# Which hemisphere am I on?

Inspired by this answer to a question on Puzzling.SE (which contains the old but wrong idea that the Coriolis force determines the direction in which a bathroom vortex rotates, and also an approach using a very short Foucault pendulum), is there a practical experiment that can be performed with household items in a closed room to determine with some accuracy whether one is currently located on the northern or southern hemisphere of the Earth? Assume the room is 2.5 meters, not 15 meters high like most Foucault installations.

• Right now it might be tricky, but you could check the heaters/AC vents to see if hot or cold air is coming in. ;) – Kyle Kanos Oct 25 '14 at 12:35
• They have different electricity sockets and power supplies in different countries, but I guess this isn't what you had in mind! – Rob Jeffries Oct 25 '14 at 12:53
• What's wrong with a short Foucault pendulum? – rob Oct 25 '14 at 13:17
• Is a wireless laptop a household item? – imallett Oct 25 '14 at 23:09

# Method 1: Foucault Pendulum

As user Rob asks, what is wrong with a short Foucault pendulum?

There is a problem, but it can be overcome inexpensively, but with some DIY effort at home. The problem is that, by dint of imperfections in the suspending fibre and bob, no pendulum will swing in a plane even if the Earth were not rotating. Instead, the bob will make an elliptical path each cycle (think of this as two vibration eigenmodes in orthogonal planes being inevitably excited by imperfections and asymmetries). As soon as there is any elliptical as opposed to straight planar motion, the ellipse precesses at a rate proportional to its minor axis. The minor axis is always nonzero owing to imperfections and asymmetries and one cannot eliminate these altogether. Therefore, a short putative Foucault pendulum will precess at a rate set wholly by its imperfections, not by the Earth's rotation. The latter is overwhelmed.

The two papers below propose and demonstrate a simple feedback circuit to impose a counteracting force to null out the elliptical motion and keep the motion planar. Using this feedback circuit, a Foucault pendulum of three metres length whose precession is dominated by the Earth's rotation can be built. Experimental results are presented showing that the device can clearly measure the Earth's rotation.

Reinhard A. Schumacher and Brandon Tarbet, "A Short Foucault Pendulum Free of Ellipsoidal Precession"

H. Richard Crane, "Short Foucault Pendulum: A Way to eliminate the precession due to ellipticity", Am. J. Phys. 49(11) 1981

# Method 2: Magnetic Dip

Build your own Dip Circle and measure the Magnetic Dip (see Wiki Page of this name) in your room. With a compass, you know which way North is, so you can tell the sign of the dip. Dip is negative in the Southern Hemisphere, and positive in the Northern.

• The dip method is by far easier to implement in a house experiment. It becomes inaccurate/indeterminate near the equator - but then so would a Foucault pendulum... – Floris Oct 25 '14 at 14:20
• +1 for the "dip". We have a short Foucault pendulum with a feedback circuit and I can vouch it works perfectly. However, I don't think I'd be able to build one in my kitchen. – Rob Jeffries Oct 25 '14 at 18:06
• @Floris: And so would the true answer anyway ;p – Lightness Races in Orbit Oct 26 '14 at 1:50
• @RobJeffries There is a very homemade looking Foucault pendulum at the amateur astronomy club I take my daughter to and it was indeed made wholly by one of the members (though I don't believe in her kitchen). It has a fibre about 1.5 metres long and, although its precession is definitely dominated by the Earth's rotation (the rate of rotation is clearly within a few percent of $2\pi\times \sin37^o$ per day where $37^o$ is my latitude), I have never tested the device's accuracy properly. – Selene Routley Oct 26 '14 at 7:24
• @Floris as you get arbitrarily close to the equator it becomes arbitrarily difficult to determine which hemisphere you're in, by any method (even by consulting a map, or things like GPS). – user253751 Oct 26 '14 at 9:01