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"Man is the measure of all things" – Protagoras (Greek Sophist, 485-411 B.C.)

## History of measurement

### The beginnings

Until the 18th century there was no unified measurement system. In spite of the attempts of Charlemagne and many kings after him, aiming to reduce the number of existing measurements, France was one of the most inventive and most chaotic countries in this area. In 1795 there were over seven hundred different "unit of measurement" in France.

Many were simply borrowed from human morphology. Their names often referred to parts of the body: the digit, the hand, the foot, the cubit, the pace, the fathom or toise, whose Latin name tensa - from brachia - the distance across a man's outstretched arms. These units of measure were not fixed: they varied from one town to another, from one occupation to another, as well on the type of object to be measured. Floor area was measured in square feet, for example, and carpet area in square ells.

Volume and length measurements were totally unrelated. For each unit of measure, the multiples and sub-multiples were fixed randomly, making calculations extremely laborious. To understand the difficulties resulting from such systems, we must consider the modern way of measuring time, a survivor of the old system of subdivisions. In this system, all calculations involve prior conversion.

A source of error and fraud in commercial transactions, this situation also put a check on the development of science. With the expansion of industry and trade, there was an increasing need for harmonisation.

### A universal measure : the metre

Politicians and scientists did their best to remedy this situation. Their intention was to produce an invariable measure by comparison with a standard borrowed from a natural phenomenon, the universal standard that Condorcet had dreamed of as far back as 1775, which would not be based on any national vanity and which could be used by all foreign nations.

The climate of reform which followed the revolution precipitated the choice of a standard. The lists of grievances claimed this universal measure to do away with the arbitrary seigneurial measurements.

On 16 February 1791, following a proposal by the Chevalier JC de Borda - the inventor of the pendulum and the "Borda repeating circle" - a commission was set up to bring in a uniform system of measurement. The commission, composed of Borda, Condorcet, Laplace, Lagrange and Monge was faced with a choice between three possible references: the length of a simple pendulum beating at a rate of one second at a latitude of 45°, the length of one quarter of the equator or, lastly, the distance from the North pole to the equator, a quarter meridian.

Since the pendulum beating at a rate of one second involved time and varied at different points on the globe (the length of the pendulum would have had to be corrected according to the acceleration due to gravity), the quarter meridian therefore appeared as the simplest solution to calculate and the most universal.

Introduced on 26 March 1791, the metre was defined as being equal to the ten millionth part of one quarter of the terrestrial meridian*. The metre materialised the idea of a "unit which in its determination was neither arbitrary nor related to any particular nation on the globe".

The exact length of the meridian still had to be found, however, which turned out to be a real adventure for the geodesists in charge of the mission, Pierre-François MECHAIN (1744-1804) and Jean-Baptiste DELAMBRE (1747-1822).

These two men alone were to carry out the triangulation work which would forever link their names to this new measurement of the meridian. Lasting almost seven years, the work took them from Dunkirk to Barcelona.

Using the triangulation system, the 18th century scientists managed to determine the exact length of a quarter meridian, equivalent to ten million metres.

See the Meridian of Delambre and Méchain between Dunkirk and Barcelona

* *At the time of the definition as it was defined and written, the definition of the meridian was considered to be that of astronomy: a meridian was a complete circle. So for the earth around 40 000 km, the 10 millionth of a quarter of the meridian corresponds to 1 m. Not to be confused with the definition of the geographical meridian which was established after the first definition of the metre and which is defined as a semicircle, therefore 20 000 km for the earth.*

### The decimal metric system, a revolutionary invention

Once the base unit of measure had been determined, all that had to be done now was "just" to establish all the other resulting units of measurement: the square metre and the cubic metre, the litre, the gram, etc.

The decimal metric system was introduced on 18 germinal year III (7 April 1795) by the law "on weights and measures". This caused a major upheaval in everyday life. Decimalisation also brought a real revolution in the calculation of areas and volumes. Conversion from a multiple to a sub-multiple unit in area, and vice versa, simply consists of moving the decimal point two places, or three places for volume.

