Metric system

The metric system is a decimalised system of measurement based on the metre and the gram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Over the last two centuries, different variants have been considered the metric system. Since the 1960s the International System of Units (SI) ("Système International d'Unités" in French, hence "SI") is the internationally recognised standard metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.

One goal of the metric system is to have a single unit for any physical quantity. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometres), and so on. There is no profusion of different units with different conversion factors, such as inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, leagues, etc. Multiples and submultiples are related to the fundamental unit by factors of powers of ten, so that one can convert by simply moving the decimal place: 1.234 metres is 1234 millimetres, 0.001234 kilometres, etc. The use of fractions, such as 2/5 of a metre, is not prohibited, but uncommon.

Time, on the other hand, has not been metricated in everyday use: years, months, weeks, days, hours, minutes, and seconds, with non-decimal conversion factors, are used. The second and its submultiples, (e.g. microsecond), are used in scientific work, but the traditional units of time are more often used than decimal multiples of a second. The original metric system was intended to be used with the units of time of the French Republican Calendar, but these fell into disuse along with the calendar.

The metric system was first introduced in late 18th century France by the chemist Lavoisier to replace the disparate systems of measures then in use with a unified, natural and universal system. In the early metric system there were several fundamental or base units, the grad or grade for angles, the metre for length, the gram for mass and the litre for capacity. These were derived from each other via the properties of natural objects, mainly the Earth and water: 1 metre was originally defined as 1/40,000,000th of the polar circumference of the Earth, and 1 litre of water weighs 1 kg and measures 1 dm³. Other units were derived from this, such as the Celsius temperature scale, where water freezes at 0 °C and boils at 100 °C at standard pressure.

Base units and prefixes

The metre was originally defined as 1/40,000,000th of the polar circumference of the Earth, then as the length of a particular bar of platinum-iridium alloy; then in terms of the wavelength of light emitted by a specified atomic transition; and now is defined as the distance travelled by light in an absolute vacuum during 1/299,792,458 of a second. The gram, originally one millionth of the mass of a cubic metre of water, is currently defined by one thousandth of the mass of a specific object that is kept in a vault in France; however there are efforts underway to redefine it in terms of physical quantities that could be reproduced in any laboratory with suitable equipment. The second, originally one 86400th of the mean solar day and now defined by atomic clocks, is usually chosen as the base unit of time. Varying choices have been made for the third base unit, the one that is needed to incorporate the field of electromagnetics; As of 2006 this is the ampere, being the base unit of electrical current. Other quantities are derived from the base units; for example, the basic unit of speed is metres per second. As each new definition is introduced, it is designed to match the previous definition as precisely as possible, so these changes of definition have not affected most practical applications. (See SI and individual unit articles for full definitions.)

The names of multiples and submultiples are formed with prefixes. They include deca- (ten), hecto- (hundred), kilo- (thousand), mega- (million), and giga- (billion); deci- (tenth), centi- (hundredth), milli- (thousandth), micro- (millionth), and nano- (billionth). The most commonly used prefixes for multiples depend on the application and sometimes tradition. For example, long distances are stated in thousands of kilometres, not megametres.

Most everyday users of the metric system measure temperature in degrees Celsius, though the SI unit is the kelvin, a scale whose units have the same "size", but which starts at absolute zero. Zero degrees Celsius equals 273.15 kelvins (the word "degree" is no longer to be used with kelvins).

Angular measurements have been decimalised, but the older non-decimal units of angle are far more widely used. The decimal unit, which is not part of SI, is the gon or grad, equal to one hundredth of a right angle. Subunits are named, rather than prefixed: the gon is divided into 100 decimal minutes, each of 100 decimal seconds. The traditional system, originally Babylonian, has 360 degrees in a circle, 60 minutes of arc in a degree, and 60 seconds of arc in a minute (the clarifier "of arc" is dropped if it is clear from the context that we are not speaking of minutes and seconds of time). Sometimes angles are given as decimal degrees, e.g., 26.4586 degrees, or in other units such as radians or angular mils.

History

The proliferation of disparate measurement systems was one of the most frequent causes of disputes amongst merchants and between citizens and tax collectors. A unified country with a single currency and a countrywide market, as most European countries were becoming by the end of the 18th century, had a very strong economic incentive and was in a position to break with this situation and standardise on a measuring system. The inconsistency problem was not one of different units but one of differing sized units so instead of simply standardizing size of the existing units, the leaders of the French revolutionary governments decided that a completely new system should be adopted.

The first official adoption of such a system occurred in France in 1791 after the French Revolution of 1789. The creators of this metric system tried to choose units that were logical and practical. The revolution gave an opportunity for drastic change with an official ideology of "pure reason". It was proposed as a considerable improvement over the inconsistent collection of customary units that existed before.

