**Gabriel Mouton** obtained his doctorate in theology in Lyon. However he spent much of his spare time studying mathematics and astronomy. He took holy orders and spent his whole career in St Paul's Church in Lyon where he was appointed in 1646. Speziali writes in [1]:-

He spent his whole life in his native city, fulfilling his clerical responsibilities and untroubled by any extraordinary events. During his leisure time he studied mathematics and astronomy and rapidly acquired a certain renown in the city. Jean Picard, who also was an abbé, held Mouton in high esteem and always visited him when in Lyons to work on the determination of the city's geographic position.

His most famous work *Observationes diametrorum solis et lunae apparentium* Ⓣ published in 1670 studied interpolation and a standard of measurement based on the pendulum. Lalande wrote:-

This volume contains interesting memoirs on interpolations and on the project of a universal standard of measurement based on the pendulum.

His methods of interpolation used successive numerical differences in a way similar to those used by Briggs in the construction of his logarithm tables. In this work Mouton became the first to propose the decimal system of measurement based on the size of the earth. He also suggested a standard linear measurement, which he called the mille, based on the length of the arc of one second of longitude at the equator on the Earth's surface and divided decimally. He suggested divisions he called the* centuria, decuria, virga, virgula, decima, centesima* and *millesima* so that a *virgula*, a ten thousandth of a mille, was about 18.5 cm or a little over 7 inches. The *virga* was quite close to the ancient French measure of a *toise* or 6 *pieds* (feet). Mouton wanted a practical means to determine the length of a *virgula*. Certainly one could not measure the circumference of the earth, so he proposed a standard based on the length of a pendulum. He conducted experiments which led him to the conclusion that a simple pendulum of length one *virgula* would oscillate 3959.2 times in 30 minutes. Mouton stated that there was a marvellous regularity in nature which made a metric system of measurement based on nature fit in with human activity.

Mouton's proposed standard of measurement was taken seriously, at least at the theoretical level, and Jean Picard strongly supported him, as did Huygens in 1673. In London the Royal Society also considered these proposals to have considerable merit. It would be over 100 years, however, before the French returned to Mouton's proposal and the definition of the metre was made in a different way to Mouton's suggestion.

Leibniz made discoveries similar to Mouton. Speziali writes in [1]:-

When Leibniz went to London in January1673, he took with him his "Dissertio de arte combinatoria" Ⓣ. He summarised its contents to John Pell and in particular, explained what he called "différences génératrices." Ⓣ Pell remarked that he had read something very similar in Mouton's book, which had appeared three years earlier. Leibniz had learned, during his stay in Paris, that the book was in preparation but did not know that it had been published. While visiting Oldenburg, Leibniz found Mouton's book and observed that Pell had been right; but he was able to prove that his own, more theoretical and general ideas and results had been reached independently of Mouton's.

Mouton also produced 10 place tables of logarithmic sines and cosines and an astronomical pendulum of remarkable precision. As an astronomical observer he made remarkably accurate observations of the apparent diameter of the sun.

**Article by:** *J J O'Connor* and *E F Robertson*