To determine the unit of mass, the commission preferred water to any other body such as mercury or gold, due to the "ease of obtaining water and distilling it…". The kilogram was defined as being equal to the mass of a cubic decimetre of water at a given temperature.

For everyday use, the first standards of the metre and the kilogram were manufactured in 1799 and deposited in the Archives of the Republic, dedicated to "all men and all times".

Both simple and universal, the decimal metric system started to spread outside France. The development of railways, the growth of industry and the increasing number of exchanges all required accurate units of measure. Adopted at the start of the 19th century in several Italian provinces, the metric system became compulsory in the Netherlands from 1816 and was chosen by Spain in 1849.

In France, after a few contradictory measures, the decimal metric system was exclusively adopted with the law of 4 July 1837, under the Guizot ministry. It had taken almost half a century to adopt a system which had been created in the enthusiasm springing from the Revolution.

After 1860, adhesion increased particularly in the Latin American countries which joined the ranks of the many countries taking up the metric system. Nevertheless, these countries were dependent on France whenever exact copies of the metre and kilogram standards were required. This subordination to France, together with the lack of uniformity in making copies, was likely to jeopardise the desired unification. To overcome these difficulties, **the Bureau International des Poids et Mesures** (B.I.P.M.) was founded in 1875, during the diplomatic conference of the metre which led, on 20 May 1875 to the signature of the treaty known as the Metre Convention by the plenipotentiaries of 17 States.

The BIPM's initial mission was to set up the Metric System throughout the world by constructing and maintaining new prototypes of the metre and the kilogram, comparing the national standards with these prototypes and perfecting the measurement methods in order to promote metrology in all fields.

The BIPM progressively focused on the study of metrological problems and physical constants which govern the precision of measurements when defining units (e.g. thermometry), then, to accompany industrial development, its scope extended to new fields : **the electrical units** (1937), **the photometric units** (1937) or **the ionising radiation measurement standards** (1960).

### From the metric system to the International System of Units (SI)

The International System of Units (SI), successor of the metric system, was officially founded in 1960 following a resolution made in the 11th *Conférence Générale des Poids et Mesures* (CGPM). All units of measurement can be reduced to a small number of fundamental standards with this system, which dedicates the necessary care to continuously improve their definition. This represents one of the missions of the national metrology laboratories.

The definitions of the SI base units have changed over the years, to meet the requirements of certain users who demanded greater precision.

The measurement methods and the standards themselves undergo constant progress and are permanently renewed; the greater the precision in the definition of the units of measure, the finer the values measured can be. The work on fundamental standards, carried out in particular by the national metrology laboratories and the Bureau International des Poids et Mesures, will probably never end.

This is reflected in the changing of the definition of the metre, away from a material object.

Although universal, the implementation of the metre unit defined as a proportion of the quarter meridian was clearly difficult to implement. This explains why its standard was first the metre stored in the Archives, the international prototype metre from 1889.

On 14 August 1960, the metre was redefined as being equal to 1 650 763,73 times the wavelength of orange radiation from the krypton 86 atom in vacuum. This definition, based on a physical phenomenon, marked the return to a natural, reproducible standard, permanent and invariable, offering an accuracy nearly fifty times greater than that of the international prototype and a better guarantee of very long term maintenance.

In 1983, following the important work on the speed of light and on atomic clocks, the metre was redefined as "the distance travelled by light in vacuum in 1/299 792 458 of a second".

*pictures extracted from the book *"L'épopée du mètre"* (published by the French Ministry in charge of Industry and Regional Planning)

## The Metre adventure

### The metre, base of the new metric system

On 19 March 1791 the metre, the base of the new metric system, was theoretically defined as being equal to the ten millionth part of one quarter of the terrestrial meridian. Practically, the length of the meridian still had to be set up, however.

In its "report on the choice of units of measurement", the Academy of Science defined the various steps that this work would involve: the length of the meridian would be determined by triangulation, from an arc of nine and a half degrees between Dunkirk and Barcelona.

