Isochronism

Isochronism names an independence. European patent EP 3 206 091 B1, "Resonateur isochrone d'horlogerie", held by ETA SA Manufacture Horlogere Suisse and published on 23 January 2019, puts the mechanical condition plainly: "Le couple est proportionnel a l'angle α dont la masse 5 correspondante pivote. La frequence est donc independante de l'amplitude de l'oscillation." Where the restoring torque is proportional to the angle turned, the frequency is independent of the amplitude of the oscillation. A watch whose balance is isochronous keeps the same rate whether it is swinging widely or narrowly, which matters because amplitude falls as the mainspring runs down.

The Seiko Museum, a museum source rather than a standards body, sets out the history: Galileo discovered the "isochronism of the pendulum", that the "period of a pendulum's swing was independent from the amplitude of the swing"; Christiaan Huygens then "developed the concept of a highly accurate, isochronic pendulum by drawing a cycloid curve unimpeded by air resistance", having "demonstrated theoretically that a large-amplitude swing was subject to large error that precluded isochronism". The museum adds that a spiral balance spring "oscillates isochronously like a pendulum but is free from the influence of gravity," which is what carried the idea from clocks into watches. The Science Museum Group's record for a Thomas Tompion balance-spring watch of 1675-1679 states that when "Christiaan Huygens (1629-1693) applied the spiral spring to the balance of a watch in 1675 it brought about an improvement in timekeeping comparable to that produced by the application of the pendulum to the clock".

What this Codex does not do: quote Huygens. He set the work out in Horologium Oscillatorium of 1673, and a full page scan of the Latin text is downloadable from the Internet Archive, but it has not been read here, so no translation is offered as his wording.