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{{Short description|French abbot and scientist (1618–1694)}}
'''Gabriel Mouton''' (]–]) was a ] abbot and scientist. He was a doctor of theology from ], but was also interested in mathematics and astronomy.
{{Use dmy dates|date=September 2022}}
{{Infobox scientist
| birth_date = 1618
| birth_place =
| death_date = {{death date |1694|09|28|df=yes}} (aged about 76)
| death_place =
| other_names =
| citizenship = <!-- use only when necessary per ] -->
| fields = Mathematics and astronomy
| workplaces =
| patrons =
| education =
| thesis_title = <!--(or | thesis1_title = and | thesis2_title = )-->
| thesis_url = <!--(or | thesis1_url = and | thesis2_url = )-->
| thesis_year = <!--(or | thesis1_year = and | thesis2_year = )-->
| doctoral_advisor = <!--(or | doctoral_advisors = )-->
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = Proposing a natural standard of length based on the circumference of the Earth.
}}
'''Gabriel Mouton''' (1618 &ndash; 28 September 1694) was a French ] and ]. He was a doctor of theology from ], but was also interested in ] and ]. His 1670 book, the ''Observationes diametrorum solis et lunae apparentium'', proposed a natural standard of length based on the circumference of the Earth, divided decimally. It was influential in the adoption of the ] in 1799.


== The milliare ==
His ] book, the ''Observationes diametrorum solis et lunae apparentium'', came to form the basis of what was to become the ] hundred years later. Based on the the measurements of the size of the ] conducted by ] of Bologna (at 373,000 Roman feet to the degree), Mouton proposed a ] 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".


{| class="wikitable floatright"
* 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
|+ '''The system of units'''
|-
! Name !! Multiple of ''virga'' !! Approx. equivalents
|-
| Milliare || 1000 || 1 minute of arc, 2&nbsp;km, 1 nautical mile
|-
| Centuria || 100 || 200 m
|-
| Decuria || 10 || 20 m
|-
| Virga || 1 || 2 m, 1 Parisian ''toise''
|-
| Virgula || 0.1 || 20&nbsp;cm
|-
| Decima || 0.01 || 2&nbsp;cm
|-
| Centesima || 0.001 || 2&nbsp;mm
|-
| Millesima || 0.0001 || 0.2&nbsp;mm
|}


Based on the measurements of the size of the ] conducted by ] of Bologna (at 321,815 Bologna feet to the degree), Mouton proposed a ] system of measurement based on the circumference of the Earth, explaining the advantages of a system based on nature.
* 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


His suggestion was a unit, the ''milliare'', that was defined as a ] along a ], and a system of sub-units, dividing successively by factors of ten into the ''centuria'', ''decuria'', ''virga'', ''virgula'', ''decima'', ''centesima'', and ''millesima''.<ref>{{cite book|url=https://archive.org/details/bub_gb_RnRltZ_INg8C |quote=decuria. |title=Observationes diametrorum solis |publisher=Ex Typographia Matthaei Liberal |access-date=22 February 2016 |last=Mouton |first=Gabriel |year=1670}}</ref> The ''virga'', 1/1000 of a minute of arc, corresponding to 64.4 Bologna inches, or ~2.04 m, was reasonably close to the then current unit of length, the Parisian ''toise'' (~1.95 m) &ndash; a feature which was meant to make acceptance of the new unit easier.
Mouton apparently noted the decimal factors


As a practical implementation, Mouton suggested that the actual standard be based on ] movement, so that a pendulum located in Lyon of length one ''virgula'' (1/10 ''virga'') would change direction 3959.2 times in half an hour. The resulting pendulum would have a length of ~20.54&nbsp;cm. <!-- Using a 45° latitude ] of 9.80665 gives ~20.538 cm. -->
* 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


His ideas attracted interest at the time, and were supported by ] as well as ] in 1673, and also studied at ] in ].{{clarify|date=January 2020}} In 1673, ] independently made proposals similar to those of Mouton.
inherent in earlier sexigesimal systems


It would be over a century later, however, that the ] weights and measures committee suggested the decimal ] that defined the ''Metre'' as, at least initially, a division of the circumference of the Earth. The first official adoption of this system occurred in France in 1791.
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.


By today's measures, his ''milliare'' corresponds directly to a nautical mile, and his ''virga'' would by definition have been 1.852 m.
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.


==See also==
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.
*]
*]


== Notes ==
Mountons investigations now related time, space and gravity.
{{Reflist}}

For practical reasons, Mouton suggested that the actual standard be based on ] 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 ] who in 1673, was a student at the ] in ], and ] 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 ], 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


== References ==
* ]: , 1901, chapter ''Les precurseurs de la reforme des poids et mesures''
* ]: ''Historie de l'astronomie'', Paris 1873


==External links== ==External links==
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* *
*{{MacTutor Biography|id=Mouton}}
*
* *


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Latest revision as of 19:41, 12 October 2023

French abbot and scientist (1618–1694)

Gabriel Mouton
Born1618
Died(1694-09-28)28 September 1694 (aged about 76)
Known forProposing a natural standard of length based on the circumference of the Earth.
Scientific career
FieldsMathematics and astronomy

Gabriel Mouton (1618 – 28 September 1694) 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, proposed a natural standard of length based on the circumference of the Earth, divided decimally. It was influential in the adoption of the metric system in 1799.

The milliare

The system of units
Name Multiple of virga Approx. equivalents
Milliare 1000 1 minute of arc, 2 km, 1 nautical mile
Centuria 100 200 m
Decuria 10 20 m
Virga 1 2 m, 1 Parisian toise
Virgula 0.1 20 cm
Decima 0.01 2 cm
Centesima 0.001 2 mm
Millesima 0.0001 0.2 mm

Based on the measurements of the size of the Earth conducted by Riccioli of Bologna (at 321,815 Bologna 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.

His suggestion was a unit, the milliare, that was defined as a minute of arc along a meridian arc, and a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima. The virga, 1/1000 of a minute of arc, corresponding to 64.4 Bologna inches, or ~2.04 m, was reasonably close to the then current unit of length, the Parisian toise (~1.95 m) – a feature which was meant to make acceptance of the new unit easier.

As a practical implementation, Mouton suggested that the actual standard be based on pendulum movement, so that a pendulum located in Lyon of length one virgula (1/10 virga) would change direction 3959.2 times in half an hour. The resulting pendulum would have a length of ~20.54 cm.

His ideas attracted interest at the time, and were supported by Jean Picard as well as Huygens in 1673, and also studied at Royal Society in London. In 1673, Leibniz independently made proposals similar to those of Mouton.

It would be over a century later, however, that the French Academy of Sciences weights and measures committee suggested the decimal metric system that defined the Metre as, at least initially, a division of the circumference of the Earth. The first official adoption of this system occurred in France in 1791.

By today's measures, his milliare corresponds directly to a nautical mile, and his virga would by definition have been 1.852 m.

See also

Notes

  1. Mouton, Gabriel (1670). Observationes diametrorum solis. Ex Typographia Matthaei Liberal. Retrieved 22 February 2016. decuria.

References

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