### Triangulation, a method known since the early 17th century

Already in 1718, Jacques Cassini used this method to measure the meridian between Dunkirk and Collioure. Triangulation consists of marking a route by a network of highly visible landmarks: tower, peak, church spire, etc., these points representing a series of connected triangles. The method involves trigonometric calculations. Knowing all the angles formed by two adjacent triangles and at least one of the lengths in one of these triangles, one can determine the lengths of all sides in both triangles.

### On 13 April 1791, the Academy appointed the members of the commissions who would perform the measurements

The triangulation and determination of the latitudes were to be carried out by Jacques Cassini's son, Legendre and Méchain.

Monge and Meusnier were to measure the bases. In June 1791, Cassini simply visited with Méchain the base of Villejuif at Juvisy (the obelisk is currently known as the *Pyramide de Juvisy*). Although Cassini expected to be able to use this old base, which had already been used by his father in 1739, his grandfather in 1701, and Abbot Picard in 1670 when they carried out their triangulation calculations ; he was unable to do so. Cassini then stayed in Paris to help Borda. Monge and Legendre did very little in fact. Meusnier left to join the Rhine army and was killed in 1793. Delambre, who had just joined the Academy of Science was then nominated to replace them.

### A precision instrument: The Borda circle

Measurement of the meridian arc involved the use of precision instruments and was partly justified by improvements to these instruments. Of much greater precision, these measurements would replace the previous ones taken fifty years before.

To determine the angles, our two geodesists were going to use the new Borda repeating circle. Using this innovation, angles could be measured to the nearest second, whereas with the quadrants used so far it had only been possible to obtain accuracy to the nearest 15 seconds. The ground measurements, in *Toise du Pérou* units, were to be made with copper-platinum bimetal rulers. Obviously, any other unit would have been suitable, since once the length of the quarter of the meridian* is determined, dividing it by 10 000 000 would give the length of a metre. In this case, the length of the first metre was therefore expressed in *Toise du Pérou* units; in 1747, La Contamine had brought back this measurement unit from his expedition to the equator, but it only became a national standard on 16 May 1766 after a royal declaration.

* *At the time of the definition as it was defined and written, the definition of the meridian was considered to be that of astronomy: a meridian was a complete circle. So for the earth around 40 000 km, the 10 millionth of a quarter of the meridian corresponds to 1 m. Not to be confused with the definition of the geographical meridian which was established after the first definition of the metre and which is defined as a semicircle, therefore 20 000 km for the Earth.*

### Two teams for measuring the meridian arc

Delambre's team included the Frenchmen Lalande and Bellet; Tranchot and Esteveny accompanied Méchain. The Academy of Science distributed the work involved in measurement of the meridian arc as follows: the two upper thirds, from Dunkirk to Rodez, were assigned to Delambre; the last third, from Rodez to Barcelona, was assigned to Méchain. This difference could be explained by the fact that Delambre's route would theoretically follow close to the points of the former triangulation, whereas Méchain would explore territory where no geodesic measurements had yet been made.

In practice, the earlier triangulation landmarks turned out to be unusable: during the turmoil of the revolution, some spires had disappeared or were about to collapse. Peak after peak, Delambre discovered that it was impossible to use Cassini's previous landmarks: the old spires had been rebuilt differently after being burnt down.

### Mark out the meridian arc: a very difficult enterprise

More than one hundred triangles were required to mark out the meridian arc; our two geodesists were to experience numerous mishaps during their expedition: arrests, temporary revocations, damaged or destroyed geodesic equipment. The marker signals they used for their observations aroused the distrust of the population; the material attached at the end of their signals was white, the colour of royalty, and therefore a counter-revolutionary colour. In spite of their passes, passports and other authorisations, our two scientists were still not safe from arrest, since the authorities which had issued these documents disappeared, making them outlaws. For instance, following the abolition of the Academies (in 1793), Delambre found that he had been excluded from the temporary commission of weights and measures (in 1794) and therefore prohibited from continuing his work, until June 1795. Méchain also experienced numerous setbacks.

