a current or stream of fresh water flowing in a bed or channel, from its source into the sea. See the article SPRING.

The great, as well as the middle-sized rivers, proceed either from a confluence of brooks and rivulets, or from lakes; but no river of considerable magnitude flows from one spring, or one lake, but is augmented by the accession of others. Thus the Wolga receives above 200 rivers and brooks before it discharges itself into the Caspian sea; and the Danube receives no fewer before it enters the Euxine sea. Some rivers are much augmented by frequent rains, or melted snow. In the country of Peru and Chili, there are small rivers that only flow in the day; because they are only fed by the snow upon the mountains of the Andes, which is then melted by the heat of the sun. There are also several rivers upon both sides the extreme parts of Africa, and in India, which for the same reason are greater by day than by night. The rivers also in these places are almost dried up in summer, but swell and overflow their banks in winter or in the wet season. The Wolga in May and June is filled with water, and overflows its shelves and islands, though at other times of the year it is so shallow, as scarcely to afford a passage for loaded ships. The Nile, the Ganges, the Indus, &c. are so much swelled with rain or melted snow, that they overflow their banks; and these deluges happen at different times of the year, because they proceed from various causes. Those that are swelled with rain, are generally highest in winter, because it is usually then more frequent than at other times of the year; but if they proceed from snow, which in some places is melted in the spring, in others in summer, or between both, the deluges of the rivers happen accordingly. Again, some rivers hide themselves under ground, and rise up in other places, as if they were new rivers. Thus the Tigris meeting with mount Taurus, runs under it, and flows out at the other side of the mountain; also, after it has run thro' the lake Tofpia, it again immerges, and being carried about 18 miles under ground, breaks out again, &c.

In a memoir of the academy of sciences lately published, we have some curious observations and conjectures concerning the disappearing of rivers, by the abbe Guettard. "It is very surprising," he observes, "if we reflect on it, that a river in its course, which is often very extensive, should not meet with spongy soils to swallow up its waters, or gulps in which they are lost: nevertheless, as there has been hitherto known but a small number of rivers whose waters thus disappear, this phenomenon has been accounted very extraordinary, both by the ancients and moderns. Pliny speaks of it with an energy familiar to him; and Seneca mentions it in his Questions Naturales: he even distinguishes these rivers into two sorts, those that are lost by degrees, and those which are swallowed up all at once or ingulphed; which would make one believe that the ancients had collected some observations concerning them.

But leaving apart what may be wonderful in these rivers, it may be asked, how they are lost? From what particular qualities of the soil over which they flow, and from what situation of the places through which they pass, does this phenomenon arise? Upon this head we find but little light in authors. We might, perhaps, be informed a great deal more, if the observations of the ancients had reached us.

M. Guettard has undertaken to remove part of this obscurity by describing what he has observed in several rivers of Normandy, which are lost and afterwards appear again; these are five in number, viz. the Rille, the Ithon, the Aure, the river of Sap-Audric, and the Drôme.

The three first disappear gradually, and then come in sight again; the fourth loses itself entirely by degrees, but afterwards re-appears; the fifth loses some of its water in its course, and ends by precipitating itself into a cavity, from whence it is never seen to rise again.

