters
1 tithe = 1, hectare
1 liter = 0, four
1 liter = 0, quarters
1 liter = 0, buckets
1 hectare = 0, tithes
n 1 barrel = 40 buckets
1 barrel = 400 damask
1 barrel = 4000 charms
1 quarter = 8 quads
1 quarter = 64 garnets
n Weights
1 pood = 16.3811229 kilograms
1 pound = 0.409528 kilograms
1 spool = 4.2659174 grams
1 share = 44.436640 milligrams
n 1 kilogram = 0.9373912 versts
1 kilogram = 2 pounds
1 gram = 0, spool
1 milligram = 0, fraction
n 1 pood = 40 pounds
1 pood = 1280 lots
1 berks = 10 poods
1 last = 2025 and 4/9 kilograms
n Monetary measures
n ruble = 2 fifty
half a dollar = 50 kopecks
five dollars = 15 kopecks
altyn = 3 kopecks
dime = 10 kopecks
n 2 money = 1 kopeck
penny = 0.5 kopeck
half a half = 0.25 kopecks
Science begins ever since
how they begin to measure ...
D. I. Mendeleev
Ponder the words of a famous scientist. The role of measurements in any science, and especially in physics, is clear from them. But, in addition, measurements are important in practical life. Can you imagine your life without measurements of time, mass, length, vehicle speed, power consumption, etc.?
How to measure a physical quantity? For this purpose they serve measuring instruments... Some of them are already known to you. it different kind rulers, watches, thermometers, scales, protractor (Fig. 20), etc.
Rice. twenty
Measuring instruments are digital and scale... In digital instruments, the measurement result is determined by numbers. This is an electronic clock (Fig. 21), a thermometer (Fig. 22), an electricity meter (Fig. 23), etc.
Rice. 21
Rice. 22
Rice. 23
Ruler, analogue clock, household thermometer, scales, protractor (see Fig. 20) are scale instruments. They have a scale. The measurement result is determined from it. The entire scale is outlined with dashes for divisions (Fig. 24). One division is not one stroke (as students sometimes mistakenly believe). This is the gap between the two nearest strokes. In Figure 25, there are two divisions between the numbers 10 and 20, and the dashes are 3. The devices that we will use in laboratory work, mostly scale.
Rice. 24
Rice. 25
To measure a physical quantity means to compare it with a homogeneous quantity taken as a unit.
For example, to measure the length of a straight line segment between points A and B, you need to apply a ruler and, using a scale (Fig. 26), determine how many millimeters fit between points A and B. The homogeneous value with which the length of segment AB was compared was a length equal to 1 mm.
Rice. 26
If a physical quantity is measured directly by reading data from the scale of the device, then such a measurement is called direct.
For example, by applying a ruler to the bar in different places, we will determine its length a (Fig. 27, a), width b and height c. We determined the value of the length, width, height directly by taking the reading off the ruler scale. From Figure 27, b it follows: a = 28 mm. This is a direct measurement.
Rice. 27
How to determine the volume of a bar?
It is necessary to carry out direct measurements of its length a, width b and height c, and then using the formula
V = a. b. c
calculate the volume of the bar.
In this case, we say that the volume of the bar was determined by the formula, that is, indirectly, and the measurement of the volume is called indirect measurement.
Rice. 28
Think and answer
- Figure 28 shows several measuring instruments.
- What are these measuring devices called?
- Which ones are digital?
- What physical quantity does each device measure?
- What is the homogeneous value on the scale of each device shown in Figure 28, with which the measured value is compared?
- Please resolve the dispute.
Tanya and Petya solve the problem: “Determine the thickness of one sheet of a book containing 300 pages with a ruler. The thickness of all sheets is 3 cm. " Petya claims that this can be done by direct measurement of the sheet thickness with a ruler. Tanya believes that determining the thickness of the sheet is an indirect measurement.
What do you think? Justify your answer.
Interesting to know!
By studying the structure of the human body and the work of its organs, scientists also carry out many measurements. It turns out that a person weighing about 70 kg has about 6 liters of blood. The human heart in a calm state beats 60-80 times per minute. For one contraction, it emits an average of 60 cm 3 of blood, per minute - about 4 liters, per day - about 6-7 tons, per year - more than 2000 tons. So our heart is a great worker!
Human blood passes through the kidneys 360 times a day, clearing it from harmful substances... The total length of the renal blood vessels is 18 km. By leading a healthy lifestyle, we help our body to function smoothly!
