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Editorial - Class In Session: Equation Of Time

Editorial Class In Session: Equation Of Time

Explaining one of the least understood watchmaking complications…

Something that we all struggle with on a daily basis is the chasm (sometimes negligible, sometimes vast, always present) between expectation and reality. As clearly demonstrated over the millennia, from Oedipus Rex to modern-day memes, life’s protagonists will continue to swim bravely out into the great sea of hopeful optimism only to be battered back to shore by the tides of FML.

Civil time is one of the biggest and most widespread examples of humans trying to wrestle reality into the neat little box of their expectations. There are very few days in a year — just four, in fact — that are exactly 24 hours long. Most days are longer or shorter than that, by a few milliseconds or up to almost 30 seconds.

Class In Session: Equation Of Time

Marine Tourbillon Équation Marchante © Breguet

The 24-hour day is an average, known as the mean solar day, and is constructed on an astronomical model that has Earth moving around the Sun at a constant speed, with a perfectly circular orbit centring on the Sun, rotating on an axis perpendicular to its orbit. Guess how many of those things are actually true? Hint: it’s zero.

Then we have the apparent solar day, which is the amount of time between consecutive appearances of the sun at the local meridian. The mean solar day is a 24-hour constant, and the apparent solar day fluctuates. And there is almost always a time discrepancy between the mean solar day and the apparent solar day.  

These little discrepancies add up over time, if you have a few weeks of apparent solar days that are consistently shorter than the mean solar day. Those few seconds of discrepancy per day accumulate, and one day you realise that while it’s 12 noon on your watch, the sun is still quite some distance from reaching its highest point in the sky, and then you think what the hell is going on? My friends, the equation of time is what’s going on.

Do you see? The equation of time is not the difference between the mean solar day and apparent solar day, as it is frequently said to be. (Mea culpa: I used to say this too.) It is the accumulated lag or gain between the two, which is caused by that difference. That means that even when the apparent solar day is exactly 24 hours long, i.e., the same length as the mean solar day, there may still be a value assigned to the equation of time for that day.

Let’s put it in a different way. Let’s say because of some exceptionally bizarre financial circumstances, every day you’re borrowing or lending between 1 to 30 cents from/to your colleague. As a result of this constant borrowing and lending, your total debit or credit to this guy goes up and down, so that even on days when you haven’t borrowed or lent a cent from/to him, you may still owe him money (or he might owe you money). The amount you borrow or lend each day is like the time difference between the mean solar day and the apparent solar day. The overall credit or debit you’ve accrued, however, that’s the equation of time.

Class In Session: Equation Of Time

Villeret Équation du Temps Marchante © Blancpain

There aren’t a whole lot of equation of time watches out there, which is lucky, because it’s a pain in the neck to explain. Also, it’s not really something that’s applicable to real life situations. Breguet does an exceptional equation of time watch — the Marine Tourbillon Équation Marchante. So does Blancpain, with their Villeret Équation du Temps Marchante. The “marchante” means that it’s a running indication, a more intuitive method of indication that distinguishes it from most other equation of time displays.

The more common (although it’s ridiculous to use the word “common” when talking about this esoteric complication) form of the equation of time display uses a hand on a counter, that moves back and forth to tell you how many minutes to add or subtract from the day in order to determine how far behind or ahead the apparent solar day is.

In horological terms, it’s pretty much the only complication that illustrates the stark difference between expectation and reality. So as much as some watch enthusiasts like to argue that it’s the least useful of all the watch complications, one could say it’s also the most existentially relevant.

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