What seems to occasion the loss of the Rille, the Ithon, and the Aure, is the nature of the soil through which they pass. M. Guettard has observed that it is in general porous, and composed of a thick sand, the grains of which are not well compacted together; it sinks suddenly down by its own weight in some places, and there forms great holes; and when the water overflows the meadows, it frequently makes many cavities in several parts of them. If we therefore suppose inequalities in the channels of these rivers, and that there are certain places in which the water stagnates longer than in others, it must there dilute the ground, if we may use that expression; and having carried away the parts which united the grains of sand together, together, those grains will become afterwards no other than a kind of sieve, through which the waters will filtrate themselves, provided nevertheless that they find passage underground through which they may run. This conjecture appears to be well founded, that each of these three rivers loses itself nearly in the same manner, that is, thro' cavities which the people of the country call betoires, and which swallow up more or less according to their largeness. M. Guettard, who has carefully examined them, remarks, that these betoires are holes in the form of a tunnel, whose diameter and aperture is at least two feet, and sometimes exceeds eleven; and whose depth varies in like manner from one and two feet to five, six, and even twenty. The water generally gets into these cavities, when the river is not very high, making a gurgling noise, and turning round in an eddy. A proof that waters are there filtered and absorbed among the grains of this sharp diluted sand, is, that frequently in a betoir two or three feet deep, and through which a great deal of water is lost, one cannot thrust a stick farther than the surface of its bottom. Wherefore as these betoires so frequently occur in the bed and banks of the Rille, the Rhon, and the Aure, it is not surprising that these rivers should be thus lost. The Rille during the summer season loses almost all its water in the space of two short leagues; the Ithon does very near the same. But M. Guettard observes something curious concerning this river, to wit, that formerly it was not lost, but kept its course without any interruption, as appears by the history of the country: very likely, the mud which had been collected together in several parts of its channel, might have occasioned the waters remaining in others, and thereby have caused many betoires. This is the more likely, as the mud having been collected together in the bed of the river Aure, it appears that, in consequence thereof, the cavities were greatly increased, which makes it lose itself much sooner than formerly; however, it has been resolved to cleanse its channel to remedy this inconvenience. Besides, possibly an earthquake happening in the country might have caused several subterraneous canals through which the water of the Ithon (which before very likely could not pass through the soil beneath its bed) has forced its way. In effect, it appears, that a soil being porous is not sufficient to cause the loss of a river; for if it were, then to do so it would occasion many fens round about, nor would it renew its course after having disappeared a certain time: it must besides, as we have before said, find ways under ground thro' which it may take its course. M. Guettard seems also much inclined to believe, that there are, in these parts, subterraneous cavities through which the waters may flow; and in consequence of this he reports a number of facts, all tending to prove the truth of it, or at least to prove that there must be hollow quarries serving for strainers to these waters. Upon which occasion he goes into a discussion of this question: Are there any subterraneous rivers, and is the prepossession of some persons in favour of this particular well founded? He makes appear by several instances which he quotes, and by many reasons which he alleges, that there are at least very great presumptions in favour of this opinion. We are too apt not to look beyond the exterior of things: we feel reliance upon the surface of the earth; when we go deep, we often find it compact. It is therefore hard for us to imagine that it can contain subterraneous cavities sufficient to form channels for hidden rivers, or for any considerable body of water; in a word, that it can contain vast caverns; and yet everything seems to indicate the contrary. A fact that is observed in the betoires of the rivers concerning which we have spoken, and particularly of the Rille, proves in some measure that there are considerable lakes of waters in the mountains which limit its course: this fact is, that in winter the greatest part of their betoires become springs, which supply anew the river's channel with as much water as they had absorbed from it during the summer. Now from whence can that water come, unless from the reservoirs or lakes that are inclosed in the mountains, which being lower than the river in summer, absorb its water, and being higher in winter by occasion of the rain they receive, send it back again in their turn?

Mr. Guettard strengthens this conjecture by several instances that render it very probable: he remarks at the same time, that this alternate effect of the betoires swallowing up the water and restoring it again, causes perhaps an invincible obstacle to the restraining of the water within the channel of the river. It has indeed been several times attempted to stop those cavities; but the water returns with such violence in winter, that it generally carries away the materials with which they were stopped.

The river of Sap-André is lost in part, as we have before said, in the same manner as the Ithon and the Rille: but there is something more remarkable in it than in those rivers; to wit, that at the extremity of its course, where there is no perceptible cavity, it is, as it were ingulphed, but without any fall: the water passes between the pebbles, and it is impossible to force a stick into that place any further than into the betoires of which we have spoken. What makes this river take that subterraneous direction, is an impediment which its stream meets with in that place: it is there stopped by a rising ground six or seven feet high, whose bottom it has very likely undermined, to gain a free passage, not having been able to make its way over it. At some distance from thence it appears again; but in winter, as there is a greater quantity of water, it passes over that eminence, and keeps an uninterrupted course.

Lastly, the Drôme, after having lost some of its water in its course, vanishes entirely near the pit of Soucy: in that place it meets with a fort of subterraneous cavity near 25 feet wide, and more than 15 deep, where the river is in a manner stopped, and into which it enters, tho' without any perceptible motion, and never appears again.

