# The Metric SystemUnits, Definitions and History

## The Metric System - Description

The metric system is a system of units for measurement developed 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 weight and the litre for capacity. These were derived from each other via the properties of natural objects, mainly water: 1 litre of water weighs 1 kg and measures 1 cubic decimetre (dm³). Other units were derived from this, such as the Celsius temperature scale, where water freezes as 0°C and boils as 100°C.

Multiples and submultiples of metric units are related by powers of ten; the names for these are formed with prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units. The most commonly used prefixes for values above the base unit are hecto- (hundred), kilo- (thousand) and mega- (million); and the most commonly used for parts of the base value (i.e. below the base value) are deci- (tenth), centi- (hundredth) and milli- (thousandth). Some of the common prefixes are, however, rarely used for some units: the expressions hectometre, megametre and megagram are hardly ever heard, neither are decigram and centigram, while hectogram (often shortened to hecto), megalitre, decimetre and centimetre are commonly used measures in many countries.

As the result of scientific progress, refinements, and different choices of base units, there have been a number of attempts at creating metric systems. The modern metric system (modern meaning post-1960) is now widely used throughout the world and is called theInternational System of Units (SI) ("Système International d'Unités" in French).

## 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 during the French Revolution of 1789 et sqq. 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 22nd, 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 grammes, 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 clearly an exponent of the Reaction, 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, most nations 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 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 fraction of a second in vacuum. Thus the definition of the metre ultimately regained a linkage with a natural property, this time a property 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 20th of May 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:

1. Confèence gènvrale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
2. Comitè 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;
3. 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 has been adopted by nearly all the world's nations through a process called metrication. Today 95% of the world's population live in metricated countries, even though scattered use of some non-metric units may persist in some of these 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 apathy. 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 after more forceful legislation is 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 using 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.

### Any laboratory should be able to replicate them

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

All multiples and submultiples of the base units should be in powers of ten. Neither fractions would be in halves as it is customary in fractions of inches, nor derived units would be related to the base units by multiples other than powers of ten, as is the case with twelve inches making a foot. The practical benefits of a decimal system can be seen in the relatively recent decimalisation of the British and Irish Pound (1971) or the stock prices in the stock exchanges in the United States (2000-2001).

It is worth noticing that the metric system also contains a base unit for angles called gon or grad based on decimal fractions where a right angle is divided in 100 gons, each gon containing 100 minutes, each decimal minute containing 100 seconds. In fact, a kilometre is the length of an arc spanning a decimal minute of a gon of latitude. This is similar to the nautical mile which is the length of a minute of a degree of latitude.

On the other hand, the metric system did not define a decimal unit of time since that was already part of the French Republican Calendar and fell into disuse along with it.

Use of decimal prefixes drove the adaptation of the metric system and have historically been seen as a self-evidently easier method of calculation. However, in the modern computer age, decimal is considered a reflection of biological accident: 10 fingers on two hands. It is no longer seen as the most natural or mathematically fundamental system of arithmetic, that mantle having passed to binary and other powers of 2 such as hexadecimal. Even modernly, one can consider: Man has "two thumbs and eight other fingers". Twice eight equals sixteen. This undermined a core rationale for the metric system's power of 10 based units.

### 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 had to be close to the size of customary units then in use. The metre, being close to a toise (French "yard" equivalent), was expected to be more popular than the failed decimal hour of the Republican Calendar which was 2.4 times the normal hour.

## Metric systems other than the 'modern metric system' (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, the gram, is so small that the platinum prototype was made of the kilogram; this still 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. MKSC, metre-kilogram-second-coulomb systems and MKSA, metre-kilogram-second-ampere systems are extensions of these.

The International System of Units (Système international d'unitès 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, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre'. This is in keeping with standard American English spelling (for example, Americans also use 'center' rather than 'centre,' using the latter only rarely for its stylistic implications). 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 use is declining.