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Authors: Christopher Knight,Alan Butler

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It was known by the time of Picard and Römer that gravity did not act equally on all parts of the planet because the Earth is an oblique spheroid rather than a perfect sphere. The astronomers seem to have favoured basing the new linear unit on the seconds pendulum measured at Paris, though Newton’s 45-degree latitude was also considered, as was a seconds pendulum set for the equator.

Despite the debates about the best way forward nothing further seems to have happened regarding the new French system until the 14th July 1789 when the Bastille was stormed, igniting a revolution that was to change that country for ever. The problem of the disparate weights and measures had been tolerated because there were always greater problems to be confronted but after the revolution, with the beginning of a completely new regime, the populace could be persuaded to change everything it had known for generations in terms of weights and measures.

Only a year after the start of the French Revolution, in 1790, the Constituent Assembly of France was on the receiving end of a report from Charles-Maurice Talleyrand Perigord, Bishop of Autun. Talleyrand was a larger-than-life character and certainly no scientist, yet he resurrected the proposition of a new system of weights and measures, based on a standard to be derived from the length of a pendulum at 45 degrees north (45 degrees being exactly halfway between the equator and the poles.)

The reason for Talleyrand’s interference in such matters probably stemmed from his success as a diplomat. At almost exactly the same time as revolutionary France was thinking in terms of a new measuring system, across the Channel in England scientific minds were also turning in the same direction. Talleyrand desperately wanted to achieve a lasting peace between France and Britain, an heroic effort that was doomed to failure. It is also known that he had friends within the British Royal Society as well as in London-based masonic lodges. He went so far as to suggest collaboration between the Académie des Sciences in Paris and the Royal Society of London in order to try and establish the length of a seconds pendulum to the very highest level of accuracy. At the time, Louis XVI was still clinging to the French throne and the Assembly passed a decree asking Louis to write to the British king, George III. The letter was to suggest that:

‘Parliament should meet with the National Assembly for the fixation of national units of weights and measures so that commissioners of the French Academy could meet with an equal number from the Royal Society in the most convenient place to determine at 45° latitude or at any other preferred latitude the length of the
[seconds]
pendulum and produce an invariable model for all weights and measures.’

It is unlikely that the request of the French Assembly was ever acted upon by Louis because no trace of such a letter exists in British archives. Louis was a worried man and doubtless thought that to force an entirely new measuring system on a country already so troubled might be the last straw. Almost in tandem with the suggested letter to Britain, the Assembly set up a commission to look into a new metric system. It was composed of five brilliant scientists and mathematicians. These men were Laplace, Lagrange, Monge, Borda and Condorcet. The report produced by this commission was presented to the French Academy on 19th March 1791.

It was at this time that the concept of the seconds pendulum was more or less abandoned as the preferred unit for the new linear measurement because it was reluctantly decided that no timepiece existed that could accurately measure one second of time. The commission was left with no option but to return to Father Mouton’s original suggestion that the new unit should be derived from an extremely accurate assessment of the distance between the North Pole and the equator and to make the new linear unit a subdivision of this distance. Despite this decision, the seconds pendulum was far from forgotten. One of the commission’s recommendations was:

‘To make observations at latitude 45° for determining the number of vibrations in a day, and in a vacuum at sea level, of a simple pendulum equal in length when at the temperature of melting ice, to the ten-millionth part of the meridian quadrant with a view to the possibility of restoring the length of the new standard unit, at any future time, by pendulum observation.’

The subdivision of polar circumference

So the seconds pendulum was retained as a safety backup should the new unit of length ever be lost. This indicates that the French team had chosen a subdivision of polar circumference that was as close to the seconds pendulum as they could achieve using a very round number. They settled on one ten-millionth part of the meridian quadrant – which meant that the new unit was one forty-millionth part the of the polar circumference of the Earth. This unit was eventually to be named the ‘metre’. It is clear from the wording of the report presented by the commission that it was aware of the very slight difference in length between the established seconds pendulum and the proposed linear unit.

The seconds pendulum was still not forgotten, even in the later stages of the drive towards the metric system. The report of the fieldwork was dated 30th April 1799. Among its observations as reported by R. D. Connor was this:

‘The length of a seconds pendulum at Paris at 0° C in vacuum at sea level is 0.99385 metres’. (
This last is equivalent to a period of a pendulum of length 1m being 2.00618 seconds at Paris, latitude 48° 52.
)

The seconds pendulum corrected metre came into official existence on 10th December 1799. However, the metric system in its entirety did not become obligatory until 1st January 1840. It is surprising how many sources still quote the Emperor Napoleon as having instigated metrication, but nothing could be further from the truth. Napoleon disliked the entire metric system and he is reported to have said:

‘I can understand
of an inch but not
of a metre!’

Having set the length for the metre the commission identified their longest unit of length as the kilometre at 1,000 metres, and the shortest was the millimetre at
of the metre. In between they added the centimetre, being ten times larger than a millimetre and 100 times smaller than the metre. Next they turned their attention to the basic units of capacity and mass, which they derived in the simplest manner possible. They took a length of one tenth of a metre (ten centimetres) and used it to dictate the sides of a cube. This cube was then filled with distilled water (under very strict temperature and pressure requirements) and the volume occupied by the water was called a litre, while its weight was designated the kilogram.

The ‘metric’ system

Suddenly the metric system had been resurrected. Because the inspiration for the metre had originally been the seconds pendulum and because the French scientists had followed the same logic as their Sumerian forebears, the double-kush was back under a new name!

It appears that none of these French scientists questioned what a second of time actually was or where it had come from, except that it represented
part of a mean solar day. They knew it had originated from ancient Mesopotamia but the Sumerian culture had not been identified at the time. It was much later that archaeological digs in the sands of Mesopotamia began to turn up scores of cuneiform tablets and slowly some people began to notice the amazing similarities between the Sumerian measurement system and the metric system. Professor Stecchini has shown how there was distinct embarrassment in academic circles at the convergence of a new and scientifically-based system with that of the most ancient documented culture on the planet.

There was once a great deal of controversy regarding Mesopotamian linear lengths, weights and measures and their ‘fit’ with the metric system. It has now become standard academic form to deny that either the Sumerians or the Babylonians could, or would have wanted to, create cubes or one-tenth the double-kush, in order to produce a fullyintegrated measuring system.

The facts are self-evident and the reason why the metric system is so similar to the Mesopotamian model is no puzzle. The metre was chosen on the grounds that it was a provable geophysical unit, adopted because it so closely approximated the seconds pendulum, which itself was captivating scientists from Newton’s time onwards. Indeed, when the Imperial Weights and Measures Acts of the 19th century were passed in Britain, instructions were given that these too were to be checked against the seconds pendulum if the created units were ever lost or damaged.

The French team that did not trust their late 18th-century timepieces would no doubt be amazed to learn that one day their metre would be defined as the distance travelled by light in a vacuum in a time interval of
second. We now have the science to measure such tiny events but it remains a fact that the true seconds pendulum lies behind this definition. Bearing in mind that a pendulum length changes somewhat according to the latitude at which it is checked, the astronomer-priests of old made an extremely good job not only of defining the second of time, but also of showing what it meant in linear terms. The double-kush pendulum ticks away seconds with an error of only one five-thousandth of a second, an error that to anyone except the most fastidious Grand Prix racing driver means nothing!

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