River flow, waves and the wearing of banks
Width and velocity, waves reared against rocks, a lettered channel, and a note on balances
Five studies of moving water and weight. The writer states the principle of continuity — widening or deepening a river slows its course in exact proportion, since entrance equals exit — and examines how a falling stream bounces at equal angles and how waves rear into 'humps' against rocks but run smooth over a fallen column. He notes that a furious current striking still water swings to the transverse sides and gnaws the banks, and counsels levelling the bed; a lettered cross-section argues the course m a c b runs swifter than the shorter m b. Beside sketches of balances he adds that two nearly equal weights cannot topple a beam, and a crossed-out line in the corner begins a personal wish, 'if it were granted me to return...'
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Width, depth and the velocity of a river
However much a river is widened, its velocity diminishes in proportion, because its entrance equals its exit: a channel one braccio square running one braccio per time becomes half a braccio per time at two braccia square, a quarter at four. Water falling on an oblique line makes equal-angled bounces and waves whose particles differ with the unevenness of the gravel.
Waves on rocks and the wearing of banks
For the lettered course m n — a b: a wave striking rock a crests at n, and striking rock b crests at m, so a wave fills with humps of differing size; a fallen column would leave it smooth. A furious current meeting still water swings to the transverse sides, drives against the bank and consumes it — so level the course and fill the low places.
A narrowed channel runs faster: a c b versus a b
For the section m a — c b: if the bed is as narrow as the falling water, line c b runs as strongly as a c, because c b has free flight at b and must swiftly clear to make room for the oncoming water. The course m a c b runs swifter than the shorter m b, driven by the blow of a c. He also records the objections that mountain waters rise from greater mountains, or that the sea is higher than the mountains.
Nearly equal weights will not topple a balance
It is impossible that weights placed at the ends of a balance and exceeding one another by only a small part should make the beam tip along a perpendicular line — that is, should carry the greater weight beneath the centre of the balance.
A crossed-out personal line
In the upper-left corner, struck through, a fragment begins: 'In truth, if it were granted me to return...', trailing off with what appear to be the starts of names.