structural:reformatting
Universal measure: the metre linked to the figure of the Earth

Galileo discovered gravitational acceleration to explain the fall of bodies at the surface of the Earth. He also observed the regularity of the period of swing of the pendulum and that this period depended on the length of the pendulum.

Kepler's laws of planetary motion served both to the discovery of Newton's law of universal gravitation and to the determination of the distance from Earth to the Sun by Giovanni Domenico Cassini. They both also used a determination of the size of the Earth, then considered as a sphere, by Jean Picard through triangulation of Paris meridian. In 1671, Jean Picard also measured the length of a seconds pendulum at Paris Observatory and proposed this unit of measurement to be called the astronomical radius (French: Rayon Astronomique). In 1675, Tito Livio Burattini suggested the term metro cattolico meaning universal measure for this unit of length, but then it was discovered that the length of a seconds pendulum varies from place to place.

Christiaan Huygens found out the centrifugal force which explained variations of gravitational acceleration depending on latitude. He also mathematically formulated the link between the length of the simple pendulum and gravitational acceleration. According to Alexis Clairaut, the study of variations in gravitational acceleration was a way to determine the figure of the Earth, whose crucial parameter was the flattening of the Earth ellipsoid. In the 18th century, in addition of its significance for cartography, geodesy grew in importance as a means of empirically demonstrating the theory of gravity, which Émilie du Châtelet promoted in France in combination with Leibniz's mathematical work and because the radius of the Earth was the unit to which all celestial distances were to be referred. Indeed, Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland and this new data called into question the value of Earth radius as Picard had calculated it.

After the Anglo-French Survey, the French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1798, which measured the distance between a belfry in Dunkirk and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon. When the length of the metre was defined as one ten-millionth of the distance from the North Pole to the Equator, the flattening of the Earth ellipsoid was assumed to be 1 / 334.

In 1841, Friedrich Wilhelm Bessel using the method of least squares calculated from several arc measurements a new value for the flattening of the Earth, which he determinated as 1 / 299.15. He also devised a new instrument for measuring gravitational acceleration which was first used in Switzerland by Emile Plantamour, Charles Sanders Peirce, and Isaac-Charles Élisée Cellérier (8.01.1818 – 2.10.1889), a Genevan mathematician soon independently discovered a mathematical formula to correct systematic errors of this device which had been noticed by Plantamour and Adolphe Hirsch. This allowed Friedrich Robert Helmert to determine a remarkably accurate value of 1 / 298.3 for the flattening of the Earth when he proposed his ellipsoid of reference in 1901. This was also the result of the Metre Convention of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following the example of Ferdinand Rudolph Hassler.