Pendulum Error
The long and short vibrations of a free pendulum will only be isochronous if the path described is a cycloid, which is a curve described by rolling a circle along a straight line. If the generating circle, instead of being rolled on another circle, were rolled along a straight edge, it would describe a cycloid. But a pendulum swung freely from a point travels through a circular path, and the long arcs are performed slower than the short ones. This divergence from the theoretical cycloid was of great importance when the arc described was large, as it was of necessity with the verge escapement, and many devices were tried to lead the pendulum through a cycloid. With an arc of about 3 deg. only, such as regulator pendulums describe now, the divergence is very small.