There’s a famous joke (forgive me if you’ve heard this one) in which a professor gives a lecture on astronomy to the general public.

At the end of the lecture, an old lady stands up. “Young man,” she says, “you’re wrong about the earth orbiting the sun. The earth is supported on the back of a giant turtle.”

With a superior smirk, the professor says, “Yes, but what is that turtle standing on?”

Triumphantly, the old lady crows, “I know what you’re getting at,
professor, and you’re very clever, but it’s no good. It’s turtles all the way
down.”

A pretty quick way to feel about as on the ball as an old lady whose brain is clearly not getting enough oxygen is to start thinking about the equation of time.

Like the apes in Kubrick’s 2001, when an equation of time watch appears in front of us, we may whoop and grovel in awe, but
how many of us really understand what it represents?

The chronograph, the moon phase, the perpetual calendar and even the repeater may challenge our ability to understand exactly how they work, but there’s usually not too much confusion about what, exactly, they are.

But what, exactly, is the meaning of that gnomic little hand, wandering back and forth between a plus and minus a quarter of an hour?

Probably the easiest description to understand is that the equation of time is the difference between the time told on a sundial, and the time told by a clock; although, this naturally raises the question of why there’s a difference — to say nothing of the question of why anyone would care.

Considering how seldom most of us pay the slightest attention to what’s going on in the sky (assuming we can even see anything other than the sun and the moon, which is by no means a given for us city slickers), the answer to neither question is especially obvious at first.

But a little thought experiment might help — and perhaps get us in the right frame of mind to understand the beauty of the equation of time complication.

Imagine that all the artificial lights that fog the evening sky are gone, and that the only source of light in your world, other than the faint flicker of whatever fire you can kindle, is the sun.

Darkness now is something unimaginably terrifying — impossible to escape, full of glowing eyes and mortal peril.

In such a world, the rising of the sun is like a delivery from death in a way the modern mind can hardly imagine — you’d pay attention too.

Celestial Mechanics (and a Beer-drinking Moose)

Having put ourselves in Fred Flintstone’s shoes (or saber-toothed tiger loafers, as the case may be), we can see that one fact must have seemed obvious to our flea-bitten ancestors — looking up at the sky, day or night, the natural conclusion to draw is that the earth is stationary, with heavenlybodies moving around it.

This is such an obvious conclusion that it was some time before it occurred to anyone that the clearly absurd ideas that the earth was actually (A) moving and (B) not the center of the universe,
might actually be true.

The Babylonians, among the first astronomers, not only charted the sky and observed the movements of the planets, but also noticed the irregular movement of the sun — especially that sometimes, it was higher in the sky at noon than at others, and that the day varied considerably in length over the course of the year.

The irregular movements of the sun were further charted by Claudius Ptolemaeus, more commonly known as Ptolemy, who lived in Roman occupied Alexandria at the beginning of the Christian era.

He gave his name to the Ptolemaic system, which was geocentric — the basic idea was that the earth stood still, while everything else circled around it. (300 years before, Aristotle had already summed up the Greek arguments for believing that the earth was circular — the Greeks had even
taken a stab at measuring its diameter.)

Ptolemy was such a good astronomer and his calculations so accurate that it was quite a few centuries before someone came along to challenge his ideas — partly because minor events in Europe like the fall of Rome and the invasion of the Huns were keeping people on their toes.

Heliocentrism, or the idea that the sun is at the center of the solar system, was an idea that had been aroundfor a while — for instance, there were elements of heliocentrism mentioned in anonymous Indian textsfrom seventh century B.C. — but credit for getting the idea on the front page is usually given to a Polish priest, physician, astronomer, mathematician, and militarycommander named Nicolaus Copernicus, who was born in 1473.

Copernicus seems to have gotten the astronomy bug in college and thought about the subject considerably — at least when he wasn’t doing things like fighting off German invasions or reforming the Polish currency.