Homework
Rice. 29
- List the measuring devices in your notebook that are in your apartment (house). Divide them into groups:
1) digital; 2) scale.
- Check the validity of the rule of Leonardo da Vinci (Fig. 29) - a brilliant Italian artist, mathematician, astronomer, engineer. For this:
- measure your height: ask someone to put on door jamb a small line with a pencil; measure the distance from the floor to the marked line;
- measure the distance along a horizontal line between the ends of the fingers (fig. 31);
- compare the value obtained in point b) with your height; for most people, these values are equal, which was first noticed by Leonardo da Vinci.
Rice. thirty
Rice. 31
Absolute measurement system physical quantities
In the last two centuries, there has been a rapid differentiation of scientific disciplines in science. In physics, in addition to the classical Newtonian dynamics, electrodynamics, aerodynamics, hydrodynamics, thermodynamics, physics of various aggregate states, special and general theory relativity, quantum mechanics and more. A narrow specialization took place. Physicists have ceased to understand each other. Superstring theory, for example, is understood only by a hundred people around the world. To get a professional understanding of superstring theory, you only need to deal with superstring theory, there is simply not enough time for the rest.
But we should not forget that such different scientific disciplines study the same physical reality - matter. Science, and especially physics, has come close to the point when further development possible only by integrating (synthesizing) various scientific directions. The considered absolute system for measuring physical quantities is the first step in this direction.
Unlike the international system of units SI, which has 7 basic and 2 additional units of measurement, in the absolute system of units of measurement one unit is used - the meter (see table). The transition to the dimensions of the absolute measurement system is carried out according to the rules:
Where: L, T and M are the dimensions of length, time and mass, respectively, in the SI system.
The physical essence of transformations (1.1) and (1.2) is that (1.1) reflects the dialectical unity of space and time, and from (1.2) it follows that the mass can be measured in square meters. True, the /> in (1.2) is not the square meters of our three-dimensional space, but the square meters of the two-dimensional space. Two-dimensional space is obtained from three-dimensional, if three-dimensional space is accelerated to a speed close to the speed of light. According to the special theory of relativity, due to the contraction of the linear dimensions in the direction of motion, the cube will turn into a plane.
The dimensions of all other physical quantities are established on the basis of the so-called "pi-theorem", which states that any correct relationship between physical quantities up to a constant dimensionless factor corresponds to some physical law.
To introduce a new dimension of any physical quantity, you need:
Choose a formula containing this quantity, in which the dimensions of all other quantities are known;
Algebraically find the expression of this quantity from the formula;
In the resulting expression, substitute the known dimensions of physical quantities;
Perform the required algebraic operations on the dimensions;
Accept the obtained result as the required dimension.
"Pi-theorem" allows not only to establish the dimensions of physical quantities, but also to derive physical laws. Consider, for example, the problem of gravitational instability of a medium.
It is known that as soon as the wavelength of the sound disturbance turns out to be greater than a certain critical value, the elastic forces (gas pressure) are not able to return the particles of the medium to their original state. It is required to establish the relationship between physical quantities.
We have physical quantities:
/> - the length of the fragments into which the homogeneous infinitely extended medium disintegrates;
/> is the density of the medium;
A is the speed of sound in the medium;
G is the gravitational constant.
In the SI system, physical quantities will have the dimension:
/> ~ L; /> ~ />; a ~ />; G ~ />
From /> />, /> and /> we compose a dimensionless complex:
where: /> and /> are unknown exponents.
Thus:
Since P, by definition, is a dimensionless quantity, we obtain a system of equations:
The solution to the system will be:
hence,
Where do we find:
Formula (1.3), up to a constant dimensionless factor, describes the well-known Jeans criterion. In the exact formula />.
Formula (1.3) satisfies the dimensions of the absolute system for measuring physical quantities. Indeed, the physical quantities included in (1.3) have dimensions:
/>~ />; />~ />; />~ />; />~ />
Substituting the dimensions of the absolute system in (1.3), we get:
Analysis of the absolute system for measuring physical quantities shows that the mechanical force, Planck's constant, electric stress and entropy have the same dimension: />. This means that the laws of mechanics, quantum mechanics, electrodynamics and thermodynamics are invariant.
