## Why are Rolex watches able to spin smoothly or what do jewelry inspectors look a…

#### Why are Rolex watches able to spin smoothly or what do jewelry inspectors look at to tell the difference between a fake and a real Rolex watch?

A real Rolex watch has a sweep second hand that appears to move steadily around the watch face. A fake, like most other watches, has a second hand that moves with a jerky motion, advancing a little bit each time the balance ring completes one half of a cycle. However, a reader has informed me that even a real Rolex moves its second hand in tiny steps—they’re just very small. If you look closely, he writes, you’ll see that the second hand makes 5 tiny steps each second. Evidently, the hand-advancing mechanism steps at a higher frequency (5 Hz) than in most other watches (1 Hz). These tiny steps are hard to see so the hand appears to move smoothly. I was relieved to hear this news because the balance ring mechanism is inherently jerky and it’s hard to imagine a balance ring-based watch that avoid the jerkiness.

## How does a “water” clock work? What would be the simplest way to make a water …

#### How does a “water” clock work? What would be the simplest way to make a water clock that would maintain accuracy to say three minutes per hour?

The most common water clock, the clepsydra, has a reservoir that drips water into a cylindrical vessel. The height of the water in that vessel indicates the amount of time that has passed since the clock was started. The simplest version of the clepsydra just has a small hole in the bottom of the reservoir and doesn’t take into account the decreasing drip rate that comes with the dropping water level in the reservoir and the decreasing water pressure at the hole. To make a more accurate clock, you should maintain a constant water level in the dripping reservoir. The simplest way to do this is to place an inverted bottle of water in the reservoir so that as the water level drops past the lip of the inverted bottle, air bubbles can enter the bottle and allow more water to flow out of the bottle and into the reservoir. If you keep the water level in the reservoir constant in this manner, you ought to be able to calibrate the clock to better than 3 minutes per hour. Use a carefully made graduated cylinder as the time-measuring cylinder and watch the water level gradually rise.