As a respectable pillar of the community, he seemed to have had little interest in upsetting the apple cart (or irritating the Church, more precisely). His career was not that of an iconoclast, but rather that of an ambitious, politically savvy, and profoundly practical man.

He hardly talked to anyone about the revolutionary ideas in the back of his mind, but he did, finally, write a little book on the subject that just barely managed to see the light of day — a copy of the first edition arrived at his bedside literally on the day he died.

Nicolaus Copernicus is usually credited for getting heliocentrism- the idea that the sun is at the center of the solar system- on the front page.

Confirmation of the Copernican heliocentric model
came through an unlikely collaboration between two
of the odder scientific geniuses of the last 2,000
years — Johannes Kepler and Tycho Brahe.

They were contemporaries, both active in the late 16th and early 17th centuries; but aside from an interest in astronomy, they had very little in common. Kepler was an avowed Copernican, who had climbed from poverty to eventually become court astrologer to the Holy Roman Emperor Rudolf II in Prague; his father was a mercenary who disappeared when Kepler was a child, and his mother was a quarrelsome herbalist who eventually got on her neighbor’s nerves so much that she was accused of witchcraft, avoiding being burned at the stake only due to the intervention of her influential son.

(Kepler wrote of his father that he was “... a man vicious, inflexible, quarrelsome and doomed to a bad end. Venus and Mars increase his malice... Saturn in the seventh house made him study gunnery...”)

Tycho Brahe, on the other hand, could hardly have been born with a bigger silver spoon in his mouth; a member of an obscenely rich noble Danish family
family, he studied astrology and astronomy in Copenhagen, and was eventually given his own private island on which to build an observatory.

Tycho was both pugnacious and eccentric — having lost his nose in a student duel, he sported an artificial one made of gold; he kept, as a court jester, a dwarf he claimed was psychic; and he owned a pet moose (who one fine night got drunk on beer and died falling down the castle steps).

Kepler didn’t think much of Tycho as a person, but Tycho’s
astronomical data was superb and with it, Kepler was able to calculate the orbits of the planets to a high degree of accuracy; and critically, for understanding the equation of time, he established that the planetary orbits were not perfect circles, but rather, elliptical.

Subsequent work by Galileo, who observed the moons of Jupiterorbiting the planet, and Sir Isaac Newton, who formulated the laws ofgravity that explained the movements of the planets around the sun, were the final nail in Ptolemy’s coffin.

Ever since, we’ve been able to consider ourselves an insignificant speck circling an unremarkable sun on the outskirts of an average and uninteresting spiral galaxy.

By the end of the 17th century, two things had become clear. The first was that the earth orbited around the sun
not in a perfect circle, but in an ellipse. The second was that the earth’s axis wasn’t perfectly vertical — in fact, it’s significantly tilted, about 23 degrees and seven minutes of arc.

Let’s now think about the seasons. The seasons are mostly due to the tilt of the earth’s axis. In the northern hemisphere, when the north pole is tipped towards the sun, days are longer and the sun is higher in the sky; when the north pole is tipped away from the sun (six months later), days are shorter and the sun is lower in the sky (and sales of booze and anti-depressants go up). If you were to measure the height of the sun above the horizon every day at exactly noon on the clock, you’d see that the sun’s height changes a little every day — highest at the summer solstice, lowest
at the winter solstice.

So far so good. But you’d notice something else, too— the moment when the sun is at the highest point
in the sky each day is not always exactly noon! In
fact, the sun’s culmination, or the time it reaches its zenith, matches the clock, disturbingly enough, only four days a year.

Annoyed by this, you decide to get to the bottom of the mystery, and so every day at noon on your clock, you take a picture of the sun. At the end of the year, you superimpose all the photos and you notice something very weird — over a year, the positions of the sun in the sky, at noon, trace out a strange-looking figure eight. What the hell??

This wacky figure eight in the sky is called an analemma, and the fact that the sun is sometimes ahead of where it should be at noon, and at other times behind where it should be at noon, is what the equation of time hand on a watch illustrates.

