River meanders eroding valleys, with mills and a weight
Why mills fail on tidal shores; how winding rivers widen their valleys
The left leaf opens with a note that mills cannot be built in ponds or on the sea because storms fill their shore-canals with sand, and beside a lettered figure it works out a weight problem in which descending weights 2 and 4 move a body b through proportional spaces toward f and g. The right leaf is filled with a series of closely related observations on how the winding courses of rivers strike and wear away the roots of the mountains, rebounding from one side to the other and, over long time, widening, lengthening and deepening their valleys. Faint diagrams of ripples, a spoked wheel and small mechanical sketches accompany the text. Further untranscribed writing is present on both leaves.
On this page
Mills cannot stand on tidal or sea shores
Mills will not be built in ponds or on the sea, because the storm fills with sand every canal that is made along their shores. A terse note on regulating by rule follows.
Descending weights 2 and 4 move body b
If a weight 2 moves b to f by descending to c, then a weight 4, descending to d, will move b through twice the space b f, so that it reaches g. The reasoning ties the fall of the driving weight to the distance the moved body travels.
Winding rivers strike and wear the mountains' roots
The courses of rivers wind through the widths of their valleys from one mountain to the opposite one, striking and consuming their roots. The wave they make follows the flight of the water and, if unimpeded, seeks out the whole length of the valley over time.
Meanders widen, lengthen and deepen valleys over time
Striking one bank and rebounding to the other, the sinuous current makes the banks themselves sinuous and moves along with the river. With length of time it seeks out the whole valley, increasing its depth, width and length and beginning the same process again until the lateral mountains are worn away.