, in Geography, a stream or current of fresh water, flowing in a bed or channel, from a source or spring, into the sea.

When the stream is not large enough to bear boats, or small vessels, loaden, it is properly called by the diminutive, rivulet or brook; but when it is considerable enough to carry larger vessels, it is called by the general name River.

Rivulets have their rise sometimes from great rains, or great quantities of thawed snow, especially in mountainous places; but they more usually arise from springs.

Rivers themselves all arise either from the confluence of several rivulets, or from lakes.


, in Physics, denotes a stream of water running by its own gravity, from the more elevated parts of the earth towards the lower parts, in a natural bed or channel open above.

When the channel is artificial, or cut by art, it is called a canal; of which there are two kinds, viz, that whose channel is every where open, without sluices, called an artificial River, and that whose water is kept up and let off by means of sluices, which is properly a canal.

Modern philosophers end eavour to reduce the motion and flux of Rivers to precise laws; and with this view they have applied geometry and mechanics to this subject; so that the doctrine of Rivers is become a part of the new philosophy.

The authors who have most distinguished themselves in this branch, are the Italians, the French, and the Dutch, but especially the first, and among them more especially Gulielmini, and Ximenes.

Rivers, says Gulielmini, usually have their sources in mountains or elevated grounds; in the descent from which it is mostly that they acquire the velocity, or acceleration, which maintains their future current. In proportion as they advance farther, this velocity diminishes, on account of the continual friction of the water against the bottom and sides of the channel; as well as from the various obstacles they meet with in their progress, and from their arriving at length in plains where the descent is less, and consequently their inclination to the horizon greater. Thus the Reno, a River in Italy, which he says gave occasion, in some measure, to his speculations, is found to have near its mouth a declivity of scarce 52 seconds.

When the acquired velocity is quite spent, through the many obstacles, so that the current becomes horizontal, there will then nothing remain to propagate the motion, and continue the stream, but the depth, or the perpendicular pressure of the water, which is always proportional to the depth. And, happily for us, this resource increases, as the occasion for it increases; for in proportion as the water loses of the velocity acquired by the descent, it rises and increases in its depth.

It appears from the laws of motion pertaining to bodies moved on inclined planes, that when water flows freely upon an inclined bed, it acquires a velocity, which is always as the square root of the quantity of descent of the bed. But in an horizontal bed, opened by sluices or otherwise, at one or both ends, the water flows out by its gravity alone.

The upper parts of the water of a River, and those at a distance from the banks, may continue to flow, from the simple cause or principle of declivity, how small soever it be; for not being detained by any obstacle, the minutest difference of level will have its effect; but the lower parts, which roll along the bottom, will scarce be sensible of so small a declivity; and will only have what motion they receive from the pressure of the superincumbent waters.

The greatest velocity of a River is about the middle of its depth and breadth, or that point which is the farthest possible from the surface of the water, and from the bottom and sides of the bed or channel. Whereas, on the contrary, the least velocity of the water is at the bottom and sides of the bed, because there the desistance arising from friction is the greatest, which is communicated to the other parts of the section of the | River inversely as the distances from the bottom and sides.

To find whether the water of a River, almost horizontal, flows by means of the velocity acquired in its descent, or by the pressure of its depth; set up an obstacle perpendicular to it; then if the water rise and swell immediately against the obstacle, it runs by virtue of its fall; but if it first stop a little while, in virtue of its pressure.

Rivers, according to this author, almost always make their own beds. If the bottom have originally been a large declivity, the water, hence falling with a great force, will have swept away the most elevated parts of the soil, and carrying them lower down, will gradually render the bottom more nearly horizontal.

The water having made its bed horizontal, becomes so itself, and consequently rakes with the less force against the bottom, till at length that force becomes only equal to the resistance of the bottom, which is now arrived at a state of permanency, at least for a considerable time; and the longer according to the quality of the soil, clay and chalk resisting longer than sand or mud.

On the other hand, the water is continually wearing away the brims of its channel, and this with the more force, as, by the direction of its stream, it impinges more directly against them. By this means it has a continual tendency to render them parallel to its own course. At the same time that it has thus rectified its edges, it has widened its own bed, and thence becoming less deep, it loses part of its force and pressure: this it continues to do till there is an equilibrium between the force of the water and the resistance of its banks, and then they will remain without farther change. And it appears by experience that these equilibriums are all real, as we find that Rivers only dig and widen to a certain pitch.

The very reverse of all these things does also on some occasions happen. Rivers, whose waters are thick and muddy, raise their bed, by depositing part of the heterogeneous matters contained in them: they also contract their banks, by a continual opposition of the same matter, in brushing over them. This matter, being thrown aside far from the stream of water, might even serve, by reason of the dullness of the motion, to form new banks.

