The abacus is the oldest calculating instrument. See what "Abacus" is in other dictionaries Abacus handheld calculator

Abacus

The development of European and Asian states and the strengthening of trade ties between them led to the need to create a device that would facilitate calculations when making trade transactions and collecting taxes. As a result, the Abacus device was created, known among almost all nations. It was first used in Babylon (around the 6th century BC).

This device was a wooden plank sprinkled with sand, on which grooves were made. These grooves contained pebbles or tokens that indicated numbers.

The appearance of the Babylonian abacus can be restored by analyzing the principles of Babylonian counting. At that time, the sexagesimal positional system was used, i.e. each digit of the number contained 60 units, and depending on its place in the number, each digit indicated either the number of units or tens, and so on. Since it was difficult to place 60 pebbles in each groove, the grooves were divided into two parts: in one, pebbles were placed that counted tens (no more than five), and in the other, pebbles that counted units (no more than nine).

In this case, the number of pebbles in the first groove indicated the number of units, in the second - tens, and so on. If in one groove the number counted by the pebbles exceeded 59, then the pebbles were removed and one pebble was placed in the next groove.

In ancient Rome, the abacus was improved and, in addition to stone slabs, bronze, ivory and colored glass were used. The vertical grooves in the Roman abacus were divided into 2 parts. The grooves in the lower field were used for counting from one to 5; if 5 balls were collected in the lower groove, then one ball was added to the upper compartment, and all the balls were removed from the lower one.

The Neapolitan Museum of Antiquities houses a Roman abacus, which is a board with slots cut along which pebbles were moved. There were eight long slits on the board and eight short ones located above the long ones. Above each long slit there is a symbol describing the purpose of the slit (from left to right):

Means that the slit is used to deposit the million discharge.

Means that the slot is used to deposit hundreds of thousands discharge.

Means that the slot is used to deposit tens of thousands discharge.

Means that the slot is used to deposit thousands place.

Indicates that the slot is used to deposit the hundreds place.

Indicates that the slot is used to deposit tens digits.

Indicates that the slot is used to deposit the ones digit.

Means that this slot is used to deposit ounces (zero to twelve).

Up to four balls were placed on the seven long left slits, each of which was equal to a unit of the corresponding digit of the number. Up to one ball was placed on the seven left short slits, indicating five discharge units. The eighth long strip (which served to count ounces) contained up to five balls, each of which designated a unit of the ounce. The eighth short contained up to one ball, indicating six units.

In addition, on the board on the right there were two more short slots with one ball and one long slot with two balls. Near these slits there were marks that meant:

Half an ounce

Quarter ounce

Sixth of an ounce

Abacus was also known in Greece. In 1846, on the Greek island of Salamis, a marble abacus was found in the form of a slab measuring 105x75 cm, dating back to the 3rd century BC. This abacus was named after the island on which it was found - the “Salaminian Board”.

The Salamis board was used for fivefold notation, which is confirmed by the letter designations on it. Pebbles symbolizing the ranks of numbers were placed only between the lines. The columns located on the left side of the slab were used to count drachmas and talents, and on the right - for fractions of drachmas (obols and halqas).

Around X-XI, the Aztecs invented their own type of abacus. Threads containing corn kernels were pulled through the wooden frame. The frame was divided into two parts. In one part three grains were strung on threads, in the other - four. To work with the Aztec abacus, they used their own special counting system.

In European countries, abacus began to spread in the 10th century. A number of works by Bernellini, Lansky and other authors devoted to abacus calculations and dating back to the 10th-12th centuries have survived to this day. The most famous are the works of the French scientist and clergyman Herbert, which describe in detail the rules of working with the abacus: multiplication, division, addition and subtraction.

Gerber proposed improving the abacus from 12 columns to 27, which made it possible to operate with huge numbers (up to ten to the twenty-seventh power). Also in this abacus three additional columns were introduced for counting money and other measures. During Herbert's time, many schools taught the art of working with the abacus, and many manuals were created for working with the device, thanks to which it became widespread and was used until the 18th century.

abacus- board) - a counting board, used for arithmetic calculations from approximately the 5th century BC. e. in Ancient Greece, Ancient Rome.

