A quality watch must give the exact time whether it has just been fully wound or is nearing the end of its run after 40 hours of operation. This essential mechanical ability is called isochronism — literally “equal time”.
The principle: Huygens and the pendulum
In 1656, Christiaan Huygens built the first pendulum clock; he then demonstrated, in his Horologium Oscillatorium published in 1673, that a pendulum whose mass moves along a cycloidal curve oscillates with a rigorously constant period, regardless of amplitude. This discovery revolutionised timekeeping. The balance-spring, invented by Huygens himself in 1675, extends the principle: under certain geometric conditions, a balance oscillating at ±250° takes very nearly as long as one oscillating at ±300°. Perfect isochronism remains an ideal: in a real watch, spring geometry, the escapement and losses always leave a residual error.
Why amplitude varies over the course of a day
When the mainspring is fully wound, it delivers high torque; the balance oscillates with large amplitude (280–310°). As the spring relaxes, torque decreases and amplitude drops. After 24 hours of running, 260° is common; near the end of the power reserve, it can fall below 220°. Without isochronism, the watch would run noticeably fast when fully wound and slow near the end of its reserve: precision would be impossible.
The real-world departures from perfect isochronism
In practice, isochronism is never perfect, due to three factors. (1) The development of the balance-spring: depending on position and amplitude, its outer coil does not develop perfectly concentrically, which shifts its centre of gravity and alters its effective stiffness. The Breguet curve (outer coil raised and bent towards the centre, described by Breguet in the early 19th century) corrects this geometry to make the development more concentric. (2) The roller jewel: at large amplitude, it engages the pallet fork at a different angle, which alters the impulse. (3) Passive resistances (friction, ageing oils) which do not vary linearly with amplitude.
The watchmaker's remedies
Watchmakers have devised several countermeasures. The Breguet balance-spring, with its raised terminal curve, makes the spring's development more concentric. The fusée-and-chain (still used by A. Lange & Söhne on the Pour le Mérite) equalises mainspring torque by keeping it constant throughout the power reserve. The constant-force mechanism (an intermediate device that accumulates and then releases a standardised amount of energy) achieves the same effect in a more compact form. Finally, modern annular balances and silicon balance-springs optimise geometry to minimise residual defects.
Frequently asked questions
Is a certified chronometer isochronous?
Close to it: the COSC criteria are precise — the mean daily rate must lie between −4 and +6 s/d, the mean variation in rates must not exceed 2 s/d, and the difference between horizontal and vertical rates must stay between −6 and +8 s/d. Testing lasts 15 days, in 5 positions and at 3 temperatures, on the uncased movement — which implies very good isochronism.
Does frequency affect isochronism?
Yes, indirectly: a high frequency (5 Hz) is less sensitive to positional disturbances, but consumes more energy, which limits the power reserve.
How can isochronism be tested at home?
On a timing machine: measure the rate at full wind, then again 12 h and 24 h later. A delta under 15 s/d between these readings is already excellent for a mass-market movement.
Isochronism, amplitude and positional rates are the core of the regulation unit described in how to learn watchmaking online — see also our article on regulating accuracy without fear.
Want to understand the finer points of watchmaking physics? Décalibre takes you step by step to the most subtle notions of regulation.