We see by these observations of M. Guettard, that rivers which lose themselves are not so few as is generally imagined, since there are five of them in this part of Normandy, which is but of small extent. One might fancy that this is owing to the nature of the ground: yet M. Guettard observes, that in a part of Lorraine, which likewise is not very extensive, five other rivers are known to lose themselves in the same manner: and without doubt we shall find by new observations that they are much more common; for, as we have remarked, it perhaps is not more surprising that a river loses itself, than it is extraordinary that it does not so.

M. M. Guettard finishes this memoir with some observations upon the Ierre. This river is lost in the same manner as the Rille; and though it is very near Paris, this singularity is unknown to almost every body; were it not for the account of M. l'Abbe le Boeuf, M. Guettard would have been also ignorant of it. And as he thinks the chief object of a naturalist's observation ought to be the public good, he examines the means which might be employed to restrain the water of the Ierre. The same object has made him add a description of the manner how the Rône is lost; or rather how its course is disturbed; for it is now very certain that it does not lose itself, but that its channel is extremely confined, in the place where it was pretended that it lost itself, by two mountains, between whose feet it runs. M. Guettard makes it appear that it might not be impossible to widen that place, and give a sufficient channel to the river; which would render it navigable, and be of vast utility to all the country.

We may add to the above account, that we have in Surrey the river Mole, which rises in Dorking hundred, and, after a considerable course, passes by Witlechill, near Dorking; a little beyond which this river hides itself, or is swallowed up, in a cavern, at the foot of the hill, from whence Cambden says it is called the Swallows; he also takes notice of its running underground for about two miles, and rising again, and spreading itself into a wide stream. It is also frequently reported that there are several of these dipping rivers in Wales, and others in the southern counties of England.

The channels of rivers, except such as were formed at the creation, Varenius thinks, are artificial. His reasons are, that, when a new spring breaks out, the water does not make itself a channel, but spreads over the adjacent land; so that men were necessitated to cut a channel for it, to secure their grounds. He adds, that a great number of channels of rivers are certainly known from history to have been dug by men.

The water of most rivers flows impregnated with particles of metals, minerals, &c. Thus some rivers bring sands intermixed with grains of gold; as in Japan, Peru, and Mexico, Africa, Cuba, &c. particularly in Guinea is a river, where the negroes separate the gold-dust from the sand, and sell it to the Europeans, who traffic thither for that very purpose. The Rhine in many places is said to bring a gold mud. As to rivers that bring grains of silver, iron, copper, lead, &c. we find no mention of them in authors; though, doubtless, there are many.

Theory of the Motion of Rivers. The running of rivers is upon the same principle as the descent of bodies on inclined planes: for water, no more than a solid, can move on an horizontal plane; the re-action of such a plane being equal and contrary to gravity, entirely destroys it, and leaves the body at rest. Here we speak of a plane of small extent, and such as coincides with the curved surface of the earth. But if we consider a large extent or long course of water, then we shall find that such water can never be at rest, but when the bottom of the channel coincides everywhere with the curved surface of the earth.

Let ADF be the curved surface of the earth, C its centre, CD, CE, two right lines drawn from thence, and EG a tangent to the earth in the point D. Then it is plain, if BD were a channel of water, the water could not run or move, because they are everywhere at an equal distance from the centre C, and therefore equally affected by gravity. But if there be any place above the surface of the earth, as E, where water can be found, it is evident that water can descend in a channel to any part of the earth's surface between B and D, because every point in the line ED is nearer to the centre of the earth, and therefore below the point or place E; and its velocity will be so much the greater as it tends to a point nearer B, and slower of all when it moves in the direction of the tangent ED.

Hence it appears, that the source E of all rivers and streams must be more than a semi-diameter of the earth CB distant from the centre C. And since all great rivers run to the sea or ocean, where they disfigure their waters at the point D, the line DC is a semidiameter, and = 4000 miles nearly. Also the course of all long rivers being in the direction of the tangent at the point D, if they were represented by the tangent-line EG, then the height of the source E above the common surface of the earth at B would be easily found. Thus, suppose ED were the river Niger in Africa, whose source is said to be more than 3000 miles from the sea; but put ED = 3000, and since CD = 4000, we shall have CE = 5000, and CE—CB = 1000 = BE = the height of the source. But since we know of no mountains above three or four miles high, it is plain the river Niger, and all such long rivers, are so far from moving in a tangent, that their course must be very nearly of the same curvature with the earth's surface, and infinitely distant from it.

