ORIGINAL: retransit
As far as Bozarth's deduction that my understanding of physics is wrong, again, why would Great Planes provide a bubble level with their balancer? I know this; when you move the supporting string fore or aft to obtain a level aircraft the point of the plumb bob moves away from its location when the model is hanging nose up or down, This tells me that the CG is moving.
The CG isn't moving. However, you just rotated the plane around it. The top part of the plane, where the bob was originally pointing just rotated forward or aft. The parts of the plane below the CG just rotated the other way.
The plumb bob pointed at the CG the first time and at it when you moved the strings. It's pointing at the CG all the time, but at different things that're in the way whenever you shift the strings.
CGs don't move unless we shift the individual parts of the plane around from one place to another in the plane.