Landmarks to establish, mountains to cross, not forgetting the historical events :

War broke out on 7 March 1793 between France and Spain, where some of his measurements had to be made. From 1793 to 1795 therefore, the Terror regime was to delay his triangulation calculations. At the same time, the metre was temporarily fixed by the law of 1 August 1793 according to the results of measuring the French meridian, published by Lacaille in the 1758 *Mémoires de l'Académie*. Moreover, the decimal subdivisions of the metre were to be the decimetre, the centimetre and the millimetre. This temporary standard metre did not correspond to the work carried out by Méchain and Delambre, but to the results of Cassini's earlier triangulation.

### 1799, a new platinum metre standard

In 1795, with the improvement of the political situation, the triangulation work was able to resume. It continued for a further three years, before the length of the quarter of the meridian could be accurately determined and a new platinum metre standard dedicated to "all times and all men " was deposited in 1799, in the archives of the republic.

**pictures extracted from the book "L'épopée du mètre" (published by the French Ministry in charge of Industry and Regional Planning)*

## Interest of metrology

Accessing knowledge often involves a number and the measurement which produces this number is not possible without units, standards and measurement instruments. This is the role of metrology, which is not only an individual discipline of the physical sciences but the base of our daily activities. Like Molière's Monsieur Jourdain who spoke prose without knowing it, we all use metrology without realising. Mr. Christian Pierret presented metrology and its various applications during a communication in a Cabinet meeting on 2 December 1998, entitled *"new ambitions for metrology at the service of competitiveness "*. The above extract reminds us that measurement is a scientific, economic and social necessity :

### Measurement increases knowledge

In fundamental research, metrology is present at every step. It is used to design the conditions for observation of a phenomenon, to build and qualify the instruments required for its observation and to determine whether the results obtained are significant. Rock dating, characterisation of gravitational fields, determination of certain chemical or physical constants all involve measurement activities.

### Measurement protects people

- Dosing of drugs or measurement of radiation in radiotherapy, food safety and many others require measuring operations that are vitally important activities for public health. The reliability of measurement instruments in operating theatres or intensive care units is critical.
- The application of labour law involves a system to monitor the hours worked, the noise and lighting levels in the workplace, measurements of ambient atmospheres (mercury vapours, fibres and particles), etc.
- Road safety implies restrictions on speed, alcohol and vehicle braking efficiency as well as measurements to ensure that they are respected.
- Protection of the environment implies statutory requirements on nuisances and the quality of air and water, and involves measurements.

### Measurement governs transactions

- All transactions made by individuals and companies involve measurements: dosing of foodstuffs, metering subscriber gas consumption or cross-border counting, petrol at the pump or on the pipeline, retail or bulk weighing, etc.
- Measurement is an essential factor in the relations between customers and subcontractors. In the absence of reliable measurements, it is impossible to guarantee that the subcontracted parts will match the customer's requirements.

### Measurement enables our industries to be innovating and competitive

- Competitiveness involves quality, which is the ability of a product to meet consumer and user requirements, and which involves all types of measurement in order to study and satisfy customer expectations (organoleptic measurement in agribusiness, performance measurements for industrial products, etc.). Quality can be demonstrated to customers through certification, itself based on measurements.
- Competitiveness assumes that industry measures and precisely controls the production volumes and the performance of the production tool, and that it minimises the costs of rejects and rework operations.

The description of these different applications leads us to make a distinction between fundamental and legal metrology. On the one hand, fundamental metrology is concerned with the creation, maintenance, improvement and transfer of metrological references. This activity is carried out by the national metrology laboratories, prior to any technological application. It is therefore important to remain attentive to the ongoing changes in the fields of industrial processes and applications, especially health and environment related applications. On the other hand, legal metrology represents one of the State's civic missions which consists of guaranteeing the reliability and stability of measurements for commercial or statutory use and preventing fraud. Metrology then becomes a means of economic regulation.