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 Earth, "F" is the component of the Coriolis force in the "x"-direction and "F" is the component of the Coriolis force in the "y"-direction. The restoring force, in the small-angle approximation, is given by Using Newton's laws of motion this leads to the system of equations Switching to complex coordinates , the equations read To first order in Ω/"ω" this equation has the solution If time is measured in days, then and the pendulum rotates by an angle of −2π sin("φ") during one day. Many physical systems precess in a similar manner to a Foucault pendulum. As early as 1836,