The reason for the discrepancy between clock time and the position of the Sun in the sky –which, naturally, is the time a Sundial's going to show –is that because of the Earth's tilted axis, and because its orbit is elliptical, the Sun appears to speed up and slow down over the course of a year.

An object orbiting along an elliptical path is going to speed up and then slow down as it zips along between the perihelion –the point closest to the Sun –and the aphelion –or point furthest from the Sun. This speeding up and slowing down contributes a variation in Sun time with a one year cycle to the Equation of Time. But the Earth's tilted axis not only makes the Sun appear sometimes higher and sometimes lower in the sky –because the tilt makes the Sun seem to wobble not only up and down, but also back and forth, it also contributes to the Equation of Time –but in a twice yearly cycle.

(above and below) Double-sided Breguet watch, grand complication no. 92.
On the white enamel dial are indicators showing the day, date and month, as well as equation of time.

The addition of both cycles together is what gives us the equation of time. If it’s not instantly crystal clear, don’t feel bad.

There’s a description of the analemma on a webpage hosted by Harvard, written by an astronomy professor, who said he decided to post his description when the necessity became clear after he found that “three PhD candidates and one PhD holder were unable to explain the analemma clearly”.

But the basics are straightforward — because of axial tilt and elliptical orbit, the sun’s position varies cyclically throughout the year, meaning the time it tells runs fast or slow relative to a clock.

Cam artists

The equation of time, in either a watch or a clock, can be indicated in various ways — the most common way is to have a sector on the dial with a hand that shows how much you would have to add or subtract to the mean solar time to get the apparent solar time, or sundial time.

The hand waggles back and forth as it’s moved by gears attached to a metal finger that traces out the contours on a vaguely kidney-shaped cam that rotates once a year, the outline of the cam corresponding to the analemma.

The equation of time is an unusual complication to begin with, even in its simplest form; a more complex and even less often seen variation is the equation of time marchante, in which there are two minute hands on the dial — one for the mean time and one for the apparent solar time (in other words, the equation of time hand).

Over the course of a year, the EOT hand slowly overtakes and then slowly falls behind the minute hand as the sun overhead gradually catches up with and then falls behind clock time.

Historically, the equation of time was (and is) a rarity.

Most often, it’s found in clocks — the stately pendulum ‘regulator’ in the great hall of the manor with its equation of time would let his lordship know how far
ahead or behind ‘official’ local time was from the sundial on the manor grounds -perhaps so as to be punctual for an assignation with the groundskeeper’s fetching daughter, who was probably telling time by the sun - rarely was it found in pocket watches.

Such watches were manufactured by a veritable who’s who of horological history: Thomas Mudge in the 18th century, and luminaries such as Leroy, Breguet and Berthoud in the 19th century, manufactured equation of time watches by request for only the most illustrious of clients.

Of course, the most famous of all watches
employing the equation of time is the missing Breguet ‘Marie Antoinette’ — the Holy Grail of vintage horology — but this is only the most extreme example.

For much of horological history, if an equation of time watch was in your waistcoat pocket, you had to be either a merchant prince or a real prince (or princess).

In a wristwatch, the equation of time is a novelty whose recent appearance is in startling contrast to the ancientness of our understanding of the sun’s irregular movement; but what has not changed is that it is rarer than hen’s teeth. One of the earliest to put an equation of time complication in a wristwatch was the firm of Breguet (appropriately enough).

In 1992, the first Breguet wristwatch with an equation of time complication found its way to retailers — this watch was priced to position it as a very exclusive model, at around US$170,000 (in the year 2000) and fewer than 20 were made per year.

.

