Isochronism

Isochronism is the property of an oscillator that takes the same time to complete a swing whatever the size of that swing. In a mechanical watch it means the balance and hairspring beat at the same rate at an amplitude of 300 degrees as they do at 220, so the watch keeps one rate whether the mainspring is fully wound or nearly flat. Nothing is perfectly isochronous; the word describes an aim and a measurable error, not an achieved state.

Where the error comes from

Three things spoil the ideal. As the hairspring breathes, its center of gravity shifts off the axis of the balance staff, loading the pivots differently at different amplitudes and differently again in each position. The escapement intervenes during part of every swing, so its impulse is a disturbance whose relative weight grows as the swing gets smaller. And pivot friction does not scale neatly with amplitude. Rate therefore becomes a function of amplitude, which is why a watchmaker reads the two together.

Why it matters

A mainspring's torque falls as it unwinds, so amplitude falls with it, typically by several tens of degrees across 24 hours and further in vertical positions. If the balance is not isochronous, that drop shows up directly as a change of rate: the watch that gained two seconds on the morning of day one loses four on the evening of day two. It is why accuracy figures are quoted over the first day of a full wind, and why chronometer testing rewinds the movement daily instead of letting it run down.

What good looks like

Three classic answers. The terminal curve of the hairspring, most famously the Breguet overcoil that lifts the outer coil above the body of the spring, lets it expand and contract concentrically so its center of gravity moves less. A free-sprung balance does away with regulator pins, so the working length of the spring cannot change as it breathes through them, and the rate is trimmed with weights on the balance rim instead. And constant-force devices, from the fusee and chain to the modern remontoir, attack the cause by flattening the torque delivered to the escapement.

A short history

The problem is as old as the balance spring. Christiaan Huygens applied a spiral spring to a balance in 1675, which made a portable oscillator practical and exposed its dependence on amplitude. Breguet's overcoil, from the end of the 18th century, was the first widely adopted fix. In 1861 Edouard Phillips derived the terminal curve conditions under which a spring expands about a fixed center, and modern overcoils and etched silicon hairsprings still follow him.

In practice

On a timing machine, isochronism error is read as the difference in rate between a fully wound movement and the same movement 24 hours later, in the same position. A few seconds a day is normal. A large swing usually means aging lubricant, a tired mainspring or a fouled hairspring rather than a flaw in the design.

You can run the test at home. Wind fully, set the watch against an internet time source, leave it dial up and read it after 24 hours, then let it run down to the last quarter of its power reserve and repeat in the same position. The difference is the error; our guide to timing your own watch has the method.

The standards take it seriously. The COSC criterion called rate resumption allows 5 seconds a day between the end of the test and its early average. METAS measures the cased watch at full wind and again at about a third of the reserve remaining, as our comparison of COSC, METAS and brand standards sets out.

Common confusions

Isochronism error is not positional variation and not beat error. Positional variation is the rate difference between two positions at one state of wind; beat error is the inequality of the two half swings. All three are separate lines on a timing machine.

A long power reserve is also not a promise of a long good rate. A stated 70 or 80 hours means the watch is still running at the end, not that it is still in specification, which is why rate figures are quoted at full wind.