The abacus board was divided into strips by lines; counting was carried out using stones or other similar objects placed on the strips. The pebble for the Greek abacus was called psiphos; from this word the name for the account was derived - psiphophoria, “laying out pebbles” (the title of a book about Indian arithmetic by Maximus Planud, who died in 1310, “ Indian psychophoria») .

Abacus in various regions

Ancient Babylon

First appeared probably in Ancient Babylon ca. 3 thousand BC e. Originally it was a board cut into strips or with indentations made. Counting marks (pebbles, bones) moved along lines or indentations. In the 5th century BC e. in Egypt, instead of lines and indentations, they began to use sticks and wire with stringed pebbles.

Ancient India

The peoples of India also used abacus. The Arabs became acquainted with the abacus from the peoples they subjugated. The titles of many Arabic arithmetic manuals include words from the root " dust».

Western Europe, VIII-X centuries

Among the Eastern Arabs, as well as among the Indians, the abacus was soon supplanted by Indian numbering, but it was firmly held by the Western Arabs, who captured Spain at the end of the 8th century. In the 10th century, the Frenchman Herbert (-) became acquainted with counting on abacus here, wrote a book about it (-) and promoted the use of abacus himself and through his students. Instead of pebbles, when counting on the abacus, tokens were used with numerical signs inscribed on them, or Roman numerals, or special numerical signs - apexes. Herbert's apexes are close in shape to the gobar numerals of Western Arabs. Herbert's apexes and his 27-column abacus, a subject of surprise to his contemporaries (reproduced in restored form from various manuscripts by Professor N. M. Bubnov, professor of history at Kyiv University, early 20th century). Through the efforts of Herbert's numerous students and followers and thanks to his influence as Pope (Sylvester II, -), the abacus became widespread in Europe. Traces of this spread remained, among other things, in various languages. English verb to checker, or checker, means graphite- the word from the same root is called cellular matter, the check, or check- bank check, exchequer- Treasury Department . The last term comes from the fact that in the bank, calculations were carried out on an abacus, the basis of which was a graphed board. Until recently the English State Treasury was called Chessboard Chamber- on the checkered cloth that covered the meeting table. The checkered tablecloth served as an abacus for calculations. Originating in the 12th century Chessboard Chamber was the supreme financial authority and the highest court in financial matters until 1873.

Far East

In Eastern countries, the Chinese analogue of abacus - suanpan and the Japanese analogue - soroban are common.

Russia, XVI century

Notes

Literature

Depman I. Ya. History of arithmetic. M.: Education, 1965, p. 79-88.

Links

// Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional ones). - St. Petersburg. , 1890-1907.

Wikimedia Foundation.

2010.:

Synonyms

See what "Abacus" is in other dictionaries: - (arch.) Abacus (device for computing). (Greek abax, abakion, Latin abacus board, counting board), 1) a counting board used for arithmetic calculations in Ancient Greece, Rome, then in Western Europe until the 18th century. The board was divided into... ...

- (from the Greek abax board), the top plate of the capital of a column, half-column, pilaster. In classical architectural orders, the abacus usually has a square outline with straight lines (in the Doric and Ionic orders) or concave (in the Corinthian order). Art encyclopedia

abacus- a, m, ABAKA and, g. abaque m., it. abaco lat. abacus gr. abax, abakos. 1. architect. In Architectural art Top slab and column capitals. Elevation 1789 The abacus is the upper part of the main pillar; otherwise the board is called.. Slab in stone,... ... Historical Dictionary Gallicisms of the Russian language

A. Mechanical wooden, bone or stone abacus, which is a device with moving along several guide plates, thanks to which calculations were made. Used in Europe and Arab countries until the middle of the 18th century... ... Dictionary of business terms