The adoption of the metric system in France was slow, but its desirability as an international system was recognised by geodesists and others. Since then a number of variations on the system evolved. Their use spread throughout the world, first to the non-English-speaking countries, and more recently to the English-speaking countries.

The whole system was derived from the properties of natural objects, namely the size of the Earth and the weight of water, and simple relations in between one unit and the other. In order to determine as precisely as possible the size of the Earth, several teams were sent over several years to measure the length of as long a segment of a meridian as feasible. It was decided to measure the meridian spanning Barcelona and Dunkirk which was the longest segment almost fully over land within French territory. It should be noticed that even though, during the many years of the measurement, hostilities broke out between France and Spain, the development of such a standard was considered of such value that Spanish troops escorted the French team while in Spanish territory to ensure their safety.

The whole process ended in the proclamation on June 22, 1799 of the metric system with the storage in the Archives of the Republic of the physical embodiments of the standard, the prototype metre and the prototype kilogram, both made in a platinum alloy, witnessed by representatives of the French and several foreign governments and most important natural philosophers of the time.

In revolutionary France the system was not particularly well accepted, and the old units, now illegal, remained in widespread use. On February 12 1812, Napoleon, who had other concerns than enforcement of the system, authorised the usage of Mesures usuelles, traditional French measures redefined on the base of Metric System (toise as 2 metres, livre as 500 grams, etc.), and finally in 1816 a law made these Mesures usuelles standards (this law was cancelled in 1825 and the metric system reinstated). It was also reinstated in 1820 by a somewhat unlikely person, King William I of the (United) Netherlands. Although he was generally considered more conservative, he was desperate to bring at least some form of unity to his rather disunited kingdom. His attempts were vain in that Belgium claimed its independence from the Netherlands, but the metric system survived and began a slow but steady conquest of the world. By the 1960s, the majority of nations were on the metric system and most that were not had started programs to fully convert to the metric system. As of 2005 only three countries, the United States, Liberia, and Myanmar (Burma) had not completed the changeover.

Later improvements in the measurement of both the size of the Earth and the properties of water revealed discrepancies between the metric standards and their originally intended values. The Industrial Revolution was well under way and the standardisation of mechanical parts, mainly bolts and nuts, was of great importance and they relied on precise measurements. Though these discrepancies would be mostly hidden in the manufacturing tolerances of those days, changing the prototypes to conform to the new and more precise measurements would have been impractical particularly since new and improved instruments would continually change them.

It was decided to break the linkage between the prototypes and the natural properties they were derived from. The prototypes then became the basis of the system. The use of prototypes, however, is problematic for a number of reasons. There is the potential for loss, damage or destruction. There is also the problem of variance of the standard with the changes that any artefact can be expected to go through, though they be slight. Also whilst there may be copies, there must be only one official prototype which cannot be universally accessible.

The metre had been defined in terms of such a prototype and remained so until in 1960. At that time, the metre was defined as a certain number of wavelengths of a particular frequency of light emitted by a certain element. Since 1983 the metre has been defined as the distance light travels in a given fraction of a second in vacuum. Thus the definition of the metre ultimately regained a linkage with a natural property, this time a property thought immutable in our universe and truly universal. The kilogram is now the only base unit still defined in terms of a prototype. Since 1899, the kilogram has been formally anchored to a single platinum-iridium cylinder in Sèvres, France.

On the May 20 1875 an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:

Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
Bureau international des poids et mesures (BIPM), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.

The SI system is used universally for all scientific purposes. It has been adopted for everyday life by most nations through a process called metrication. As of 2006, 95% of the world's population live in metricated countries, although non-metric units are still used for some purposes in some countries. The only, and particularly noticeable holdout to full metrication is the United States and, to a lesser degree, the United Kingdom, mainly due to public attachment to the "traditional" units. Most government business is now done fully in metric. However, efforts are underway to convert the public sphere to metric, although significant progress is likely only if the change is required by laws yet to be passed.

Goals

The metric system was designed with several goals in mind.

Neutral and universal

The designers of the metric system meant to make it as neutral as possible so that it could be adopted universally.

When the metric system was being developed, France was introducing the French Republican Calendar which was falling in disuse and was finally abolished due in part to two design faults: dates were counted from the day the French First Republic was proclaimed and the names of the months were related to purely local events, such as Brumaire (Misty), Nivose (Snowy) which did not hold true even within the French territory itself.

Other units were derived from the length of the foot of some ruler and often changed along with succession. The new units should have no dependency to such national, local or temporal circumstances.

Replicatable

The usual way to establish a standard was to make prototypes of the base units and distribute copies. This would make the new standard reliant on the original prototypes which would be in conflict with the previous goal since all countries would have to refer to the one holding the prototypes.

