# 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, and was decimally divided. 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. Mouton's publication appeared two years after John Wilkins, then president of the Royal Society, published a similar proposal.[1][2]

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.[3] 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. Wilkins however proposed using a pendulum that was 0.994 m in length.

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.

## Notes

1. ^ An Essay towards a Real Character and a Philosophical Language (Reproduction)
2. ^ An Essay towards a Real Character and a Philosophical Language (Transcription)
3. ^ Mouton, Gabriel (1670). "Observationes diametrorum solis". Retrieved 2016-02-22.

## 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