Since bodies move on planes ever so little inclined, except so far as they are prevented by friction, and since the friction of the particles of water among themselves is inconsiderable, it follows that the water situated on a plane ever so little inclined, will commence a motion; and if the plane be considerably inclined, and the quantity of water great, its velocity will be proportional, and its momentum such as will soon begin to wear away the earth, and create itself a course or channel to glide in. In rivers that are made, it is usual to allow the fall of one foot in 300.

If we allow the same declivity to rivers which make their own way, then we find their height at their source above the surface of the sea, as in example of the Niger thus: As 300 : 1 :: 5280 : 300 = the height at one mile, or 5280 feet. Then again say, as 1 : 5280 :: 3000 : 5280 X 3000 = 5280 X 10 = 10 miles. From whence it is evident, that the continents and islands ought to be much above the surface of the sea, to give a necessary descent and course to the waters through them.

Let ABCD be the section of a reservoir, and Fig. 3. no. BCIK the section of a canal of water supplied from thence, and ABN the horizontal line. Now, since the particles of water are governed by the common laws of gravity, the velocity of a particle at any part of the bottom of the canal, as F or H, will be the same as it would acquire by falling thro' the perpendicular altitude OF or LH, that is, as √OF to √LH. Hence the velocity of the stream is accelerated. For the same reason the velocity of a particle at the bottom of the stream H is to the velocity of a particle at the top G, as \( \sqrt{LH} \) to \( \sqrt{MG} \); consequently the stream moves with a greater celerity at bottom than at top.

The quantity of the water which passes through the section of the stream HG, is the same that passes thro' the section of the reservoir BC in the same time. The same may be said of any other section FE; therefore the quantity of water, passing by any two sections of the stream FE and GH, in the same time, is the same.

Since there runs the same quantity of water by GH as by FE in the same time; and since the velocity at GH is greater than at FE; and lastly, since the breadth of the canal is supposed to be everywhere the same; therefore it follows, that the depth GH must be less than the depth FE, and so the depth of the stream must continually decrease as it runs.

As the stream proceeds, the depth HG decreasing, the lines MG and LH will approach nearer to an equality; and therefore, the different velocities of the water at top and bottom will approach much faster to an equality, as being proportionate to the square roots of those lines. This approach to an equality is much farther promoted, by the upper parts being continually accelerated by the lower, and the lower parts retarded continually by the slower motion of the waters above, and pressing upon them.

Since the difference of the descending velocities is greatest near the head of the stream, the waters will there fall or descend with the greatest impetuosity, or cause the loudest noise. But in the course of rivers, the accelerated velocity is quickly reduced to an equable or uniform velocity, by the resistance it meets with from the bottom and sides of the channel, which resistance will be as the squares of the velocities, and therefore soon becomes so great as to equal the accelerating force, and be communicated to the middle part of the stream, causing the whole to move uniformly. Hence, in rivers, the motion of the water is slowed at the sides and bottom of the channel, because there the resistance begins, which is afterwards communicated to all the other parts; and in different parts of the same river, the uniform velocity is greatest, where the bottom of the channel has the greatest inclination, or declivity, because the relative gravity of the moving particles is here greatest. Again, in those parts of the river where the velocity of the stream is least, the depth of the water is greatest, and vice versa, because equal quantities pass through unequal sections of the river in the same time. Hence also it follows, that the momentum of running water must be every where the same, or a given quantity.

The many advantages which accrue to a country from an abundance of rivers, especially large navigable ones, are too obvious to require any particular detail; but the disadvantages and calamities occasioned by them are frequently no less obvious and fatal. Whole tracts of country are sometimes overflowed on a sudden, and everything swept away at once; or if the deluge proceeds not such a length, yet by the quantity of stagnating water which is left, marshes are produced, which bring on the most violent diseases in the neighbouring parts. It becomes therefore an object well worthy the public attention how to secure the banks of rivers, or to form their channels in such a manner that the superfluous water may be carried off into the ocean without producing the mischievous effects abovementioned.

