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Horological Meandering

You would still need to provide energy to the third barrel

 

If you do that you are just subtracting energy from the rest of the movement, since you are creating more friction by increasing the number of interacting parts.
All of the energy employed with the intent of making the power reserve be longer would actually make it shorter, because of the increased mechanical complexity.
So it would be an overall reduction of the efficiency of the movement.

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