### Compton's Water Based Foucault Pendulum

A further review of the article[1] I mentioned yesterday, (Dr. Tatum on the Coriolis effect as a navigational aid for birds), turned up a very interesting reference to Arthur Compton of Compton scattering fame (picture 1)!

It turns out that Compton built an apparatus in 1915 at Wooster University, (now Wooster College) that accurately measured the rotation speed of the Earth allowing Compton to determine the length of a day, his latitude and longitude all without any astronomical references.  It was a sort of Foucault pendulum constructed with a tube of water.

To read all about Compton's apparatus and method in Scientific American, go to [5]:

or in the blog version of this post, just scroll to the bottom of the post for an embedded version of the article.

Picture 2, below, shows a simplified version of Compton's apparatus sitting directly on the axis of rotation of the Earth.  Here's the basic idea.  The circular tube is filled with water and the tube is rotating along with the Earth.  After some time, the rotational speed of the water will match the rotational speed of the tube and there will be no relative motion between the two.  At this point, flip the tube over 180 degrees.  The water will tend to keep rotating in the direction it was going in while the tube will now be moving in the opposite direction.  By measuring the speed of the water, you get a measure of the Earth's rotational speed.

Big deal you say.  A Foucault pendulum can give the same results you say.  Well, as it turns out, it has a few drawbacks with respect to Compton's apparatus.  Consider the case where either apparatus wasn't sitting at the Earth's pole.  Then, you only get a measure of the Earth's rotation with respect to the axis of rotation perpendicular to the horizontal plane at your location.  With a pendulum, you're done.  You can show that the Earth  is rotating, and knowing your location on the Earth, and making an assumption about the Earth's axis of rotation, you can determine how quickly the Earth is rotating.  The annoying part, however, is making that assumption about the Earth's axis of rotation.  With Compton's apparatus, you simply make two more measurements.  Your second measurement is made with the plane of the ring perpendicular to the horizontal plane at your location.  Then, you merely rotate the tube 90 degrees while still keeping it's plane perpendicular to horizontal.  You now have three perpendicular components of the Earth's rotational speed and can re-construct both the Earth's total rotational speed and the direction of the axis of location.  Compton's results are reported in the Scientific American article and shown below in picture  3:

Compton's article in Scientific American:

References:
http://www.jstor.org/discover/10.2307/4085812?uid=3739920&uid=2&uid=4&uid=3739256&sid=21101730076791

2.  +American Physical Society's Physical Review article on Compton's apparatus
http://prola.aps.org.lib-ezproxy.tamu.edu:2048/abstract/PR/v5/i2/p109_1
DOI: 10.1103/PhysRev.5.109

3.  Science Magazine on Compton's apparatus
http://www.sciencemag.org/search?submit=yes&volume=37&firstpage=803&journal_search_volume_go.x=-258&journal_search_volume_go.y=-370&journal_search_volume_go=go&andorexactfulltext=and&andorexacttitleabs=and&andorexactfulltext=and&andorexacttitleabs=and

4.  Compton biography
http://www.sciencedirect.com.lib-ezproxy.tamu.edu:2048/science/article/pii/0360301681900900

5.  Free Scientific American article

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Kids R Kapable

Just a little note to concerned ‘grownups’ everywhere.  If you look at a kid—and I mean really look—I don’t mean notice a person shorter than you, I mean make eye contact, notice their facial expression and observe their body language—If you look at a kid, don’t assume they need your help unless they’re obviously distressed, or ask for it.  You might think this is difficult call to make.  You might think, not having kids of your own, that you’re unable to make this determination.  You are.  You do in fact, already have the skills even if you’ve never been around kids  It’s a remarkably simple call to make, just use the exact same criteria you would for determining if an adult was in distress.  Because, guess what, kids and adults are in fact the same species of animal and communicate in the same way.  Honest.  If someone—adult or child—doesn’t need your help, feel free to say hello, give a wave, give a smile, but don’t—do not—try to force help on anyone that doesn’t want or need it.

Y…