Bouncing balls equal free flight; the fall of water
An experiment measuring a marble's bounces against a marked staff, and the speed of falling water
Leonardo argues that a hard sphere driven with a given force travels as far through a series of bounces on smooth stone as it would thrown freely through the air (the ball a reaching c in flight and b by bouncing), and turns this into a rapt address to the "Prime Mover" whose order lets a blocked motion recover its full "voyage" by rebounding. He proposes a careful experiment to test it: throw a glass marble onto a stone floor beside a tall staff marked with colours, and have observers note the colour each bounce reaches. Two closing propositions on falling water hold that a stream descending nearer the vertical strikes with greater force, and that a stream near its fall begins to bend at the surface first.
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Bouncing travels as far as free flight
Any spherical body with a dense, resistant surface, moved by an equal power, makes as much movement through bounces on hard, smooth concrete as when thrown freely through the air. The diagram shows a single ball a whose path reaches c through the air and b by bouncing.
Address to the Prime Mover on the recovery of motion
Leonardo praises the justice of the Prime Mover, who ordained that when a power meant to thrust something a hundred braccia meets an obstacle, the blow generates new motion whose successive bounces recover the entire proper voyage. Measured, the bounced path equals the length the thing would travel thrown with the same force through the air.
Experiment with a glass marble and a marked staff
Throw a little glass marble onto bare flat stone beside a long staff marked with various colours; observers note from a distance which colour the marble reaches at each bounce. Fix the staff at top or base so no hand blocks the view, and make the first bounce between two right angles so the marble always falls in the same place; then throw the marble in free flight with the same power and measure to find the second voyage matches the first. Labels b, a and c.
Water falling nearer the vertical strikes harder
Water falling by a line closer to the perpendicular descends more rapidly and delivers a greater blow and weight to the place it strikes. The diagram of a waterfall from brink m shows descent angles n, o and p.
A falling stream bends first at its surface
For any course of water close to its fall, the downward bending begins on the surface rather than on the bottom. A sketch shows a waterfall beginning its bend through the air and striking the surface at about forty-five degrees.