Straight river-beds, river bends, and a bird riding the wind
River-current hydraulics with geometric circle studies and a note on soaring flight
The left folio carries two upside-down columns on the behaviour of straight rivers: why their beds run deepest at the middle, where reflected currents collide and leap up, and why river bends migrate from place to place as the depths shift. The lower left of the right folio explains how a soaring bird rises in circles by taking the wind at its centre of gravity, angling its shoulders up or down as the wind strikes its forehead or its tail. The right half is filled with pen constructions of triangles inscribed in circles, and a brief note fixes a n as the semi-diameter of a circle; a small sketch of two weights hung from a bar appears at the lower left. Further writing on the right half of the sheet is present but not transcribed here.
On this page
Why the beds of straight rivers are deepest in the middle
The current of a straight river is higher and deeper at the centre than at its sides. This happens because the central current is the meeting or intersection of the reflected water: waves rebound from the banks, return to the opposite shore with contrary motions, and, unable to penetrate one another, leap upward and then fall back with gained weight.
Why river bends shift from one place to another
The bends of rivers move because in each place their depths change position. Leonardo adds that water, once it descends into water, no longer weighs and no longer desires to travel toward the centre of the world.
How a bird takes the wind at its centre of gravity
The bird rises in circles by means of the wind, which always strikes it from below along an oblique line. When the wind hits its forehead it lifts its wings and shoulders toward the sky; when the wind hits its tail it drops its shoulders toward the earth, always taking the wind at its centre of gravity, whether ahead, behind, or to the side.
Fixing a n as the semi-diameter of the circle
Among the compass constructions of triangles set within circles, a short caption instructs that the segment a n be taken as the semi-diameter of the circle. It anchors one of the several inscribed-figure diagrams on the right half of the sheet.