Micron-level accuracy over a meter?

Yep. That's what I missed the first time. I didn't expect that calibrated clocks would be set up at the measuring locations.
OK! So why is it important that the Kater pendulum is a "ideal pendulum?" Could you not just use a simple pendulum and check it's period against the calibrated simple pendulum? Maybe it's because a compound pendulum would be affected by gravity a little differently? That could create accuracy issue with the computation of g? Sorry to drag this out! I know you want to get to the actual machining!
 
For an ideal pendulum, calculating g is easy, from T=2*Pi*sqrt(L/g), where T is the period and L is the length.

For a hundred years or more, people tried to make a conventional pendulum that was good enough for that equation. Use as frictionless of a pivot as you can (e.g. a knife edge), a long and very thin yet non-stretchable rod or wire, a very dense and heavy bob that is in a simple shape such as a sphere, and so on. But it just wasn't good enough for those 6 digits of resolution.

Kater's pendulum doesn't magically become ideal, but it's a configuration that mimics an ideal pendulum sufficiently for a similarly-simple equation to work (see the wiki page on it).
 
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When I worked as a student assistant in the Physics Dept. of the university I attended, one of the first assignments that I had was to make a drive for the Foucault pendulum that was a centerpiece of the new Science building.

The pendulum was mounted on the rooftop about 40' above and had a hollow cast aluminum sphere about 20" in diameter filled with lead shot. There was a 24 hour clock dial below the bob and the bob had a small cone attached for a pointer. It was suspended from a steel cable about 3'16" in diameter and the pivot was a 1/2" drill chuck. The intent was to detect when the bob passed through center and fire a Helmholtz coil which would give an impulse to a second drill chuck located about 10" below the pivot to make up for the energy lost due to drag.

Because the Earth rotated under the pendulum, a simple photocell, triggering when the cable passed through center couldn't be used. I eventually made a fine wire whisker which was fastened to the end of the pointer , along with an aluminum disk at the center of the dial and insulated from the dial to detect the center crossing. I also added an iron core to the coil and we had a working pendulum drive. It was still working many years later when I paid a visit.

I don't recall that I had calculated the period from the known length but I almost certainly did. That was 55 years ago.
 
As a child, I loved the Foucault pendulum at the Smithsonian. I think they removed it about 20 years ago. Such a cool exhibit.

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