A Thinning Stream of Liquid Divides as It Falls
Why a falling liquid grows longer and thinner and finally splits into branches
Leonardo reasons that as a falling liquid of a given weight grows thinner it meets less air resistance and so speeds up, which in turn makes it longer and thinner still, so that in principle it would accelerate without limit. To prevent this, nature (or rather necessity) makes the descent become pyramidal and then form intersections, exchanging its extremes from right to left so that the stream begins to divide. The farther it falls the more it divides, and through these many ramifications it grows lighter and its disordered motion is retarded. The argument extends his study of continuous falling matter begun on the preceding folios.
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A thinning body speeds up without limit unless it divides
As the same weight of liquid becomes thinner it meets less air resistance and gains velocity; being faster it grows longer and thinner still, so that it would accelerate to infinity. Necessity therefore forces the stream to divide, and through its ramifications it becomes lighter and its disordered motion is slowed.
The pyramidal stream makes intersections and branches
As soon as the descent begins to become pyramidal it makes intersections, exchanging its extremes from right to left, and begins to divide. The farther it descends the more it divides, breaking into many ramifications.