# Gabriel Mouton

**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

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*.[1] 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.^{[clarification needed]} 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

- Mouton, Gabriel (1670).
*Observationes diametrorum solis*. Ex Typographia Matthaei Liberal. Retrieved 2016-02-22.decuria.

## References

- G. Bigourdan:
*Le systeme metrique des poids et mesures*, 1901, chapter*Les precurseurs de la reforme des poids et mesures* - Ferdinand Hoefer:
*Historie de l'astronomie*, Paris 1873