- (from the Greek abax board), 1) a board for arithmetic calculations, divided into strips, where pebbles and bones were moved (as in Russian abacus), in Ancient Greece, Rome, then in Western Europe until the 18th century. 2) In classical architectural orders... ... Modern encyclopedia

- (from the Greek abax board) 1) a board divided into strips on which pebbles and bones were moved (as in Russian abacus), for arithmetic calculations in Dr. Greece, Rome, then to the West. Europe until the 18th century.2) In architectural orders, the top plate of the capital... ... Big Encyclopedic Dictionary

ABAC, a counting device used in the Middle and Far East for addition and subtraction. The most common form of abacus consists of beads strung on a stretched wire and forming columns corresponding to the digits of units... ... Scientific and technical encyclopedic dictionary

In the ancient Turkic language it means elder brother, uncle. Among the Mongols: a statue that is worshiped, an idol. Tatar, Turkic, Muslim male names. Glossary of terms... Dictionary of personal names

Abacus and abacus

A truly revolutionary event in the history of counting was the appearance of instruments

united by a common name - abacus. The abacus could have the shape of a wooden board,

clay tiles or just a outlined piece of earth. It is important that on the abacus

places (columns or lines) for individual digits of numbers were noted.

The abacus was first mentioned by the historian of the ancient world, Herodotus. The abacus was wide

widespread in the ancient world. Its variants were used in Ancient Rome and

Babylon, China, Japan and many other countries. Math problem

was considered solved if its solution could be reproduced on

abacus. Abacus (Greek abax, abakion, Latin abacus - board, counting board), a counting board used for arithmetic calculations in Ancient Greece, Rome, then in Western Europe until the 18th century. There was a joke in Ancient Greece:

“A courtier is like an abacus stone: if he wants a counter, it will cost him a whole talent, but if he wants it, he will only pay a halq.”

The board was divided into stripes, and counting was carried out by moving the scoring marks (domes, stones, etc.) located in the stripes. In the countries of the Far East, the Chinese analogue of the abacus - suan-pan - is widespread, in Russia - the abacus.

Abacus did not penetrate into Russia

later than the 16th century, but most likely it happened much earlier. Russian

variants of the abacus were “counting with bones” and “counting with planks”.

The most primitive abacus, indeed, was such a tablet. Lines were drawn on it with a sharp stick, and pebbles were placed in the resulting columns. This means that there were columns of units, tens, hundreds, and so on.

It is not known exactly where exactly the first abacus appeared. Possibly in Phenicia. The Greeks moved stones from left to right. In contrast, the Egyptians did it from right to left. In ancient Rome, the abacus was called "calculi" or "abaculi" and was made of bronze, stone, ivory or colored glass. From the word “calculus”, meaning “pebble”, “pebble”, came the Latin word “calculatore” (to calculate) and the modern “calculator”. A bronze Roman abacus has been preserved, on which the pebbles moved in vertical grooves. At the bottom were pebbles for counting to five, and at the top were pebbles corresponding to five. Chinese abacus - xuanpan

- appeared in the 6th century AD, and its modern appearance - around the 12th century. Xuanpan is a rectangular frame in which 9 or more parallel wires or ropes are stretched. Perpendicular to this direction, the suanpan is divided by a ruler into two unequal parts: the “ground”, in which there are 5 balls strung on each wire, and the “sky” - here there are 2 balls. The balls in the “earth” are like five fingers of a hand, and the balls in the “sky” are like two hands. The wires are decimal places: ones, tens, and so on.

With the help of suan-pan it was possible not only to add, but also to multiply, divide, operate with fractions, and extract square and cube roots. In all likelihood, this was the first positional decimal number system known to us. Xuan-pan helped make fundamental discoveries in mathematics. Working with numerators and denominators led to the concept of a fraction as a number. About the Russian abacus -, appeared at the turn of the 16th - 17th centuries. The abacus has a horizontal arrangement of knitting needles with bones and is based on a decimal rather than a quinary number system. Russian abacuses were widely used not only for calculations, but also as a teaching aid for initial training in arithmetic.

