Kater's pendulum minutes per day slower than at Paris, or equivalently the length of a pendulum with a swing of one second there was 1¼ Paris "lines", or 2.6 mm, shorter than at Paris. It was realized by the scientists of the day, and proven by Isaac Newton in 1687, that this was due to the fact that the Earth was not a perfect sphere but slightly oblate; it was thicker at the equator because of the Earth's rotation. Since the surface was farther from the Earth's center at Cayenne than at Paris, gravity was weaker there. Since that time pendulums began
Foucault pendulum to describe the rotation angle of the swing plane of Foucault's pendulum. From the perspective of an Earth-bound coordinate system with its "x"-axis pointing east and its "y"-axis pointing north, the precession of the pendulum is described by the Coriolis force. Consider a planar pendulum with natural frequency "ω" in the small angle approximation. There are two forces acting on the pendulum bob: the restoring force provided by gravity and the wire, and the Coriolis force. The Coriolis force at latitude "φ" is horizontal in the small angle approximation and is given by where Ω is the rotational frequency of