Pressure in Bellows: Equal Distribution of Enclosed Air
A heavy weight on a stack of vessels and holes, and why wind pushes equally on every wall
Three linked demonstrations reason about how a heavy weight pressing on a system of bellows, vessels and holes transmits its force. Leonardo computes that a hole entering the vessel 100 times feels a hundredth of a 100,000-pound load, and that through successive stages the force at the last hole falls to 1/8 of an ounce and 1/3; he argues from the inflating of balls and bellows that enclosed wind pushes equally on every wall through equal openings. A second figure offers a rival calculation, which he marks as false yet worth debating. Cylinder-and-bellows diagrams run down the right margin.
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Weight transmitted through stacked vessels and holes
If weight m is 100,000 pounds and hole n at the bottom of vessel a enters 100 times, the hundredth of the load bears on it as 100 pounds; through the stages the force on the last hole p drops to 1/8 ounce and 1/3. The enclosed wind, he reasons, pushes equally through every resistance, as seen in inflating balls and deflating bellows.
Smaller bellows drives its wind with greater impetus
For a cylinder whose hole n enters the whole bellows ten thousand times, one pound exerts force at n. Among bellows of various sizes but equal nozzles, pressed by equal weights, the one of smaller figure will drive out its enclosed wind with greater impetus.
Rival demonstration proposed for debate
In the analogous figure the hole m enters a hundred times, so ten thousand pounds press with 100 pounds at m. If the middle reservoir fills and empties with equal fury through equal-sized holes, this statement is true and the one above false — yet he offers it for debate.