To distinguish positive numbers from negative ones, various sticks were used in suan-pan. Positive numbers were indicated by red or square sticks, while negative numbers were black or triangular.

The Russian abacus appeared at the turn of the 16th-17th centuries. The most common counting tool in pre-Petrine Rus' was “counting with dice,” which was a special board or table. Before carrying out the calculations, they had to be plotted with horizontal lines. Four arithmetic operations were carried out using a pebble, a fruit stone or a special token.

The abacus began to lose its significance as a universal calculating device, gradually turning into an auxiliary one. With the help of the new system, it turned out to be much more convenient to perform mathematical calculations in writing, on paper, than using an abacus. This process was accompanied by an intense struggle, as it was then believed, between two sciences: mathematics on the abacus and mathematics without the abacus - on paper. This struggle is known as the opposition between the Abacusists and the Algorithmicists. calculating device of Major General of the Russian Army F.M. Svobodsky, invented by him in 1828. developed simple rules for reducing arithmetic operations to a sequence of addition and subtraction, which, together with memorizing several simple auxiliary tables (like the multiplication table), significantly reduced the calculation time. This device - for repeated addition and subtraction - is based on the operating principle of the same Russian abacus.

Abacus - counting board used by many peoples. The Greeks and Egyptians used abacus with painted lines or hollowed out grooves. Pebbles were placed along the lines or in the grooves. Each pebble meant a unit of calculation, and the line itself represented a rank of this unit.

Calculations using the Greek and Egyptian abacus, as well as using the suan-pan and soroban, were carried out as follows. In each groove (on each line or on each twig) there were five pebbles (or balls). The pebble in the first groove meant one. The pebble in the second groove is five units. The pebble in the third groove is twenty-five units. The pebble in the fourth groove is one hundred and twenty-five units.

Thus, the abacus and its early analogues used a five-fold number system. The main advantage of the abacus was the clarity of calculations and the so-called positional system of representing numbers. The result of the calculations did not require any decoding - it was enough to look at the arrangement of the stones on the abacus to instantly determine what number was obtained. The disadvantage of the ancient abacus was precisely the five-fold number system, which did not correspond to the decimal system invented later and did not allow operating with fractions.

Decimal abacus , or Russian abacus the decimal number system is used and the ability to operate with tenths and hundredths of fractional parts has appearedat the turn of the 16th and 17th centuries .

The abacus differs from the classic abacus by increasing the number capacity of each number series and by its design. The abacus is a frame with thin rods inside. Round knuckles are mounted on the rods - ten pieces on each rod. The bottom two rows represent hundredths and tenths. Then comes the intermediate row (usually it is highlighted by four dominoes, which are not involved in the calculations). Then comes the first row of dominoes, each of which represents a unit, the second row, in which each domino represents a ten, then, accordingly, there are hundreds, thousands, tens of thousands, and so on. Later, expanded modifications of accounts appeared - the fractional part could reach four rows, and the part of integers could reach seven rows.

For clarity of calculations, the dominoes of Russian abacuses were two-colored. The fifth and sixth dominoes on each axis were colored darker (black), the rest were colored lighter (brown or yellow). The two-color coloring of the dominoes made it possible to very quickly determine which number was scored on the abacus, since four light dominoes and two dark ones on the left side were quickly identified as the number 6 than six single-color dominoes.

It should be noted that since the emergence of the Russian abacus, scores have changed little over time. The rods on which the knuckles were located acquired a convex profile - so that the knuckles would not spontaneously mix from one side to the other. The rods themselves began to be made of thick metal wire, and the knuckles and frame of the scores were made of oak wood.

Abacus has successfully survived to this day and has left the scene only in recent decades, giving way to electronic calculators. However, the Russian abacus was and remains the most effective tool for teaching counting. A person who can count quickly on an abacus can count faster in his head.

Although abacus simplifies repetitive, cumbersome calculations, it does not simplify multiplication and division operations. Multiplying and dividing using the abacus is, in any case, repeatedly adding and subtracting.

