Weights and gravity, shore waves, and a crossbow's true range
Mechanics of the balance and seat of gravity on 39v; waves, basins and ballistics on 36r
On 39v Leonardo reasons that a balance shortens its "potential arms" as it nears the centre of the world, that air grows thinner nearer the heat that warms it, and that the seat of gravity lies not in the heavy body but all along its support (frame n m o p about the world-centre s, with weights c and d). On 36r he turns to water: waves striking an oblique shore lose depth, drag sand seaward and are thrown back by the returning wave, while basins empty and fill in turn; a separate note explains that the true range of a crossbow can only be known from a high vantage (a b c). Lettered diagrams accompany each argument, and further untranscribed sketches (including a feather- or bird-like form) appear on 36r.
On this page
A balance shortens its arms near the world's centre
One and the same balance shortens its potential arms the nearer it draws to the centre of the world; and, by analogy, air becomes the more rarefied the nearer it draws to the heat that warms it. The demonstration is left incomplete beside the figure.
The seat of gravity lies along the whole support
Gravity is not seated in the heavy body but entire throughout the whole length of its support and in every part of it. With the world-centre at s and a uniform frame n m o p, equal weights c and d hung at a and b stay balanced until the lengths of their pendants are varied, when the bodies cease to be equidistant from the world-centre though their weights remain so.
Waves on an oblique shore and the movement of sand
A wave reaching an oblique shore always loses depth; the wave that flees the shore washes and carries sand back, and on meeting the oncoming wave is thrown back with its sand, so the sand does not spread into the second wave. The wave covering the shore is thus made turbid by the sand taken from the returning wave before it.
Finding the true range of a crossbow
It is impossible to know the true range of a crossbow unless you are in a high place when you release it. The figure a b c shows the true way to know it, since the range cannot be judged where the arrow does not fall in a straight line and remain fixed in the same direction.
Basins that empty and fill
A fragmentary note beside a lettered figure describes an upper basin emptying into another and filling in turn, and a channel that does not pour over. The passage survives only in pieces but concerns the emptying and filling of connected water basins.