On the Motion and Measurement of Water

LEONARDO DA VINCI 279

...from the top of which a river descends, and it runs down to the depth of its sphere. This water can descend along the straight line (fig. 5, plate I) CON, and along the curved line ABC. Because its height from the Center of the World N is greater along the line CN than along AN, or along ON. And the same applies to the curve, which is higher at CN than at BN, or at AN; thus, one concludes that it is not necessary for the water's path to be more curved than straight, etc. Leonardo is arguing that gravity—the "pull" toward the Center of the World—is the primary driver of water's motion, regardless of whether the path is a straight incline or a curve following the Earth's arc.

CHAPTER XII.

The question is asked whether a river, in passing through a lake, disrupts the uniform distance that the surface of such a lake had from the center of the World before the aforementioned river passed through it (fig. 6, plate I). This is a fine question; and you will show that such a surface does indeed ruin that uniform distance from the center of the World to make room and passage for the said river, based on the fourth [principle] of this work, which shows that water does not move unless it descends.

And here one must understand if the outlet of such a river has a width similar to its entrance. If it does, then it is necessary that such water has a uniform flow, as according to the 39th [proposition] of the 8th [book]; which says that the motion of every river, in an equal amount of time, delivers an equal weight of water in every part of its length. Now, if the river brings in water that requires a drop of one cubit braccio: an Italian unit of measurement, literally meaning "arm," roughly 23 inches or 58 centimeters per mile, and the width of the outlet is equal to the width of the entrance as stated, it is necessary that the entire river passing through the lake also has a drop of one cubit per mile. Consequently, the surface of such a lake will be at varying distances from the center of the World. And the water will have such a course: that part of the lake water will have the slowest motion which is found furthest from the shortest line connecting the entrance to the exit of the river passing through that lake. Leonardo correctly observes that for water to flow through a body of water, there must be a slight slope or pressure gradient, meaning the lake is no longer perfectly "flat" or equidistant from the Earth's center.

CHAPTER XIII.

The sphere of water increases and decreases, perceptibly or imperceptibly, according to the greater or lesser, more universal or less universal floods of water returned to that sphere by the water of rivers, and rains, etc.