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 this resource increases, as the occasion for it increases ; for in proportion as the water loses of the velo city 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 greatest velocity of a river is about the middle of its depth and breadth, or that point which is the furthest possible from the surface of the water, and from the bottom and sides of the bed or chan nel.. Whereas, on the contrary, the least velocity of the water is at the bottom and sides of the bed, because there the resis ance 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 al most 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 obsta cle, 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 bot tom 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 hori zontal, becomes so itself, and consequent ly rakes with the less force against the bottom, till at length that force becomes only equal to the resistance of the bot tom, 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 resist lonzer than sand or mud.
On the other hand, the water is conti nually wearing away the brims of its chan nel, 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 ren. der 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, aid then they will remain without further change. And it appears, by experience, that these equilibriums are all real, as we find that rivers only deepen and widen to a certain pitch, The union of two rivers into one makes the whole flow the swifter, because, in stead of the friction of four shores, they have only two to overcome, and one bot tom instead of two ; also the stream be ing further 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 fbr mer 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, precise ly 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 shows that the swiftest cur rent is at the bottom ; and when it re mains perpendicular, it is a sign that the velocities at the top and bottom are equal. This instrument, being placed in the cur rent of a river or canal, receives all the percussions of the water throughout the whole depth, and will have an equal ve locity 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 instru ment must he 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 veloci ties, from the spaces run over in certain times, the arithmetical mean proportional of all these trials, which is found by di viding 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 mul tiplied 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, be cause it is only affected by the water of that sole part of the current where it re mains 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 velo. city increases in the inverse ratio of the breadth of the bed, and also of the mag nitude 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 agree. able to observation; as it is well known, that the velocity of flowing waters de. pends much more on the quantity ant' depth of the water, and on the com pression 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 beginning than toward the end of its course, where it should be almost insensible.