If these various causes of resistance to the motion of flowing waters did not exist, viz, the attraction and continual friction of the bottom and sides, the inequalities in both, the windings and angles that occur in their course, and the diminution of their declivity the farther they recede from their springs, the velocity of their currents would be accelerated to 10, 15, or even 20 times more than it is at present in the same Rivers, by which they would become absolutely unnavigable.

The union of two Rivers into one, makes the whole flow the swifter, because, instead of the friction of four shores, they have only two to overcome, and one bottom instead of two; also the stream, being farther distant from the banks, goes on with the less interruption, besides, that a greater quantity of water, moving with a greater velocity, digs deeper in the bed, and of course retrenches of its former width. Hence also it is, that Rivers, by being united, take up less space on the surface of the earth, and are more advantageous to low grounds, which drain their superfluous moisture into them, and have also less occasion for dykes to prevent their overflowing.

A very good and simple method of measuring the velocity of the current of a River, or canal, is the following. Take a cylindrical piece of dry, light wood, and of a length something less than the depth of the water in the River; about one end of it let there be suspended as many small weights, as may keep the cylinder in a vertical or upright position, with its head just above water. To the centre of this end fix a small straight rod, precisely in the direction of the cylinder's axis; to the end that, when the instrument is suspended in the water, the deviations of the rod from a perpendicularity to the surface of it, may indicate which end of the cylinder goes foremost, by which may be discovered the different velocities of the water at different depths; for when the rod inclines forward, according to the direction of the current, it is a proof that the surface of the water has the greatest velocity; but when it reclines backward, it shews that the swiftest current is at the bottom; and when it remains perpendicular, it is a sign that the velocities at the top and bottom are equal.

This instrument, being placed in the current of a River or canal, receives all the percussions of the water throughout the whole depth, and will have an equal velocity with that of the whole current from the surface to the bottom at the place where it is put in, and by that means may be found, both with exactness and ease, the mean velocity of that part of the River for any determinate distance and time.

But to obtain the mean velocity of the whole section of the River, the instrument must be put successively both in the middle and towards the sides, because the velocities at those places are often very different from each other. Having by this means found the several velocities, from the spaces run over in certain times, the arithmetical mean proportional of all these trials, which is found by dividing the common sum of them all by the number of the trials, will be the mean velocity of the River or canal. And if this medium velocity be multiplied by the area of the transverse section of the waters at any place, the product will be the quantity running through that place in a second of time.

If it be required to find the velocity of the current only at the surface, or at the middle, or at the bottom, a sphere of wood loaded, or a common bottle corked with a little water in it, of such a weight as will remain suspended in equilibrium with the water at the surface or depth which we want to measure, will be better for the purpose than the cylinder, because it is only affected by the water of that sole part of the current where it remains suspended.

It follows from what has been said in the former part of this article, that the deeper the waters are in their bed in proportion to its breadth, the more their motion is accelerated; so that their velocity increases in the inverse ratio of the breadth of the bed, and also | of the magnitude of the section; whence, in order to augment the velocity of water in a River or canal, without augmenting the declivity of the bed, we must increase the depth of the channel, and diminish its breadth. And these principles are agreeable to observation; as it is well known, that the velocity of flowing waters depends much more on the quantity and depth of the water, and on the compression of the upper parts on the lower, than on the declivity of the bed; and therefore the declivity of a River must be made much greater in the begiuning than toward the end of its course; where it should be almost insensible. If the depth or volume of water in a River or canal be considerable, it will suffice, in the part next the mouth, to allow one foot of declivity through 6000, or 8000, or even (according to Dechales, De Fontibus et Fluviis, prop. 49) 10000 feet in horizontal extent; at most it need not be above 1 in 6 or 7 thousand. From hence the quantity of declivity in equal spaces must slowly and gradually increase as far as the current is to be made fit for navigation; but in such a manner, as that at this upper end there may not be above one foot of perpendicular declivity in 4000 feet of horizontal extent.

To conclude this article, M. de Buffon observes, that people accustomed to Rivers can easily foretell when there is going to be a sudden increase of water in the bed from floods produced by sudden falls of rain in the higher countries through which the Rivers pass. This they perceive by a particular motion in the water, which they express by saying, that the River's bottom moves, that is, the water at the bottom of the channel runs off faster than usual; and this increase of motion at the bottom of a River always announces a sudden increase of water coming down the stream. Nor, says he, is their opinion ill grounded; because the motion and weight of the waters coming down, though not yet arrived, must act upon the waters in the lower parts of the River, and communicate by impulsion part of their motion to them, within a certain distance.

On the subject of this article, see an elaborate treatise on Rivers and canals, in the Philos. Trans. vol. 69, pa. 555 &c, by Mr. Mann, who has availed himself of the observations of Gulielmini, and most other writers.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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