Fizeau–Foucault apparatus unit. At the time, Foucault was working at the Paris Observatory under Urbain le Verrier. It was le Verrier's belief, based on extensive celestial mechanics calculations, that the consensus value for the speed of light was perhaps 4% too high. Technical limitations prevented Foucault from separating mirrors R and M by more than about 20 meters. Despite this limited path length, Foucault was able to measure the displacement of the slit image (less than 1 mm) with considerable accuracy. In addition, unlike the case with Fizeau's experiment (which required gauging the rotation rate of an adjustable-speed toothed wheel), he could
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,