On the bending of springs; tempering iron; dragging loads
The convex side stretches, the concave compresses; centre of force and gravity
Headed 'On the bending of springs,' folio 84v argues that when a straight spring is bent its outer convex side rarefies while its inner concave side condenses, the change working pyramidally so that the middle of its height neither grows nor shrinks but behaves like a balance. Adjacent notes on ironwork explain how to make iron soft by slow heating and cooling under ashes, that red-hot iron is longer than cold, and that a tightly bent spring-iron is harder toward the centre of its curve. A second thread, 'On dragging,' treats how a long body being hauled cannot match its mover's speed until its central line aligns with the line of force, defining the centre of force, of weight, and the central line. Small lettered diagrams (a, b, m, n, r, o and d, b, c) illustrate the motions and cords discussed.
On this page
Why a bent spring stretches outside and compresses inside
In bending a straight spring, its crown (convex side) must rarefy and its hollow (concave side) condense, the change working after the manner of a pyramid. In the middle of the spring's height there is never any change: as much as the sides draw near at the bottom, so much they draw apart at the top, like a balance.
Softening iron and the hardness of a tightly bent spring
Iron to be made soft is heated by itself and cooled slowly in the same fire under ashes. Red-hot iron is longer than cold iron, and a thin tempered spring-iron bent into the smallest circle is harder toward the centre of the curve, where it condenses, than toward the outer ends, where it rarefies.
Dragging a long body: aligning it to the line of force
A thing of long shape that is dragged never moves as fast as its mover unless its whole central line is first aligned to the centre and path of the force that draws it. The note proposes to define the centre of force, the centre of weight, and the central line.
Comparing the motions at a and b about the pole n
The motion made by a equals that of its mover m, but b's motion is never as swift, save when its mover n is brought to the height of r or the lowness of o. The pole n, Leonardo warns, is unfastened.