The designers developed definitions of the base units such that any laboratory equipped with proper instruments should be able to make their own models of them. The original base units of the metric system could be derived from the length of a meridian of the Earth and the weight of a certain volume of pure water. They discarded the use of a pendulum since its period or, inversely, the length of the string holding the bob for the same period changes around the Earth. Likewise, they discarded using the circumference of the Earth over the Equator since not all countries have access to the Equator while all countries have access to a section of a meridian.

Decimal multiples

The metric system is decimal, in the sense that all multiples and submultiples of the base units are factors of powers of ten of the unit. Fractions of a unit (e.g. 29/64) are not used formally. The practical benefits of a decimal system are such that it has been used to replace other non-decimal systems outside the metric system of measurements; for example currencies.

The simplicity of decimal prefixes encouraged the adoption of the metric system. Clearly the advantages of decimal prefixes derive from our using base 10 arithmetic, a consequence of our happening to have 10 digits (fingers and thumbs). At most, differences in expressing results are simply a matter of shifting the decimal point or changing an exponent; for example, the speed of light may be expressed as 299,792.458 km/s or 2.99792458×10⁸m/s.

Common prefixes

All derived units would use a common set of prefixes for each multiple. Thus the prefix kilo could be used both for weight (kilogram) or length (kilometre) both indicating a thousand times the base unit. This did not prevent the popular use of names for some derived units such as the tonne which is a megagram while a quintal is accepted as 100 kilograms; both are derived from old customary units and were rounded to metric.

Practical

The base units were chosen to be of similar magnitude to customary units. The metre, being close to a toise (French yard equivalent), became more popular than the failed decimal hour of the Republican Calendar which was 2.4 times the normal hour.

The kilometre was originally defined as the length of an arc spanning a decimal minute of latitude, a similar definition to that of the nautical mile which was the length of an arc of one (non-decimal) minute of latitude.

Coincidental similarities to real-life values

Two important values, when they were expressed in the metric system, turned to be very close to a multiple of 10. The standard gravity on Earth g_n has been defined to be 9.80665 m/s² exactly, which is the value at about 45° north or south of the equator. Accordingly the force exerted on a mass of one kilogram in earth gravity (F = m·a) is about ten newtons (kg-m/s²). This simplified the metrication of many machines such as locomotives, which were simply re-labeled from e.g. "85 tonnes" to "850 kN".

Also, the standard atmospheric pressure, previously expressed in atmospheres, when given in pascals, is 101.325 kPa. Since the difference between 10 atmospheres and 1 MPa is only 1.3%, many devices were simply re-labeled by dividing the scale by ten, e.g. 1 atm was changed to 0.1 MPa.

Metric systems other than the modern (SI)

The original French system

The original French system somewhat continued the tradition of having separate base units for geometrically related dimensions, i.e. metre for lengths, are (100 m²) for areas, stere (1 m³) for dry capacities and litre (1 dm³) for liquid capacities. The hectare, equal to a hundred ares, which is the area of a square 100 metres on a side (about 2.5 acres), is still in use to measure fields.

The base unit of mass is the kilogram. This is the only base unit that has a prefix, for historical reasons. Originally the kilogram was called the "grave", and the "gramme" was an alternative name for a thousandth of a grave. After the French Revolution, the word "grave" carried negative connotations, as a synonym for the title "count". The grave was renamed the kilogram ^*. This also serves as the prototype in the SI. It included only few prefixes from milli, one thousandth to myria ten thousand.

Several national variants existed thereof with aliases for some common subdivisions. In general this entailed a redefinition of other units in use, e.g. 500-gram pounds or 10-kilometre miles. An example of these is mesures usuelles (or metrified English unit though never officially adopted). However it is debatable whether such systems are true metric systems.

Centimetre-gram-second systems

Early on in the history of the metric system various centimetre gram second system of units (CGS) had been in use. These units were particularly convenient in science and technology.

Metre-kilogram-second systems

Later metric systems were based on the metre, kilogram and second (MKS) to improve the value of the units for practical applications. Metre-kilogram-second-coulomb (MKSC) and metre-kilogram-second-ampere (MKSA) systems are extensions of these.

The International System of Units (Système international d'unités or SI) is the current international standard metric system and the system most widely used around the world. It is based on the metre, kilogram, second, ampere, kelvin, candela and mole.

Metre-tonne-second systems

The metre-tonne-second system of units (MTS) was based on the metre, tonne and second. It was invented in France and mostly used in the Soviet Union from 1933 to 1955.

Gravitational systems

Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, TME, mug or metric slug.

Spelling variations

Several nations, notably the United States, use the spellings 'meter', 'liter', etc. instead of 'metre', 'litre', in keeping with standard American English spelling (see also American and British English differences). In addition, the official US spelling for the SI prefix 'deca' is 'deka'.

The US government has approved these spellings for official use. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and its use is declining.

External Links

CBC Digital Archives - For Good Measure: Canada Converts to Metric

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