For example, Newton's second law and Ohm's law for a section of an electrical circuit have the same formal notation:
/>~ />(1.4)
/>~ />(1.5)
At high speeds of motion, a variable dimensionless factor of the special theory of relativity is introduced into Newton's second law (1.4):
If the same factor is introduced into Ohm's law (1.5), then we get:
According to (1.6), Ohm's law allows for the appearance of superconductivity, since /> at low temperatures can take on a value close to zero. If physics from the very beginning used an absolute system for measuring physical quantities, then the phenomenon of superconductivity would be predicted theoretically at first, and only then discovered experimentally, and not vice versa.
There is a lot of talk about the accelerated expansion of the Universe. Measure expansion acceleration modern technical means can not. Let us apply an absolute system for measuring physical quantities to solve this problem.
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It is quite natural to assume that the acceleration of the expansion of the Universe /> depends on the distance between space objects /> and on the rate of expansion of the Universe />. The solution of the problem by the above method gives the formula:
An analysis of the physical meaning of formula (1.7) is beyond the scope of the problem under discussion. We will only say that in the exact formula />.
The invariance of physical laws makes it possible to clarify the physical essence of many physical concepts. One of these "dark" concepts is the concept of entropy. In thermodynamics, mechanical acceleration /> ~ /> corresponds to the mass density of entropy
where: S - entropy;
m is the mass of the system.
The resulting expression indicates that the entropy, in spite of the existing delusion, can not only be calculated, but also measured. Consider, for example, a metal spiral spring, which can be considered a mechanical system of atoms in the crystal lattice of a metal. If you compress the spring, the crystal lattice deforms and creates elastic forces that can always be measured. The spring force will be the same mechanical entropy. If the entropy is divided by the mass of the spring, then we get the mass density of the entropy of the spring, as a system of atoms in the crystal lattice.
The spring can also be represented as one of the elements of the gravitational system, the second element of which is our Earth. The gravitational entropy of such a system will be the force of attraction, which can be measured in several ways. Dividing the force of attraction by the mass of the spring, we obtain the gravitational density of entropy. The gravitational entropy density is the acceleration of gravity.
Finally, in accordance with the dimensions of physical quantities in the absolute system of measurement, the entropy of a gas is the force with which the gas presses on the walls of the vessel in which it is enclosed. Specific gas entropy is simply gas pressure.
Important information about internal structure elementary particles can be obtained proceeding from the invariance of the laws of electrodynamics and aerodynamics, and the invariance of the laws of thermodynamics and information theory allows filling the equations of information theory with physical content.
The absolute system for measuring physical quantities refutes the widespread misconception about the invariance of Coulomb's law and the law universal gravitation... The dimension of the mass /> ~ /> does not coincide with the dimension electric charge q ~ />, so the law of gravity describes the interaction of two spheres, or material points, and Coulomb's law describes the interaction of two conductors with current, or circles.
Using the absolute system of measuring physical quantities, we can formally derive the famous formula of Einstein:
/>~ />(1.8)
Between special relativity and quantum theory there is no irresistible chasm. Planck's formula can also be obtained purely formally:
It is possible to further demonstrate the invariance of the laws of mechanics, electrodynamics, thermodynamics and quantum mechanics, but the examples considered are enough to understand that all physical laws are special cases of some general laws of space-time transformations. Those interested in these laws will find them in the author's book "Theory of multidimensional spaces". - M .: Kom Kniga, 2007.
Transition from the dimensions of the international system (SI) to the dimensions of the absolute system (AS) of measuring physical quantities
1. Basic units
The name of the physical quantity
Dimension in the system
The name of the physical quantity
Kilogram
Electric current strength
Thermodynamic temperature
Amount of substance
The power of light
2. Additional units
Flat angle
Solid angle
Steradian
3. Derived units
3.1 Space-time units
Square meter
Speed
Continuation
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Ampere per square meter
Electric charge
The electric charge density is linear
Pendant per meter
Surface electric charge density
Pendant per square meter
Magnetomotive force
Magnetic field strength
Ampere per meter
Inductance
Magnetic constant
Henry per meter
Magnetic moment of electric current
Ampere - square meter
Magnetization
Ampere per meter
Reluctance
Ampere to Weber
3.5 Energy photometry
Light flow
Weightiness
Radiation flux
Energy illumination and luminosity
Watt per square meter
Energy brightness
Watt per steradian square meter
Radiant luminosity spectral density:
By wavelength
By frequency
Watt per m3