Making Scales for Reading the Azimuth and Amplitude

The concept of the scales for reading off the azimuth and amplitude of the paraconical pendulum is straightforward, if it be remembered that A PARACONICAL PENDULUM HAS NO CENTER! so that no bottom dead center can be assumed.

You print something like the following on a piece of stiff cardboard or the like, for the bottom layer (it could be more sophisticated):

Then you print an image like the following for the middle layer. You should either print it on transparency plastic, or lop off the white bits at the left side. Note that the relative scale has not been preserved in these web images; you will have to make your own versions.

And if you want to monitor the amplitude of the oscillations of the pendulum - which usually you do - you print an image like the following one for the top layer. Of course you must ensure that the scale is correct.

Then you push a drawing pin through them, all together in order through the cross marks, and pin them down to your underlying table. Note: you are not trying to get the drawing pin directly under the bob; rather, it should be about 12 cm behind the position directly under the bob. And you glue the bottom layer down - the exact angular position of the zero is not important - while leaving the middle and top layers to swivel freely:

With the top scale swung out of the way, you measure the azimuth by sighting the pendulum pointer against the parallel lines of the middle layer and swiveling that layer around the drawing pin until the pointer is running true. This is very easy and can be done very accurately; a little knob glued at the corner of the second layer helps. Then you just read off the azimuth value. No center is involved!

When you want to read the amplitude, which may not necessarily be every time you release the pendulum, you just swivel the top centimetric scale around the drawing pin, back into place along the line of swing, and - from the side - read off the maximum swing amplitude at each end of the pendulum's path. Again, this can be done quite accurately.

Until we get electronic instrumentation rigged up, this will be quite satisfactory. I think it provides results just as accurate as those Allais achieved. We didn't even try to measure the minor axis of the ellipse, because I have no confidence in being able to read off such sub-millimetric values from a moving target simply by eye - whatever Allais may say.

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