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Gabriel Mouton

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Gabriel Mouton (1618–1694-09-28) was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy.

His 1670 book, the Observationes diametrorum solis et lunae apparentium, came to form the basis of what was to become the metric system hundred years later. Based on the the measurements of the size of the Earth conducted by Riccioli of Bologna (at 373,000 Roman feet to the degree), Mouton proposed a decimal system of measurement based on the circumference of the Earth, explaining the advantages of a system based on nature. Mouton's proposed virga, was essentially the same as the French "toise".

  • In 1670 Abbe Mouton suggested a primary length standard equal to 1 minute of arc on a great circle of the earth. For this basic length Mouton offered the name milliare. This was to be subdivided by seven sub units with each one to be 1/10 the length of the one preceeding or
  • 1 Milliare = 1 minute of arc = 1.85 km
  • 1 Centuria = .1 minute of arc = 185 m
  • 1 Decuria = .01 minutes of arc = 18.5 m
  • 1 Virga = .001 minutes of arc = 1.85 m
  • 1 Virgula = .0001 minutes of arc = 185 mm
  • 1 Decima = .00001 minute of arc = 18.5 mm
  • 1 Centesima = .000001 minute of arc = 1.85 mm
  • 1 Millesima = .0000001 minute of arc = .185 mm

Mouton apparently noted the decimal factors

  • 1 Milliare = 10 stadia of 6000 pous
  • 1 Centuria = 1 Greek stadion of 600 pous
  • 1 Centuria = 1 Roman Stadium of 625 pes
  • 1 Centuria = 1 English furlong of 625 fote
  • 1 Decuria = 10 Greek orquia = 60 pous
  • 1 Virga = 1 Greek orquia or fathom = 6 pous
  • 1 Virgula = 10 Roman digitus = 2 hands
  • 1 Decima = 1 Roman digitus

inherent in earlier sexigesimal systems

Mouton's work relates time, space and gravity as well as connecting ancient units to the concept by identity. Consequently in 1670 we have a degree of the earth's great circle is 111 km but its also 69.17 statute miles of the newly defined statute mile of 1593 and 365,240 feet of that mile.

Mouton pointed out that a standard seconds pendulum could define its own length. Its period is inversely proportional to the sgrt of the gravitational intensity or gravitational acceleration when the pendulum is swinging.

In Moutons time the second was thought to be a new invention. The division of time into a second or second minute was a result of the work of Galileo Galilei (1564-1642) and his recent (from Mouton's perspective) investigations of gravitational attraction as he found it useful to have such a division to time a ball rolling down a slope.

Mountons investigations now related time, space and gravity.

For practical reasons, Mouton suggested that the actual standard be based on pendulum movement. "At sea level in latitude 45 degrees, halfway between the pole and the equator, the standard acceleration due to gravity is .980621 m/s2 so a pendulum of length .993577 m will complete 1/2 a cycle of swinging to and fro in 1 second. This is called a seconds pendulum. 1867.3 times the seconds pendulums length would define amilliare of length 1.855 3 km. The virga being 1/1000 milliare would be matched by 1.867 3 times the length of the standard sedconds pendulum."

Jean Piccard (1620-82 was on a similar path of investigation so about 1673 both Mouton and Picard measured the length of each others pendulims at Lyons.

Others who played a role were Huygens who in 1673, was a student at the Royal Society in London, and Leibniz who independently made proposals similar to those of Mouton in 1673.

As it happened the French Academy of Sciences weights and measures committee composed of Jean Charles Borda, Joseph Louis Lagrange, M.J.A.N. de Cariat, Marquis de Condorcet, Gaspard Monge also found this work interesting and communicated it to Antoine Lavosier. Also involved were Joseph Louise Lagrange and the two astronomer geodists selected by Borda J.B.J. de Lambre and P.F.A Mechain who surveyed 10 degrees of latitude from the English channel to Spain between 1792 and 1799.

Although both at war with one another when invited by Tallerand to sit on the committee of 1812 that was deciding on the implementation of the metric system both the Americans and British refused to be a part of this "almost impracicticable system" and set in stone their resistance to this French invention.

Within about a century from the development of Mouton's original concept in 1837 the metric system was established in France by Law.

By todays measures, his milliare corresponds directly to the ancient nautical mile, and his virga would by definition have been 1.852 m to 1.855 m which mean that the earliest proposal for the metric system is clearly based on research of older systems by Mouton and others.

Reference

  • Lucas N. H. Bunt Phillip S.Jones Jack D. Bedient 1976 The Historical Roots of Elementary Mathematics Publisher Dover ISBN 0486255638
  • H Arthur Klein 1976 The World of Measurements Simon and Schuster
  • R. A. Cordingley 1951 Norman's Parrallel of the Orders of Architecture Alex Trianti Ltd
  • Jean Gimpel 1976 The Medieval Machine Holt Rheinhart & Winston ISBN 0030146364
  • Lionel Casson 1991 The Ancient Mariners PUP ISBN 06910147879
  • Francis H. Moffitt 1987 Surveying Harper & Row ISBN 0060445548


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