Watch Of Wonder: The Jules Audemars Equation Of Time

One of the most surprising truths you learn if you get curious about astronomy, is that the universe – even our little pocket of it – is a less orderly place than you might think. Calendars and watches all represent without exception, some degree of compromise with the fact that natural cycles like the rotation of the Earth on its axis, the Earth’s orbit around the Sun, and aspects of the sky as seen from Earth like sunrises and sunsets, do not fit neatly with each other. The mismatch most watch enthusiasts are likely to be at least somewhat familiar with, is that between the number of days and the length of the year. Thanks to the fact that the year is not a whole number of days – the approximation used by the Gregorian calendar is 364.2425 days – it’s necessary to make corrections to the calendar on a regular basis in order to keep the calendar from drifting out of synchrony with the seasons. You could just try to ignore the change and let the dates fall where they may but good luck getting people to celebrate Christmas when it’s high summer (although in the Southern hemisphere that’s exactly what happens).

However, watchmaking is nothing if not the pursuit of incremental improvements in the face of the impossibility of perfection, and back in 2000, Audemars Piguet released a remarkable watch demonstrating just how far the state of the art of watchmaking could pursue exactness in displaying astronomical phenomenon.

The Jules Audemars Equation Of Time was not the first wristwatch to show the Equation of Time – Breguet’s Classique Grand Complication from 1992 preceded it and there was also, believe it or not, an Equation Of Time wristwatch from Longines – the Ephemerides Solaires, released as a limited edition of 1,000 pieces in steel and 200 in gold, in 1989. However, credit for the first watch with a sunrise/sunset complication generally goes to Audemars Piguet, as the Ephemerides Solaires showed sunrise and sunset times only for St. Imier (there were no other options) and only approximately at that. The Jules Audemars Equation Of Time is a perpetual calendar, and also shows the Equation Of Time, and the times for sunrise and sunset, at any location specified by the owner, as well as showing the time of true solar noon at that location, also known as “solar culmination” – the moment when the Sun is at its highest point in the sky. The watch shown here uses New York City as its reference location, and as to what 11h55′ might mean, more on that in a minute.

The signature complication, if not the most mechanically complex in the watch, is the Equation Of Time. Most of us realize that the time shown on clocks and watches is not the actual time at our present location; instead, it’s determined by the time zone in which we’re located. (More precisely, it’s determined by the time zone in which local, state/provincial, and national laws determine we’re located, which leads to its own sort of chaos masquerading as order, but that’s another story). That time is “civil time” but prior to the establishment of time zones, towns and cities set their clocks to “mean solar time.” Mean solar time is so called because it’s based on a 24 hour day, which is an average of the actual length of the day over the course of a year. A day can be defined in several ways; a solar day, is the length of time it takes for the Sun to return to the same position in the sky (when a day starts can therefore be somewhat arbitrary as well). An actual solar day, therefore, varies in length throughout the year because the time it takes for the Sun, as observed from Earth, to return to the same point in the sky varies over the course of a year.

This is basically thanks to the fact that the Earth’s axis is tilted about 23.44 degrees from the plane of its orbit and also the fact that the Earth’s orbit is an ellipse, not a perfect circle. From this you might conclude that a planet with zero axial tilt and a perfectly circular orbit would have no Equation Of Time – that is, that every day would be of the same length over the course of a year – and you would be correct. You might also conclude that the Equation Of Time is different for every planet in the solar system as the eccentricity of of every orbit varies as well as each planet’s axial tilt, and you would be correct again.

So why do watch and clockmakers care about the Equation Of Time? Suppose you have a clock with a seconds pendulum, which beats 86,400 times per day – that’s a mean solar day. Now, suppose you want to set the clock from a sundial you have in your garden (this scenario also presumes you have a country estate and generational wealth). However, to do so, you need to know what the Equation Of Time is for the date on which you want to set your clock. You can then go ahead and set your clock by the sundial, and then add or subtract whatever the Equation Of Time is for that day, and you will then have a clock that tells the mean solar time for your location. And in fact, many longcase pendulum clocks used to have Equation Of Time tables pasted into the backs of their cabinets.

The Equation Of Time is a combination of a curve representing variations due to axial tilt, and one representing variations in orbital eccentricity, and if you put the two together here’s what you get:

… the horizontal X axis represents mean solar time, and the vertical Y axis shows how many minutes ahead or behind mean solar time the actual local solar time is, on any given day; as you can see; the Equation Of Time is zero four times a year.