In a treatise on rivers and canals published in the Phil. Transac. vol. 69, by Mr Mann, he treats this subject at great length. Having laid down a number of theorems concerning the descent of the water in rivers similar to those abovementioned, he points out a method of determining whether the motion of a river in any particular place is derived from the inclination of the bottom of its channel, or merely from the pressure of the upper parts of the water upon the lower. For this purpose, says he, a pole must be thrust down to the bottom, and held perpendicularly to the current of the water, with its upper end above the surface; if the water swells and rises immediately against the pole, it shows that its flowing is by virtue of a preceding declivity; if, on the contrary, the water stops for some moments before it begins to rise against the pole, it is a proof that it flows by means of the compression of the upper waters upon the lower.

The best and most simple method of measuring the velocity of the current of a river, according to our author, is as follows. "Take a cylindrical piece of dry light wood, and of a length something less than the depth of the water in the river; round one end of it let there be suspended as many small weights as may be necessary to keep up the cylinder in a perpendicular situation in the water, and in such a manner that the other end of it may just appear above the surface of the water. Fix to the centre of that end which appears above water a small and 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 advances the fastest, whereby may be discovered the different velocities of the water at different depths: for if the rod inclines forwards according to the direction of the current, it is a proof that the surface of the water has the greatest velocity; but if it inclines back, it shows that the swiftest current is at the bottom; if it remains perpendicular, it is sign that the velocities at the surface 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 ease and exactness, 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 difference of time required for the currents to run over an equal space, or the different distances run over in equal times; the mean proportional of all these trials, which is found by dividing the common sum of them all by the number of trials, will be the mean velocity of the river or canal.

If it be required to find the velocity of the current rent only at the surface, or at the middle, or at the bottom, a sphere of wood, 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 a cylinder, because it is only affected by the water of that part of the current where it remains suspended.

"It is very easy to guide both the cylinder and the globe in that part which we want to measure, by means of two threads or small cords, which two persons must hold and direct, one on each side the river; taking care at the same time neither to retard nor accelerate the motion of the instrument."

Our author next proceeds to deduce from his theory the best methods of removing the defects and inconveniences which must necessarily happen to rivers and canals in a series of years. From the theory formerly laid down he draws the following conclusion, 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 an inverse ratio of the breadth of the bed, and also of the greatness of the section; from whence are deduced the two following universal practical rules:

1st, To augment the velocity of water in a river or canal, without augmenting the declivity of the bed, we must increase the depth and diminish the breadth of its bed.

2ndly, But to diminish the velocity of water in a river or canal, we must, on the contrary, increase the breadth and diminish the depth of its bed.

The above proposition is perfectly conformable to observation and experience: for it is constantly seen, that the current is the swiftest where the waters are deepest and the breadth of the bed the least, and that they flow slowest where their depth is the least and the breadth of the bed the greatest. "The velocity of waters," says M. de Buffon, "augments in the same proportion as the section of the channel through which they pass diminishes, the force of impulsion from the back-waters being supposed always the same. Nothing," continues he, "produces so great a diminution in the swiftness of a current as its growing shallow; and, on the contrary, the increase of the volume of water augments its velocity more than any other cause whatever." The celebrated Wolfe, in his Hydraulics, affirms us, that "it is a constant and universal practice, for accelerating the current of waters, to deepen the bed, and at the same time to render it narrower."

When the velocity which a river has acquired by the elevation of its springs and the impulse of the back-water, is at last totally destroyed by the different causes of resistance becoming exactly equal or greater than the first, the bed and current at the same time being horizontal, nothing else remains to propagate the motion, except the sole perpendicular compression of the upper waters upon the lower, which is always in a direct ratio of their depth. But this necessary resource, this remaining cause of motion in rivers, augments in proportion as all the others diminish, and as the want of it increases: for as the waters of rivers in extensive plains lose the acceleration of motion acquired in their descent from their springs, their quantity accumulates in the same bed by the junction of several streams together, and their depth increases in consequence thereof.

This junction and successive accumulation of many streams in the same bed, which we see universally in a greater or lesser degree in all rivers throughout the known world, and which is so absolutely necessary to the motion of their waters, can only be attributed, says Signor Guglielmini, to the infinite wisdom of the supreme Author of Nature.

