Sand ripples, weights on inclined lines, and birds in flight
Rivers laying down sand, wind-driven ripples, the descent of weights, and a bird's use of wings and tail
A crowded leaf mixing several of Leonardo's favourite themes: the way rivers strip fertile soil and later deposit sand, and how wind blowing across sand raises ripples exactly as water raises ridges on a shallow bottom, which he proposes to test on a board strewn with sand. The lower half turns to mechanics, weighing along which line a suspended weight will descend and at what velocity, and closes with two notes on how a bird tilts its wings and tail to angle itself in the air. A short word-riddle about two brothers who seem to become four opens the sheet. Small diagrams accompany each note: an inclined framework, a funnel, pendant weights, and a bird seen from behind.
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Rivers stripping fertile soil and laying down sand
Rivers of sudden course carry away the rich soils and afterwards deposit sand, when it happens that their beds are being filled up. A companion note concerns the bottom of shallow waters, that is, the shore.
Wind-made sand ripples tested on a sand-strewn board (a, b, c)
Leonardo says he has seen sand moved by the wind behave like silt moved by water on a shallow bottom: as the wind runs from a to b the sand rises a b then falls b c, forming the angle a b c, always equal to the others at the same level, and the same proportion recurs in every following wave. To find the reason he would spread sand two braccia long and an inch high on a board and present it to the wind at varying slopes; a straw or stone in the path breaks a wave into a transverse valley, and a cross-wind makes the straight ridges sinuous.
Along which line a weight descends: oblique m r or median g c
The weight m will move along the line from n toward a, and the weight v along m r; but it is doubted whether v goes by v s, by k r, or by the middle line g c. Leonardo argues that, moving by neither the one nor the other oblique, it will descend the median g c with a velocity of exactly 5 degrees, against 4 degrees on the oblique.
A bird angling its wings and tail in the air
When the bird makes itself oblique with its wings together with its tail, as in the figure above. And when a second bird tilts so that it slides down along the slope of its wings, it twists its tail out of that slope, facing the motion, so that the breast then falls more than the tail.
Word-riddle: two brothers who seem to be four
We are two brothers, and each of us has a brother: here the manner of speaking makes it seem that 2 brothers become 4.