The Reasons of Motive Forces

Book One,

A rectangular ornamental woodcut border featuring floral and scrollwork patterns.

THEOREM VI.

Hero’s Spiritalia, Theorem 36. original: "Herone spiritali 36. Theore." This refers to Hero of Alexandria’s Pneumatica, a foundational Greek text on pressurized air and water machines.

THE fourth means of making water rise is by the aid of air, and I will also give an example of this through Hero’s machine, which is of a very elegant and ingenious invention. Let there be two vessels marked A and B, well closed and soldered on all sides, and placed one above the other according to the distance one wishes to make the water rise; and three pipes, C D, E F, and G H, shall be soldered to the said vessels in the following manner. Let C D be soldered through vessel A, in such a way that the end C passes through the top side of the said vessel, and the end D shall approach the bottom of vessel B as closely as necessary to allow the water to pass. Afterward, let the pipe E F be soldered with the end E on the top side of vessel B, and the end F shall approach the top side of vessel A as closely as necessary to allow the air to pass. Let the other pipe G H be soldered through the top side of vessel A, so that the end H is only as far from the bottom of the vessel as is needed to let the water pass. There will also be a vent hole marked I, through which vessel A shall be filled; afterward, it must be well stopped, and water poured into the small recipient A basin or funnel-like container. above vessel A. This water will descend through pipe C D to the lower vessel; which, being sealed on all sides, the air can only escape through pipe E F to go to the upper vessel; and being unable to escape further, it will push the water through pipe G H, which will fall into the small recipient, and descend through pipe C D. This movement will continue as long as there is water in the upper vessel.

A technical woodcut illustration of the hydraulic machine described. It shows two stacked rectangular tanks (A and B). A funnel-like basin sits atop tank A. Various pipes (labeled G, H, I, C, D, E, F) connect the tanks and the basin. Water is shown pouring from pipe G into the top basin, creating a continuous fountain-like cycle.

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I thought it would be well to demonstrate the height to which the preceding machine raises its water, especially since those designed in the books of Hero and Cardano Girolamo Cardano (1501–1576), an Italian polymath who wrote extensively on mechanics and mathematics. cannot throw their water upward when the upper vessel is nearly empty, because the vessels are joined to each other without any distance between them. Therefore, when the said machine begins to run, the water descending through pipe C D will cause that of the upper vessel to rise (in pipe G) from H to L, because the said distance is equal to C D. But when the vessel is nearly empty, then the height of the water in pipe C D will not be so great, for the lower vessel, being nearly full, shortens the said height by the height of the said vessel; and the upper one, being nearly empty, lengthens the height of pipe G. Thus, subtracting the thickness of the two vessels, the water will rise to point M when the machine comes to fail.

A simplified schematic diagram of the same hydraulic system, illustrating the vertical heights and pressures. Points are labeled A, B, C, D, E, F, G, H, I, L, and M along the pipes and tank levels to show how the pressure changes as the water levels shift within the tanks.