The rapidity of running waters does not exactly, nor even nearly, follow the proportion of the declivity of their channels. One river whose inclination is uniform and double that of another, ought, according to appearance, to flow only as rapid again, but in fact it flows much faster. Its rapidity, instead of being doubled, is sometimes triple, quadruple, &c. This rapidity depends much more on the quantity of water and the weight of the upper waters than on the declivity. When we are desirous to hollow the bed of a river, we need not equally
distribute the inclination throughout its whole length, in order to give a greater rapidity, as it is more easily effected by making the descent much greater at the beginning, than at the mouth, where it may almost be insensible, as we see it in natural rivers, and yet they preserve a rapidity so much the greater as the river is fuller of water; in great rivers, where the ground is level, the water does not cease flowing, and even rapidly, not only with its original velocity, but also with the addition of that which it has acquired by the action and weight of the upper waters. To render this fact more conceivable, let us suppose the Seine between the Pont-neuf and Pont-royal to be perfectly level, and ten feet deep throughout: let us then suppose that the bed of the river below Pont-royal and above Pont-neuf were left entirely dry, the water would instantly run up and down the channel, and continue to do so until it had recovered an equilibrium; for the weight of the water would keep it in motion, nor would it cease flowing until its particles became equally pressed and have sunk to a perfect level. The weight of water therefore greatly contributes to its velocity, and this is the reason that the greatest rapidity of the current is neither of the surface
nor at the bottom of the water, but nearly in the middle of its depth, being pressed by the action of its weight at its surface, and by the re-action from the bottom. Still more, if a river has acquired a great rapidity, it will not only preserve it in passing a level country, but even surmount an eminence without spreading much on either side, or at least without causing any great inundation.
We might be inclined to think that bridges, locks, and other obstacles raised on rivers, considerably diminishes the celerity of the water's course; nevertheless that occasions but little difference. Water rises on meeting with any obstacle, and having surmounted it, the elevation causes it to act with more rapidity in its fall, so that in fact it suffers little or no diminution in its celerity, by these seeming retardments. Sinuosities, projections, and islands, also but very little diminish the velocity of the course of rivers. A considerable diminution is produced by the sinking of the water, and, on the contrary, its augmentation increases its velocity; thus if a river is shallow the stream passes slowly along, and if deep with a proportionate rapidity.
If rivers were always nearly of an equal fulness, the best means of diminishing their rapidity, and confining them within their banks, would be to enlarge their channel; but as almost all rivers are subject to increase and diminish, to confine them we must retrench the channel, because in shallow waters, if the channel is very broad, the water which passes in the middle hollows a winding bed, and when it begins to swell follows the direction it took in this particular bed, and striking forcibly against the banks of the channel destroys them and does great injuries. These effects of the water's fury might be prevented by making, at particular distances, small gulphs in the earth; that is, by cutting through one of these banks to a certain distance in the land. In order that these gulphs might be advantageously placed, they should be made in the obtuse angle of the river, for then the current of the water in turning would run into them, and of course its velocity would be diminished. This mode might be proper to prevent the fall of bridges in places where it is not possible to make bars near the bridge which sustain the action of the weight of the water.
The manner in which inundations are occasioned merits peculiar attention. When a river swells, the rapidity of the water always increases till it begins to overflow the banks; at that instant the velocity diminishes, which causes inundations to continue for several days; for when even a less quantity of water comes after the overflowing than before, the inundation will still be made, because it depends much more on the velocity of the water than on the quantity; if it was not so rivers would overflow for an hour or two and then return to their beds, which never occurs; the inundations always remaining for several days; whether the rain ceases, or a less quantity of water is brought, because the overflowing has diminished the velocity, and consequently, although the like quantity of water is no longer carried in the same time as before, yet the effects are the same as if the greater quantity had come there. It might be remarked on the occasion of this diminution, that if a constant wind blows against the current of the river, the inundation will be much greater than it would have been without this accidental cause, which diminishes the celerity of the
water; on the contrary, if the wind blows in the same directions with the current, the inundation will be much less, and will more speedily decline.
"The swelling of the Nile, says M. Granger, and its inundations, has a long time employed the learned; most of them have looked upon it as marvellous, although nothing can be more natural, and is every day to be seen in every country throughout the world. It is the rains which fall in Abyssinia and Ethiopia which cause the swelling and inundation of that river, though the north wind must be regarded as the principal cause. 1. Because the north wind drives the clouds which contain this rain into Abyssinia. 2. Because, blowing against the mouths of the Nile, it causes the waters to return against the stream, and thus prevents them from running out in any great quantity: this circumstance may be every season observed, for when the wind, being at the north, suddenly veers to the south, the Nile loses in one day more than it gathers in four."
Inundations are generally greatest in the upper part of rivers, because the velocity of a river continues always increasing until it arrives at the sea, for the reasons we have related.
Father Costelli, who has written very sensibly on this subject, remarks, that the height of the banks made to confine the Po from overflowing diminishes as they advance towards the sea; so that at Ferrara, which is 50 or 60 miles from the sea, they are near 20 feet high above the common surface of the Po, but that at 10 or 12 miles from it they are not above 12 feet, although the channel of the river is as narrow there as at Ferrara[306:A].