How a watch works

The barrel turns slowly with a lot of force; the escapement needs to be fed quickly with very little. The gear train in between does that conversion. In patent language, the going train is "a going train wheel assembly generally connecting the energy source to the escapement and ensuring the reduction of the torque applied by the energy source".^[patent] The ratios are chosen to produce turns of known length: describing the minute display, the same patent has a part that "performs one revolution in one hour", with the hand fixed to it sweeping "the graduated scale in one hour".^[patent]

There is a second, separate set of wheels that people often merge with the first. The motion work is "a motion work wheel assembly generally connecting the display means to correction means": the gearing under the dial that drives the hour hand from the minute hand and lets the crown set them.^[patent]

Left alone, a wound spring would spin the train until it ran out, in a few seconds. The escapement stops that: it locks the train, releases exactly one tooth, locks again. The sound you hear is precisely that event; a learned society puts it in one line: "the ticking of a timekeeper is the sound of the escapement stopping a wheel tooth".^{[Antiquarian Horological Society]}

While it is releasing, the escapement also does the other half of its job: it gives the oscillator a push to replace the energy lost to friction and air. A patent describes the exchange as the point at which "the energy of the mainspring is transmitted to the balance wheel in order to give it the energy necessary to keep it oscillating".^[patent] Release and push, several times a second, for as long as the watch runs.

Almost every mechanical watch made today uses one design. The Seiko Museum records that the club tooth escapement, "combining a lever and an escape wheel with teeth resembling golf clubs", is the one that "gained widespread use that continues to this day".^{[Seiko Museum]} A patent describes the moment of release in it: "unlocking occurs when the balance wheel comes into contact in the fork of the anchor", and that unlocking "causes a slight recoil of the escape wheel".^[patent]

The timekeeping element is a weighted wheel on a fine spiral spring. The Seiko Museum describes the construction: the balance wheel "comprises a fine 'hairspring' fitted into a metal wheel, with one end of the spring fixed to the wheel and the other fixed to the body of the timepiece".^{[Seiko Museum]} Wound one way, the spring pulls it back; it overshoots, and the spring pulls it the other way. It swings back and forth at a rate set by its own physics rather than by how hard it was pushed.

That last property is the whole trick, and it has a name: isochronism. The museum states it as "like the pendulum, the hairspring is isochronous, so the cycle remains unchanged even when the oscillation angle shifts".^{[Seiko Museum]} A patent states the engineering condition more carefully: that an oscillator's "rate must be as independent as possible of oscillation amplitude".^[patent] The word to notice is possible. Real isochronism is approached, not achieved, and the gap is where a watch loses time.

Now the earlier problem resolves. The mainspring's force falls as it unwinds, so the escapement's push weakens, so the balance swings through a smaller arc. Because the balance's period barely depends on how far it swings, the watch keeps time anyway. The oscillator's indifference to the push is what makes a variable power source acceptable.

Frequency is quoted two ways. A patent gives the usual engineering range: "the usual frequencies of the watch oscillators range from 2.5 Hz to 5 Hz, in steps of 0.5 Hz", chosen so a second contains a whole number of swings.^[patent] The trade more often counts vibrations per hour, and another patent gives those: "the usual regulating bodies perform 28,800 or sometimes 36,000 vibrations per hour, which makes it possible to measure the time with a resolution of 0.125 or 0.1 seconds respectively".^[patent] The two scales describe the same thing, and no single authority found here states the conversion between them in one place, so the glossary entry for vibrations per hour sets out the arithmetic openly as this Codex's own.

Position. Gravity pulls on the balance differently depending on how the watch is lying. A patent describing an isochronous oscillator notes that in the vertical positions the "rate characteristics as a function of amplitude are similar to each other, but very far from" the horizontal characteristic.^[patent] A watch that gains on its back may lose on its side, which is why a watch on a wrist behaves differently from one in a drawer.

Magnetism. Fields do lasting damage to some hairspring alloys: they "modify the elastic properties of spiral springs in an irreversible manner and consequently change the natural frequency of the mechanical oscillator".^[patent] Irreversible is the important word: the spring's properties change, and the watch's rate changes with them.

Temperature and state of wind complete the set: metal stiffness varies with temperature, and amplitude varies with how recently the watch was wound.

This is why chronometer testing measures across conditions rather than just counting seconds. COSC tests a mechanical watch "over a testing period of 15 days", during which "the watch is tested in five different positions and at three different temperatures (8°, 23°, and 38°C)",^[COSC] and requires that it "maintain an average daily rate between -4 and +6 seconds per day".^[COSC] A rate figure without the conditions attached describes almost nothing, which is the point of publishing the conditions.