Description

IVK is produced in three versions: according to TU InKS.425210.001, InKS.425210.002 and InKS.425210.003. The IVC consists of a processor with built-in coprocessors, a display and a keyboard built into the case.

Depending on the selected configuration, the IVK may have digital communication ports RS232/RS485, USB, an Ethernet communication interface (10/100BaseT), pulse input counters, input/output modules for analog and frequency signals with support for a hot-swappable mechanism.

The IVK according to TU InKS.425210.003 provides for the possibility of implementing process control algorithms.

The principle of operation of the IVK is to measure and convert input signals coming from measuring transducers of flow (vortex, turbine, rotary, ultrasonic, Coriolis (mass)), pressure, pressure difference, temperature, input signals of thermoelectric converters according to GOST 6616-94 and resistance thermometers according to GOST 6651-2009 (for IVK according to TU InKS.425210.002), frequency measuring signals from density measuring transducers.

Thus, the IVK provides measurement of the following flow parameters:

Natural gas and APG: volume flow (volume) under operating conditions, pressure, temperature, pressure drop on standard orifice devices (diaphragm according to GOST 8.586.2-2005 and Venturi pipe according to GOST 8.586.4-2005) or on averaging pressure tubes " ANNUBAR" according to MI 2667-2011;

Oil and petroleum products, liquid hydrocarbon media: mass flow (mass), volumetric flow (volume) under operating conditions, density under operating conditions, pressure, temperature;

Single-phase liquids with homogeneous physical properties: mass flow (mass), density under operating conditions, pressure, temperature.

IVK calculates the volume flow (volume) of natural gas and APG, reduced to standard conditions, and the mass flow (mass) of liquid using the variable pressure drop method in accordance with the calculation algorithms given in GOST 8.586.2-2005, GOST 8.586.4- 2005, GOST 8.586.5-2005 and MI 2667-2011.

IVK brings the volumetric flow rate (volume) of natural gas and APG under operating conditions to standard conditions in accordance with GOST 2939-63, by automatically electronically correcting the readings of flow measuring transducers: vortex, turbine, rotary, ultrasonic for temperature and pressure of the measured medium (natural gas and APG), the compressibility coefficient of the measured medium (natural gas) in accordance with GOST R 8.740-2011 and PR 50.2.019-2006 for volumetric flow converters.

Calculation of the physical properties of natural gas is carried out by IVK in accordance with GOST 30319.096, GOST 30319.1-96, GOST 30319.2-96 and GOST 30319.3-96. The compressibility coefficient of natural gas is calculated by IVK using any of the four methods presented in GOST 30319.2-96: modified method NX19 mod., modified equation of state GERG-91 mod., equation of state VNITs SMV, equation of state AGA8-92 DC.

Calculation of the physical properties of APG is carried out by IVK in accordance with GSSSD MR 113-03. Calculation of the calorific value, relative density, Wobbe number and energy content of natural gas is carried out by IVK in accordance with GOST 31369-2008 and PR 50.2.019-2006; Determination of the dew point temperature of natural gas from water is carried out by IVK in accordance with GOST R 53763-2009.

IVC calculates mass flow (mass), bringing the volume and density of oil, petroleum products, liquid hydrocarbon media to standard conditions in accordance with GOST R 8.595-2004.

The IVK allows you to keep track of the volumetric flow rate (volume) of natural gas and APG, reduced to standard conditions, the mass flow rate (mass) of oil, petroleum products, liquid hydrocarbon media, single-phase liquids with homogeneous physical properties using no more than three measuring lines for the IVK according to specifications InKS.425210.001, no more than six - for IVK according to TU InKS.425210.002 and no more than twelve - for IVK according to TU InKS.425210.003.

IVK ABAC+ according to specifications

InKS.425210.001 and IVK ABAC+ according to TU InKS.425210.003

InKS.425210.002

The software ensures the implementation of the functions of the IVK. The IVK software is divided into metrologically significant and metrologically insignificant parts. The first stores all procedures, functions and subroutines that perform registration, processing, storage, control, indication and transmission of the results of measurements and calculations of the IVK; as well as software protection and identification. The second stores all libraries, procedures and routines for interacting with operating system and peripheral devices (not related to measurements and calculations of the IVK).

