I'll call your bluff tw! I think your answer while it maybe the form of calculation is not the reason for the variable inductance...

Let me share the cross over of physics and electronics that is going on here (based on what you imply is happening, resonance and gas production). Meyers used frequency presets for his input, he had set frequencies to work with. Variable inductors are easier to make than trimmers and pots(this point is important, especially for the KISS part). His whole cell and electronics is designed to resonate. We all know the LC Resonance calculations. So his inductors then capacitance cell is in a LC circuit.

Have any of you measured the capacitance of your cells when they are immersed in water verses when they are empty? You will find there is a dramatic difference. So how do we ensure that resonance continues when our capacitance changes?

You can adjust circuit frequency, inductance or capacitance. He had set frequencies, so he needed to bridge the steps in frequencies. I would say he did the calculations for his cell (based on capacitance) and then made his inductors. Realizing how wide the range is on a variable inductor he more than likely only needed one in his circuit to bridge out the frequecy steps. This would also be why he stated that the gap in the cell could be changed also. Change the gap size to adjust the cell capacity to ensure resonance. Covering all 3 variable to maintain resonance in patents meant no technical work around.

So yes you are right, partially. There is a relation between the cell dimensions and the variable inductor. Your answer is far more complicated than it needed to be and is a bit backwards. The inductance/frequency range needs to accommodate the cell from 0 production (full capacitance) to full production (lowest capacitance).

The unfortunate thing is that a cell full of H2 O2 is not the same capacitance as air. Something else to consider is a moving dielectric has different properties to a stationary one.

Having 2 inductors in a resonant circuit won't turn a signal from square to analogous. A transformer will though.

Stans system is different from AP's in every way except concept and working principal... As their origins and original purpose were different. AP's came from observations from his experiments on his own line in health and well being, more accidental. Stan, I would say, didn't want anything to do with the rest of what AP was doing so took the PRINCIPAL and the PROCESS of what was happening and made something that did only that. One small part in what AP's machine can do. (instead of using a bus to get yourself to and from work you take the principal and concept and take a car

bad link but simple)

What you have done is dictated the dimensions and thus capacity range of Stans cell based on the information you aquired. What i have done is shown you how to know what inductor you need for your already made cell...