To show the equation of time in a clock or watch, you need to have a cam that rotates once a year, and the curvature of whose circumference corresponds to the curve show in the chart above. What you get is a cam which is roughly kidney shaped. You set up your gear train so the cam rotates once per year and then set up a lever, whose tip rests on the edge of the cam so it moves back and forth over the course of a year, and put a rack on the other end of the lever that moves a gear back and forth. Put a hand on the pinion of the gear, and you’ve got an Equation Of Time indication:

… as seen under the dial of the Jules Audemars Equation Of Time. The movement, caliber 2120/2808, is based as you may have already guessed on the legendary ultra thin AP caliber 2120/1, which remains, to this day, the thinnest full-rotor automatic movement ever made (it was used by Vacheron, Patek, and AP, although never by Jaeger-LeCoultre, which supplied the movement; it was the first movement used in the Royal Oak). You can see the Equation cam clearly on the lower left, with the lever, rack, and second lever and rack extending to the center of the movement (this is necessary because the Equation hand in the JAEOT pivots on the same axis as the hour and minute hands).

The times for sunrise and sunset are shown on subdials to the left and right – the actual time the Sun rises and sets varies with latitude (think, for instance, of how long the winter night is in the Arctic, versus New York; in New York the difference between the times of sunrise and sunset can be as much as four hours). These times can also be encoded on rotating cams – the Jules Audemars Equation Of Time was, again, not the first wristwatch to show sunrise and sunset times, nor the first watch (the famous Henry Graves Supercomplication, for instance, showed times of sunrise and sunset in New York) but it was the first wristwatch to show those times clearly, and legibly, with to the minute precision; it would be followed just a few months later by the Eos watch, designed by Martin Braun. 

Times of sunrise and sunset are location dependent, so cams had to be cut for specific locations depending on the owner’s preferences. If you decided you wanted a different location shown, the watch – and this is true of any sunrise/sunset complication with the exception of the Krayon Anywhere watch, which has a variable width internal cam that can be reset for a new location without cutting a new one; and the Krayon Everywhere watch, which can be reset for a new location by the owner, thanks to a mechanical system for changing the reference latitude and longitude.

Another unique feature of the Jules Audemars Equation Of Time is its ability to show the time of solar culmination – the point when the Sun is at its zenith in the sky. As far as I know, the JAEOT remains the only watch with this ability.

On the rehaut (outer flange) of the dial, there’s the reference city for which the sunrise/sunset cams have been cut, and also, somewhat more enigmatically, there’s a time shown in hours and minutes. That time is the local solar time at which the Sun is at its zenith on the days of the year when the Equation Of Time is zero – and if you look at where the zero is on the Equation Of Time sector, for this watch, it’s right at 11:55. That means that at 11:55 on the four days when the Equation is zero, the minute hand, at 11:55, will be exactly superimposed on the Equation hand. On other days, the superimposition of the minute and seconds hands will still show the time of solar culmination, but with the correction for the Equation Of Time for that day.

All this and a perpetual calendar too, and a high precision moonphase accurate to one day’s error in 122 years. And one of the most unapologetically aristocratic movements ever to appear in a wristwatch.

I have written so often (and so long-windedly) about the AP 2120/1 that I won’t rehash those points again, but boy the movement was a beauty. An aristocrat among its peers (and this is back when aristocratic movements weren’t as thin on the ground as they are now) it had a number of technical features unique to ultra-thin watchmaking and unique to the 2120, including its cantilevered “hanging” barrel, and the rotor which is supported on its periphery by ruby rollers (you can just see one of the mountings for one set of rollers at about 8:00 in the picture).

It’s a magnificent watch, audaciously conceived and flawlessly executed, with a unique combination of complications, some unique functionality (that indication of solar culmination specifically) and more than anything else, it’s a mechanical and horological ode to the Music Of The Spheres, encoding as it does a wealth of information about the complex orbital and rotational relationships between the Earth and the Sun (including the perpetual calendar).

Of course, all this beauty is, in the end, just an approximation – a perpetual calendar complication typically doesn’t include the 100 and 400 year rules which are really the essence of the Gregorian calendar (even the late unlamented Julian calendar had leap years) and then, there’s the fact that the actual length of any given solar year is not exactly the same from one year to the next. We have moved on from such graceful Newtonian standards to the icy, cosmos-defying precision of atomic, optical atomic, and now nuclear atomic clocks. Still, though, a watch like this, like all mechanical astronomical complications, illustrates the correspondence between the laws of science and the sometimes elusive rules of beauty and elegance striven for in scientific theory and mathematics – an obsession without which we wouldn’t have transcended mechanical horology at all.

See It Here