Water waves, reflected light rays, and a well-bucket hoist
Wave mechanics, mirror reflection, geometry, and pulley devices, with a note to query Lorenzo de' Medici
The two folios interweave the physics of water waves with the geometry of reflected light. On the left folio Leonardo works from the definition of the circle through two triangles to the problem of finding the incident and reflected ray on a spherical body, concluding that the true length of such rays on a mirror of any shape cannot be found; a further note argues that equal motions appear slower the farther they lie from the eye. The right folio treats waves raised by the wind, the collision of incident and reflected water where sediment settles, and where the crest of a wave truly stands, alongside a well-bucket (sechia) hauled down and up by cords n and m and several pulley trains. A memorandum reminds him, on meeting Lorenzo de' Medici, to ask about the water treatise of the Bishop of Padua.
On this page
Waves raised by the wind and where their crests fall
Among wind-driven waves, the most prominent is the one nearest to the water returning backward; the action of moving water on still air mirrors that of moving air on still water. Elsewhere the crest of wave a b falls because it strikes the air that presses upon it at n a and m b.
Incident and reflected rays on a spherical body
Given the point of luminous incidence upon a spherical body, it is possible to find the line of the incident ray and that of the reflected ray, as at the point a on the circle and a c. Yet on a mirror of any shape the true length of the incident or reflected ray at the given point cannot be found.
A well-bucket lowered and raised by cords n and m
The bucket's descent is quick and worked by cord n; its return upward is fast and pulled by cord m. In the companion figure the descent pulled by n is slow while the bucket's return pulled by m is fast.
Two triangles and the construction of the two circles
Leonardo sets down two triangles governed by the definition of the circle, then makes the greater circle and places the lesser one so its centre touches the greater's circumference at a. Lines a g and a f are drawn so that b e and d c are equidistant.
Why nearer motions appear faster to the eye
Among things of equal movement, the more distant seems slower and the nearer seems faster. Motion n m, being nearer to the eye by 4/5 than the equal-time motion d e, will appear faster than it by 4/5.
Where incident and reflected water contend
At a b the incident water a b m contends with the reflected water n a b, and there sediment settles, because the colliding waters slow their motion and rise less, their motions being interrupted.
