Water rising from reservoirs pressed by equal weights
Notes on discharge time, water displacement, and jet height, with two small reservoir sketches
The notes pose a hydraulic problem about 'bottini' (small reservoirs or cisterns) of equal height but varying width: what proportion the time of descent of the counterweight pressing one reservoir bears to that of another, and how emptying a vessel through its lower spout compares with its upper spout. Leonardo adds the principle that a body entering still water raises on the surface a volume of water equal to its own size, with a caveat for loaded wood or lead. He then states two proportional rules relating the heights to which water jets rise from equal pipes to the sizes and widths of the reservoirs pressed by equal weights. Two small labelled sketches of reservoirs stand at the upper left.
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Discharge of reservoirs and height of the rising jets
Leonardo asks what proportion the time of descent bears when reservoirs of equal height but various thickness are pressed by counterweights, and how pouring through a lower versus an upper spout affects filling time. He then gives proportional rules: the heights to which waters rise through equal pipes from reservoirs pressed by equal weights match the proportion of the sizes, and of the widths, of the opposite reservoirs.
A weight entering still water displaces its own volume
Every weight that enters still water throws up, or raises on the surface, as much water as its own size, provided the weight itself is of water. If instead it is loaded wood or lead, Leonardo notes, there is variation.
Two sketches of 'bottini' (reservoirs)
At the upper left of the sheet are two small labelled sketches of bottini, the reservoirs the notes discuss, drawn as tall vessels of differing width. They illustrate the compared cases of equal height and varied thickness referred to in the text.