Bellows, Steelyard and the Mechanics of Lifting Arms
A steelyard equalized by a wheel, an oil-filled bellows, and the economy of small descent
Two mechanical diagrams at the upper right show a steelyard fitted with a wheel and a bellows-driven lifting device with a U-shaped conduit. Leonardo argues that the arms of a steelyard stay proportionate at every angle unless a wheel keeps the shorter arm from shrinking, and he insists the bellows be filled with oil rather than air or water. The main column analyzes the paired arms K a and K b, showing that a small descent of the load carries little material but preserves the balance's power, so one should make the load large when its descent is small. He grounds the reasoning in his 'fourth of the weights' about balance arms in angular conjunction at their pole.
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The steelyard arms and the equalizing wheel
Leonardo states that the arms of the steelyard stay proportionate through every degree of obliquity. This equality fails, he notes, only where a wheel is introduced, as here, because the wheel never lets the shorter arm diminish.
Why the bellows must be full of oil
The bellows, he insists, must always be full of oil and never of air or water. Air is condensable and rarefiable, water makes things rot, but oil does neither; oil only freezes, and even that if it is not kept underground.
Balance arms K a and K b and the value of a small descent
When arm K a is at c, arm K b is at d; as K b descends to K f, K a rises to K e. The smaller the motion, the less material m carries up, so the load must be made larger when its descent is small; the long arms then overcome the inequality generated in the balance b K e a K.