There, matters stood for some time. Interestingly enough, Breguet was preceded by a firm that one would not immediately have associated with such a traditionally haut de gamme complication: Longines

In 1989, for the 100th anniversary of the firm, Longines produced the Ephémérides Solaires wristwatch, a very complicated piece with several astronomical indications which shows the equation of time, but not as a mechanical indication; instead, the EOT is shown on a rotating bezel in the form of a fluctuating line going around the bezel’s circumference, through a scale for each month showing the equation.

One of the most important, as well as the most aesthetically compelling, of all Equation of Time wristwatches is by Audemars Piguet.

The Jules Audemars Equation of Time (pictured left)is perhaps one of the most technically accurate and interesting of all EOT wristwatches.

First produced in 2000, it is the antithesis of what many of today’s new Audemars Piguet Offshore-besotted customers might think of as a representative AP watch, and yet its elegant marriage of astronomical

Not only does the Jules Audemars Equation of Time show the EOT indication, it also shows the correct time for sunrise and sunset — a rarity among rarities — and is a perpetual calendar and a super-accurate moon phase watch as well, with a lunar indication accurate to within one day in approximately 122 years.

Sharing the rare distinction of being an equation of time
wristwatch that also displays the sunrise and sunset time,
is the Martin Braun Boreas.

Martin Braun’s EOS wristwatch was, in 2000, one of the first wristwatches to show local sunrise and sunset times and the addition of the equation of time to the sunrise and sunset indications of the EOS is a natural extension of
Braun’s fascination — and expertise — with astronomical complications.

Among the most eerily beautiful equation of time wristwatches ever made is the Jaquet Droz pieces and which has long since sold out.

The equation of time indication generally takes the form of a sector on the dial showing the adjustment to be made in minutes plus or minus from mean time, and so it is on the Jaquet Droz EOT.

However, rather than cramp the indication into a small, single sector on the dial, the EOT hand is given a generous sweep of 180 degrees of dial space; and the gold sun tipping the EOT hand swings through a considerable space on the dial, as if to evoke the stately minuet of the planets through vastness of space itself.

The complications encased in its ponderously hypertrophied frame are a veritable catalog of horological astronomy — indications for not only the equation of time, but also sidereal time, a planispheric display of the night sky, the times for sunrise and sunset, a perpetual calendar, the phases and age of the moon... all find their place among the more prosaic indications of the hours and minutes, to say nothing of a view of a tourbillon regulator and, oh by the way, in all modesty, a new escapement as well.

If horological altitude sickness has not yet afflicted you, then a watch guaranteed to leave you gasping is the Patek Philippe Star Caliber 2000, one of the most incredible horological devices ever constructed — the word ‘watch’ seems woefully inadequate.

This mechanical microcosm shows virtually every astronomical
function of any importance ever conceived; naturally, it displays the
equation of time, but it does so not with a hand sweeping back and forth through a sector on the dial, but with an equation of time marchante — that is, with an additional minute hand that runs ahead or behind the normal minute hand, creeping forwards or backwards through the year as the sun falls behind or overtakes the clock.

It was joined by the Jaeger-LeCoultre Gyrotourbillon in 2005, which combines a marchante EOT hand with an instantaneous, double retrograde perpetual calendar, a unique multi-axis tourbillon, and an eight day power reserve with an up/down indication.

So what’s all the fuss about, then?

Why is this complication which is, even in the artificial hothouse inbred atmosphere of mechanical horology, conspicuous in the absence of any conceivable practical application in modern life, so revered as to be found in some of the most regally aloof watches on the planet? And what do dead astronomers — gold noses and beer-drinking mooses notwithstanding — have to do with any of this?

The equation of time holds a special place in horology. Not only is it a complication that reaches across the vastness of space, reminding us that our docile civil time is a toddling newcomer to the cosmos, it reaches across time as well, back into our own history, and reminds us of the giant effort across a span of thousands of years in which human intelligence unshelled celestial mechanics from the obscuring husk of external appearances.

That may seem like a lot of symbolic freight for that little lumpen cam to bear, but then, aren’t rich pleasures in small packages what watchmaking is all about?