We've covered how to prove that the earth revolves around the sun, just in case you're sent back in time. Now your patrons grow impatient. What have you done for them lately? Keep the grog flowing by explaining Foucault's Pendulum.
By the time Foucault's Pendulum arrived on the scene, it was already a well-known fact that the earth rotated on its axis. However, proof of that fact meant tiresome star gazing, or dangerous journeys to measure polar flattening – the way the earth bulges at the sides and flattens at the north and south poles due to its rotation. The pendulum was a way to demonstrate the way the earth moved in the comfort of a high-ceilinged room.
The reasoning behind Foucault's Pendulum is easy to understand if we picture a pendulum set up directly over the North or South Pole. It would take force for the pendulum to alter its swinging motion. Assuming it were hung on a hinge that would let it swing freely, it would keep its regular swing as the earth twists around beneath it. At least, that would be what it would look like from outer space. The earthbound, however, would see it as the pendulum twisting three-hundred-and-sixty degrees without any external force acting on it.
Easy to prove, right?
Oh, but there's a catch. Most people do not live at the northern or southern poles. If the earth rotates, there is an external force acting on the pendulum; the earth dragging the building that the pendulum is housed in around in a circle every day. Instead of sitting above the rotation of the earth and swinging independently, the pendulum is precessing around the axis of the earth.
Precession is a difficult motion to describe, but it is one that most people are familiar with. If anyone has every spun a top, they've probably observed that once the top loses some energy, it falls sideways without toppling entirely, and spins around at an angle to the ground.
Just like the top precesses at an angle to the vertical, the pendulum precesses at an angle to the rotational axis of the earth. This precession causes the perceived rotation of the pendulum to ‘lag'.
The greater the angle to the earth's rotational axis, the slower the pendulum seems to rotate, until at the equator, the pendulum doesn't rotate at all. (My apologies to those time travelers reading this at the equator. I guess your days of free grog are over.)
For those of you fortunate enough to be below or above the equator, this is what you need to craft a pendulum of your own.
The first thing you need is lots of head room. Although in theory the pendulum could be any size, a long string will mean a slow swing. A slow swing will mean less air resistance, and resistance of any kind is your enemy in this particular endeavor.
To make resistance futile, you'll also need a heavy bob for the pendulum, minimizing the effects of air currents in the room. It'll also pay to make sure that the hinge or object that the pendulum is suspended from does not hinder the pendulum's movement in any way.
Last, but definitely not least, you will need to know what latitude you are at. The farther north or south you are, the more the pendulum will seem to twist, and the more flagons of ale will get poured down your throat for being such a genius. Here's the formula for figuring out how many degrees the pendulum will turn in a day.
N = 360 sin (Your Latitude)
It will require some patience, and some markings on the floor to provide a frame of reference for how much the pendulum moves, but as you watch, you'll notice the pendulum seem to shift without any force acting on it. Since you've created a system that ensures that nothing is moving the pendulum, the only conclusion is that you yourselves are moving and it is following a fixed path.
Or that you're a witch.
My advice is to have an escape route ready, just in case.
Top image via Klaus Fehrenbach