Protection of IVK software from unintentional and intentional changes and ensuring its compliance with the approved type is carried out by separating, identifying and protecting against unauthorized access to the software.

Table 1

Identification of the IVK software is carried out by displaying the structure of identification data on the display. The part of this structure related to the identification of a metrologically significant part of the IVK software is a hash sum (checksum) over the significant parts.

IVK software is protected from unauthorized access, changes in algorithms and set parameters by entering a login and password, maintaining a read-only event log. Access to the metrologically significant part of the IVK software is closed to the user. When changing the set parameters (initial data) in the IVK software, confirmation of changes is provided, changes are checked for compliance with the requirements of the implemented algorithms, while messages about events (changes) are recorded in the event log, which is read-only. Data containing measurement results are protected from any distortion by coding. IVC software has security level C.

Name
Name	InKS.425210.	InKS.425210.	InKS.425210.
Input ranges
voltage, V	from 0 to 5 from 1 to 5	from 0 to 5 from 1 to 5 from 0 to 10
DC current, mA		from 0 to 5 from 0 to 20 from 4 to 20
pulse, Hz	from 0 to 12000
frequency, Hz	from 0 to 12000
thermoelectric converters according to GOST 6616-94 with a nominal static characteristic (NSC): With output signal, mV		from minus 200 to 760 from minus 230 to 1370 from minus 240 to 1000 from minus 240 to 400 ± 80
Resistance thermometers according to GOST 66512009 (type Pt100): Temperature, °C Resistance, Ohm		from minus 200 to 800 from 0 to 500
Output ranges
voltage, V		from 0 to 10 from 0 to 5 from 1 to 5 from 2 to 10
DC current, mA		from 0 to 5 from 4 to 20 from 0 to 20
Limits of the permissible reduced error of the IVK when converting the input analog signal into the value of the measured physical quantity
voltage: Main, % Additional, %/°С Under operating conditions, %
DC power: Main, % Additional, %/°С Under operating conditions, %

Name
Name	InKS.425210.	InKS.425210.	InKS.425210.
thermoelectric converter according to GOST 6616 with nominal static characteristic (NSC): With output signal ± 80 mV, %
resistance thermometer according to GOST R 8.625 (type Pt100): Temperature, % Resistance, %
Limits of permissible error of the IVK when converting the input frequency signal into the value of the measured physical quantity
absolute, Hz absolute, units of the smallest size. relative: Main, % Additional, %/°С
Limits of the permissible reduced error of the IVK when converting the value of a physical quantity into an output analog signal
voltage: Main, % Additional, %/°С Under operating conditions, %
DC power Main, % Additional, %/°С Under operating conditions, %
Limits of permissible absolute error of the IVK when converting the input pulse signal into the value of the measured physical quantity, number of pulses per 10,000 pulses
Limits of permissible relative error of the IVK when measuring a time interval, %
Limits of permissible relative error of the IVK:
when calculating the volumetric flow rate (volume) of natural gas and APG, reduced to standard conditions, %
when bringing the volumetric flow rate (volume) of natural gas and APG under operating conditions to standard conditions, %
when calculating the mass flow (mass) of oil and petroleum products, liquid hydrocarbon media, single-phase liquids with homogeneous physical properties, %

Name
	InKS.425210.	InKS.425210.	InKS.425210.
terms of Use
ambient temperature, °C		from minus 40 to 60	from minus 40 to 70
normal ambient temperature, °C
relative humidity, %	from 5 to 95 without condensation
atmospheric pressure, kPa	from 84 to 106.7
Supply voltage (DC source), V
Power consumption, W, no more
Overall dimensions, mm, no more
Weight, kg, no more
Mean time between failures, hours, not less
Average service life, years, not less

Notes:

* - error at normal ambient temperature;

** - additional error caused by a change in ambient temperature for every 1°C from normal (for IVK according to TU InKS.425210.001 and InKS.425210.003);

*** - error at ambient temperature different from normal (for IVK according to TU InKS.425210.002).

Type approval mark

applied to the IVK body using silk-screen printing and title page passports by printing.

