The true ounce of water: flow from spouts at different heights
A vessel with five openings and the proportion of discharge to the head of water above
Under the heading 'Quantity of the true ounce of water,' Leonardo studies a vessel with five openings, a b c d e, each throwing a jet. He argues that the quantity discharged through a given spout in a given time matches the height of water standing above it, so opening c pours twice as much as b because it bears twice the weight of water. He distinguishes water, of indefinite length, from a dense solid falling through air, which must open the resisting air before it. A marginal calculation works the proportions in numbers: when the head a b is removed, spout c loses half its power, dropping from 6 to 3, while spout d loses a third, dropping from 9 to 6.
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Discharge is proportional to the head of water above the spout
For water kept at an ordered height, the quantity poured through a given spout in a given time follows the height of that spout. Spout c pours twice as much as b in the same time, because c has twice as much weight of water above it. A tall vessel with five openings a b c d e stands at the upper right.
Why water differs from a dense solid falling through air
Water striking the air makes a continuous hole in it, whereas a dense compact body descending through air must open the air before it, which resists and condenses, so it does not yield passage as freely as it does to water of indefinite length.
Numerical loss of power when the head a b is removed
Removing the height a b, spout c of power 6 is reduced to 3, losing half, while spout d of power 9 is reduced to 6, losing a third, because a b enters three times into a d. Thus c loses the half and d the third.