Percussion, Resistance and the Powers of Ten
Ballistics of the pop-gun ball, the thread of equal resistance, and a scale of tenfold numbers
A page of physical propositions built around percussion and resistance. Leonardo defines the natural plane against the mathematical plane, argues that every blow struck in water or air spreads out in the form of a sector, and studies the ball of a pop-gun (scoppietto) driven through cloth or a wine-jar by the air shut in behind it. A long numbered scale running one to thirteen sets out the powers of ten up to a thousand millions, feeding a note that a ball driven by a million of millions of degrees of force is reduced to unity after passing twelve cloths; at the lower right two fish and a bow-and-arrow illustrate the paradox of the thread of equal resistance that should never break.
On this page
A blow in water or air spreads as a sector
Every power of percussion delivered within water or within air goes on dilating in the form of a sector through that medium. It is a general rule for how impact propagates outward.
The thread of equal resistance never breaks
A thread of equal resistance throughout will never break; to test it Leonardo would tie a hair between two oxen pulling in opposite directions. He argues the hair must be made as much thicker at the middle as its position there makes it weaker, so that it would all fly to powder at once rather than snap in one place.
The pop-gun ball and the air enclosed behind it
When the ball of the scoppietto passes through the wine-vessel, the air that drives it is shut in behind it; at a the ball has a power of one moving toward the centre of the world. A companion note argues a wave of air cannot drive the ball through the iron barrel unless it is denser than the ball, in which case the ball shatters.
A scale of the powers of ten
A ruled scale numbered 1 to 13 lays out the powers of ten from 10, 100, 1000 up through a hundred millions and a thousand millions. It provides the numerical ladder used in the adjacent ballistics note.
A ball reduced to unity after twelve cloths
Point a is one, born from a million of millions after passing through twelve cloths. In twelve braccia of space a ball moved by a million of millions of degrees of power is reduced to a single unit once it has passed a.
The natural plane and the mathematical plane
The natural plane is one whose every part is of equal height, met by a straight line only at a point; the mathematical plane has parts of unequal height, and a straight line touching its extremities touches it entirely. Their junction is made at a single point.