One of the departments at work is moving offices around, so there are piles of junk in the hallways, some of it cool, most of it not.

One thing I picked up was a Gerber Variable Scale, invented by H. Joseph Gerber as a more elegant solution to an engineering problem that had originally required the use of his pyjama elastic.

The main feature of the scale is a spring with a triangular cross-section. On the window side, the coils are painted white, except that every fifth coil is painted alternately red and yellow. The spring can be extended by means of a slider. In effect, this gives you a ruler where you can adjust the spacing between marks.

Beneath that, there are three scales: one showing the length in inches of the spring, one giving the number of coils per inch, and another giving the log_{10} of the length of the spring. This can be used to solve various problems.

One obvious application is if you want to measure distances on a map. With a conventional ruler, you’d have to measure the length in centimeters, then multiply by the map scale (number of kilometers per centimeter). With the variable scale, on the other hand, you can simply extend the coil so that the distance between two red coils corresponds to 1km at the map’s scale, and read the measurements right off the map.

Or let’s say that you’ve drawn a line segment and want to subdivide it into three equal segments. Simply extend the spring until the full segment is 9 red segments in length, then make tick marks at the 3^{d} and 6^{th} red segment.

And just today, I ran across an article over at Bad Astronony that showed a photo of Uranus with a scale bar showing 32,000 km. Phil’s text says that the Earth is 12,800 km across, but this isn’t shown on the photo. I bet this variable scale can show 12,800 km at the same scale.

I can see I’m going to have to spend some time RTFMing.

Those are really neat. My dad has one from his days in college working for his masters in Mechanical Engineering.