Weight on a Wheel, Clock Timing, and the Shape of a Plunge Pool
How a weight's distance from the axle slows a wheel, and why falling water hollows a quarter-sphere
Two notes accompany a small circular diagram at upper right and sketches of falling water at lower right. In the first, Leonardo states that the further a heavy body is fixed from a wheel's centre, the harder its revolution becomes even with an unchanged mover, and that this is why moving a clock's balance-weights nearer or farther from its middle lengthens or shortens the hours. In the second, on three figures of waterfalls, he claims the plunge pool that receives falling water takes the form of a quarter of a concave sphere in uniformly resistant ground, because the central water runs higher and faster and so carries its fall further than the slower water at the sides.
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A weight far from the axle resists rotation
The more remote from the centre of the wheel the heavy body a is attached, the more difficult the revolving motion of that wheel around its pole becomes, even though the mover does not change.
Regulating a clock by the position of its weights
The same principle governs the balance [tempo] of clocks: setting the two weights nearer to or farther from the middle of the balance makes the hours shorter or longer.
A plunge pool shaped like a quarter-sphere
The depth that receives a waterfall always takes the figure of a quarter of a concave sphere where the ground resists uniformly. This follows because the straight course of the water is higher and faster in the middle than at the sides, so the faster central water throws its fall further forward.