What on Earth even is an “Equation of Time”?

What motivates watchmakers? What has driven them, for centuries, to perfect tiny mechanisms by making progressively more complex modifications to conceive and realize? Undoubtedly the pursuit of absolute precision, the desire to achieve, with their creations, a constancy of motion comparable to that established by celestial laws. Many watches contain gears and levers whose sole purpose is to overcome friction and gravity: the tourbillon, the chain transmission, the coaxial escapement… and yet, there is a complication whose purpose is to modify, day by day, the speed at which the hands move: the equation of time.

For those not familiar with astronomy, this introduction might seem absurd: why should a clock mark the days differently? The explanation, of course, is there; and it is particularly fascinating as it demonstrates once again how the stubbornness and ingenuity of watchmakers can encapsulate a faithful reproduction of our universe in just a few millimetres!

Sidereal time and solar time

It is not our task – nor our desire – to bore you with exaggeratedly complex notions of physics and astronomy; however, a brief technical digression is necessary to explain the reasons behind the equation of time. It is essential to distinguish between sidereal time and solar time. Sidereal time is calculated in relation to the stars, and it is on the basis of this that the length of the day is set at 24 hours (or, to be more precise, 23 hours, 56 minutes, and 4.0905 seconds): this is the time taken by the Earth to complete one complete rotation, and thus to observe the stars in the same position as the previous day. Solar time, on the other hand, refers to a specific star – the Sun – and is influenced by the planet’s irregular orbit. Simply put, the Sun will move faster or slower in the sky according to the time of year. One must bear in mind that this does not depend on the season and, thus, on the star’s height on the horizon but only on the time it takes to move over a given arc of degrees in the sky.

Schematic representation of the Earth’s orbit. Credits Encyclopaedia Britannica.

From sundial to clock

The easiest way to notice this discrepancy is to compare the time marked by your watch with that indicated on a sundial: the difference between the two will vary from +16′ 25″ on 31 October to -14′ 15″ on 11 February. As the diagram shows, solar day and sidereal day coincide on four occasions each year: in mid-April, mid-June, late August, and in the second half of December. It is easy to see that the curve of the time equation does not have a regular pattern, just as day length does in relation to the seasons.

Tower clocks and wristwatches

Although the exact course of the equation of time is known, developing a complication capable of visualizing it effectively is quite otherwise. Technically, it is achieved by an irregularly shaped wheel which, with its rotation, controls the advance or retreat of a minute hand. Generally, the indication is on a sub-dial, but in some cases – of extreme complexity in terms of construction – the sphere of the equation of time is mounted in the center and rotates together with the hours and minutes, varying its speed just as the sun would in the sky. In this case, it is called a marching equation of time.

The clock of the Forum Carolino in Naples. Credits GrandeNapoli.

The greatest obstacle lies in the fact that the discrepancy between sidereal and solar time varies daily, according to a cycle that repeats itself every year: that is to say, the wheel of the equation of time will make one complete rotation every 365 revolutions of the hour hand. The first examples of watches with such a complication were large tower clocks, such as the one in the Foro Carolino in Piazza Dante in Naples, dated 1853; only later were attempts made to miniaturize the mechanisms, first producing pocket watches and finally, wristwatches. The first of this type was the Longines, which did not incorporate a complication but merely displayed the course of the equation on the bezel, divided into twelve months. Although not particularly interesting from a mechanical point of view, the watch makes the correspondence between the equation of time and the earth’s elliptical orbit visually intuitive.

Longines Ephemerides Solaires. Credits Segnatempo.

Breguet, for the first time on the wrist

The first caliber capable of mechanically displaying the equation of time was Breguet’s 502QPET, dating to 1991 and cased in the reference 3477. It was not yet a marching equation of time, but the balance of the dial, which also displays a perpetual calendar and power reserve, made it one of the most beautiful timepieces in the history of the celebrated French maison: its charm enabled it to remain in the catalog for over twenty years.

Audemars Piguet, in a specific location

Another notable variation on the theme is the Audemars Piguet Calibre 2120/2808, cased in the Jules Audemars and Royal Oak, which for the first time displayed the equation of time and the times of sunrise and sunset, as well as showing the mean time of culmination (solar noon) in the city chosen by the owner. These extremely rare timepieces are made extremely fascinating by the connection established between the watch and the wearer; to be able to read specific information about one’s city of residence on a mechanical watch is certainly priceless.

Vacheron Constantin Celestia, the most complicated

The most radiant example of watchmaking devoted to displaying solar time, however, is probably the Vacheron Constantin Les Cabinotiers Celestia. Unveiled at the 2017 SIHH, the watch is still the most complex timepiece ever produced by Vacheron; it integrates 23 astronomical complications, giving the impression that you can carry the entire universe on your wrist, and displays the equation of time in the most complex and fascinating way possible: with a marching sphere in rose gold, elegantly decorated with a sun at the end.

Vacheron Constantin Les Cabinotiers Celestia. Credits Horbiter.

Few complications manage to express the connection between watchmaking and astronomy so poetically, and miniaturize celestial laws to such an extent that you can comfortably observe them on your wrist. If we then consider the technical difficulty inherent in the equation of time, these timepieces become true masterpieces, and it is easy to see why this complication, so rare to see, is one of our favourites.

In the past, we have had the privilege of offering a few timepieces with the equation of time (we still have one in stock) and we are sure that more will come in the future: if you would like to add one to the collection, we would be honored to make your dream come true! Do not hesitate to contact our specialists for information or to submit your wishes to them!

written by Alvise Mori

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