The idea for the overcoil came from the horologist Breguet who reasoned that if the outer coil of a flat hairspring was bent uo and laid over the top of the main body of the spring, then the spring would wind and unwind more concentrically. As a result, the spring would not exert a side thrust and the force on the balance would be proportional to the angle through which it turned.
However, through experimentation, it was found that an isochronal error opposite to that produced by a flat hairspring was present when the overcoil was laid straight across the spring as shown in Fig. 1. The hairspring in this condition will produce a faster rate in the low arcs than in the high arcs. That is to say, a watch with such a spring will run slow when first wound and will gain as it runs down.
It is obvious that betweeen the two extremes just described, there must be a place to lay the overcoil which will cause the balance wheel to perform its vibrations in the same period of time regardless of whether it swings in a small or large arc of motion.
In Fig. 2 are shown three basic types of overcoils that are in common use today. If any one of these types is selected for a given watch, then due consideration must be had for the location of portion AB of the overcoil relative to the balance staff. If AB should be located too close to the balance staff, the hairspring will cause the watch to have a gaining rate in the low arcs and a losing rate in the high arcs of motion. If AB should be located too far from the balance staff, then the hairspring will cause the watch to have a losing rate in the low arcs and a gaining rate in the high arcs of motion.
In the watch, an efficient overcoil keeps the other coils of the hairspring concentric as they wind and unwind, thus removing side thrust which is a major contributing cause of isochronal errors.