Timely Lesson

This lesson is not timely, because it is like three weeks late for the first lesson of the summer. It is timely, because it is about time-keepers.

On Monday, I commented on a Day and Night watch that doesn't tell time, it just tells you whether it is day or night. I quoted a source which cited the Wall Street Journal, and one bit of that quote kept bugging me.

They claimed the watch worked "...using a complex measurement of the Earth's gravity." That didn't seem right to me. The Earth's gravity doesn't change from day to night. While it is true that the gravitational field at the Earth does change with the position of the sun (and thus from day to night), that would be a really complex measurement, because the sun's gravitational pull at your location isn't always straight up or straight down, and because the moon's gravitational pull would have to be factored out somehow.

I was puzzled, so I looked into it. From what I read, there doesn't appear to be any "complex measurement of the Earth's gravity." Perhaps what led the writer to that conclusion is that the watch uses tourbillons - the spinning mechanisms in expensive watches that generally spin once per minute, like a second hand. The Day & Night watch seems to have two of these - a daytime tourbillon with a sun which spins for twelve hours, and a nighttime tourbillon with a moon which spins the other twelve hours.

What does a tourbillon have to do with gravity? Well, the tourbillon was an ingenious invention meant to counteract the effects of Earth's gravity, which made pocket watches less accurate.

Which leads to the question: Why does gravity make pocket watches less accurate?

First, consider how a watch keeps time. Generally time is kept by a harmonic oscillator (such as a pendulum in a grandfather clock or balance wheel in a watch), but oscillations of these timekeepers die out quickly. A source of energy is needed, like a coiled spring. However, you don't want the spring to directly run the timepiece, because it would just unwind all at once and it would run too fast, and run out of energy too fast.

Instead an escapement is used, which couples the energy source to the oscillator. In the escapement, the escape wheel is powered by the spring, but it doesn't just spin out of control; it has teeth that get caught on anchors or pallets. These anchors or pallets are atttached to the oscillator, and only move out of the way with each oscillation. Thus the rate of rotation of the escape wheel is determined by the oscillator, but the coiled spring provides the power to keep it moving.

This is all well if the balance wheel is perfectly symmetric. Suppose it isn't symmetric because one spot on the wheel is heavier than equal sized spots elsewhere on the wheel. Depending on the location of the excess weight it can make the watch run a tiny bit too fast or a tiny bit too slow. A watch that is kept in your pocket tends to keep the same orientation, thus the location of the extra weight would not change, and the watch would continue to run too fast or too slow.

Enter the tourbillon. The tourbillon rotates, often once per minute as I said, and it rotates the whole timekeeping mechanism with it. Thus the extra weight will be at different orientations at different times, and the balance wheel will sometimes swing a tiny bit too fast and sometimes a tiny bit too slow, and it will all cancel out to a generally more accurate watch. Instead of actually measuring the earth's gravity, the tourbillon just negates its effects.

Does your watch have a tourbillon? Probably not, unless it is a pocket watch and/or you spent too much for it. Wristwatches turn to different orientations automatically as you move your arms, so you really don't need a tourbillon. Why then do expensive watches have tourbillons? Because they look complicated and expensive. I would have to say conspicuous consumption. And the Day & Night watch is the epitome of that!

_{P.S. When I read that the Day & Night watch sold out in 48 hours at $300,000, I was amazed, until I read that they only made nine.}