ISOCHRONISM

Isochronism is the property of an oscillator to maintain a constant Period — the duration of its oscillations — regardless of its Amplitude. Herein lies the precision of a watch: a Balance–Hairspring (balance spring) that is perfectly isochronous beats at the same rate, whether its amplitude is large (fully wound watch, lying flat) or smaller (Power reserve running low, vertical position). Sensed by Galileo while observing the Pendulum, the principle was established theoretically by Christian Huygens, who showed that the cycloid ensures rigorous isochronism. In practice, perfect isochronism does not exist: the rate varies slightly depending on the amplitude, and the regulator’s role is to reduce these variations, in particular through the choice and fine-tuning of the hairspring (Breguet’s terminal curve, balance-hairspring pairing). Isochronism defects are among the main causes of rate differences between positions. Mastering them is at the heart of chronometry and certification criteria. (see the Regulation / Adjustment)

The mathematical foundations of Hairspring (balance spring) Isochronism were laid by the French engineer Édouard Phillips, professor of mechanics at the École polytechnique, in his Mémoire sur le spiral réglant des chronomètres et des montres (1861, completed in 1864): in it he established the curvature conditions for the ends of the spring — known as Phillips curves — allowing their center of gravity to remain on the Balance Axis, completing the empirical terminal curve described by Breguet as early as 1795. Today, Silicon or athermal alloy Hairsprings (balance springs) rely on numerically calculated involutes, close to these historical principles. The rate difference between high- and low-Amplitude positions, measured during chronometric testing according to the ISO 3159 standard, remains the practical Indicator of the Isochronism quality of a Movement.