Completeness

Table 3

Name	Quantity
Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”.
Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Manual.
Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Passport.
Instructions. GSI. Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Verification method.
Configuration software“Interface of the complex for measuring and computing flow and quantity of liquids and gases “ABAC+”.

Verification

carried out according to the document MP 17-30138-2012 “Instructions. GSI. Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Verification methodology”, approved by the GCI SI LLC “STP” on September 18, 2012.

List of basic verification tools (standards):

Multifunctional calibrator MC5-R.

Information about measurement methods

The measurement procedure is described in the operating manual.

Regulatory documents establishing requirements for IVK

1. GOST 2939-63 “Gases. Conditions for determining volume."

2. GOST 30319.0-96 “Natural gas. Methods for calculating physical properties. General provisions".

3. GOST 30319.1-96 “Natural gas. Methods for calculating physical properties. Determination of the physical properties of natural gas, its components and products of its processing.”

4. GOST 30319.2-96 “Natural gas. Methods for calculating physical properties. Determination of the compressibility coefficient."

5. GOST 30319.3-96 “Natural gas. Methods for calculating physical properties. Determination of physical properties using the equation of state.”

6. GOST 31369-2008 “Natural gas. Calculation of calorific value, density, relative density and Wobbe number based on component composition.”

7. GOST 6616-94 “Thermoelectric converters. General technical conditions".

8. GOST 6651-2009 “GSI. Resistance thermal converters made of platinum, copper and nickel. General technical requirements and test methods".

9. GOST 8.586.1-2005 “GSI. Measurement of flow and quantity of liquids and gases using standard restriction devices. The principle of the measurement method and general requirements."

10. GOST 8.586.2-2005 “GSI. Measurement of flow and quantity of liquids and gases using standard restriction devices. Diaphragms. Technical requirements".

11. GOST 8.586.4-2005 “GSI. Measurement of flow and quantity of liquids and gases using standard restriction devices. Venturi tubes. Technical requirements".

12. GOST 8.586.5-2005 “GSI. Measurement of flow and quantity of liquids and gases using standard restriction devices. Methodology for performing measurements."

13. GOST R 8.585-2001 “GSI. Thermocouples. Nominal static characteristics of transformation".

14. GOST R 8.615-2005 “GSI. Measuring the amount of oil and petroleum gas extracted from the subsurface. General metrological and technical requirements".

15. GOST R 8.733-2011 “GSI. Systems for measuring the quantity and parameters of free petroleum gas. General metrological and technical requirements".

16. GOST R 8.740-2011 “GSI. Gas consumption and quantity. Measurement technique using turbine, rotary and vortex flowmeters and counters.”

17. GOST R 8.595-2004 “GSI. Mass of oil and petroleum products. General requirements for measurement techniques."

18. GOST R 53763-2009 “Natural flammable gases. Determination of dew point temperature from water."

19. GSSSD MR 113-03 “GSSSD Methodology. Determination of density, compressibility factor, adiabatic index and dynamic viscosity coefficient of wet petroleum gas in the temperature range 263...500 K at pressures up to 15 MPa."

20. PR 50.2.019-2006 “GSOEI. Methodology for performing measurements using turbine, rotary and vortex counters.”

22. InKS.425210.001 TU “Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Technical conditions".

23. InKS.425210.002 TU “Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Technical specifications"

24. InKS.425210.003 TU “Complexes for measuring and computing the flow and quantity of liquids and gases “ABAC+”. Technical conditions".

Carrying out government accounting operations, trade and commodity exchange operations.

Computer tips for novice users

The abacus is the oldest calculating instrument. See what "Abacus" is in other dictionaries Abacus handheld calculator

Abacus