The velocity of flowing waters is very far from being in proportion to the quantity of declivity in their bed. If it was, a river whose declivity is uniform and double to that of another, ought only to run with double the swiftness when compared to it: but in effect it is found to have a much greater, and its rapidity, instead of being only double, will be triple, quadruple, and sometimes even more; for its velocity depends much more on the quantity and depth of the water, and on the compression of the upper waters on the lower, than on the declivity of the bed. Consequently, whenever the bed of a river or canal is to be dug, the declivity must not be distributed equally throughout the whole length; but, to give a slower current to the water, the declivity must be made much greater in the beginning of its course than towards the end where it disembogues itself, and where the declivity must be almost insensible, as we see is the case in all natural rivers: for when they approach near the sea, their declivity is little or nothing; yet they flow with a rapidity which is so much greater, as they contain a greater volume of water; so that in great rivers, although a large extent of their bed next the sea should be absolutely horizontal, and without any declivity at all, yet their waters do not cease to flow, and to flow even with great rapidity, both from the impulsion of the back waters, and from the compression of the upper waters upon the lower in the same section.

Whoever is well acquainted with the principles of the higher geometry, will easily perceive that it would be no difficult matter so to dig the bed of a canal or river, that the velocity of the current should be everywhere equal. It would be only giving it the form of a curve along which a moving body should recede from a given point, and describe spaces everywhere proportional to the times, allowance being made therein for the quantity of effect of the compression of the upper waters upon the lower. This curve is what is called the horizontal isochronic, being the flattest of an infinity of others which would equally answer the problem where fluids were not concerned. Upon these curves may be seen Leibnitz, Huygens, and the two Bernouilli's, who were the first that determined and analysed them, and also many succeeding geometers, if any one is desirous to occupy himself in such speculations as are more curious than useful.

Notwithstanding all we have said concerning the necessity of augmenting the depth of a river in a greater proportion than its breadth, if we would accelerate its current; yet it is certain, that this can only be done to a certain point, without destroying that equilibrium which ought to reign between the depth and the breadth of the section of the stream, and thereby putting the river into a state of continual violence, which will incessantly exert itself to the destruction of the banks and weirs made to keep it in, and that action will always exert itself in a direct ratio of the greater or less want of equilibrium, as it would be easy. easy to demonstrate by the principles of hydraulics. These same principles give likewise the just proportions of this equilibrium between the perpendicular and lateral compression of the water in any river or canal whatsoever, which vary in an inverse proportion, according to the different degrees of the declivity and velocity of the current; and in a direct one of the greater or less coherence and hardness of the substances which compose the bed. Rivers which flow in beds composed of homogeneous matter of little consistency, such as sand, &c., are always more broad than deep, when compared to those which run in beds of matter of greater tenacity. It is manifest, that the equilibrium here spoken of is real, because rivers remaining in the same state only widen their beds to a certain pitch which they do not surpass.

M. de Buffon remarks, "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 in their dialect, by saying that the river's bottom moves; that is, the water at the bottom of a channel runs off faster than usual; and this increase of motion at the bottom of the river always announces a sudden increase of water coming down the stream. Nor does their opinion therein," continues the same author, "seem to be ill-grounded on the nature of things: for 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 thereto; since a canal or river contained in its bed is to be considered in some degree as a column of water contained in a long tube, where the motion is communicated at once throughout the whole length." In a river or canal, open above, it is only communicated to a certain distance; that is, as far as the impulsive force of the new increase and superior rapidity of the back-waters acts upon the stream, which will always be as far as till this force is gradually, and at last wholly, destroyed by the superior gravitation of the superincumbent waters in the stream. Something of the same kind happens when a very great additional weight comes suddenly upon the surface of a river or canal; for instance, by the launching of a ship or of several boats together upon it. These causes increase the velocity of the water in the lower parts of the bed, and moreover retard its motion at the surface, which effect may properly be called making the river's bottom move. For the same reason, the increase of weight of the waters in a sudden flood, as well as the increase of their impulsive force, must contribute to produce this effect, and, by increasing the motion in the bottom of the river, may hinder for some space of time the stream from sensibly rising in the bed.

All obstacles whatever in the bed of a river or canal, such as rocks, trunks of trees, banks of sand and mud, &c., must necessarily hinder proportionably the free running off of the water; for it is evident, from what we have said, that the waters so far back from these obstacles, until the horizontal level of the bottom of the bed becomes higher than the top of the obstacles, must be entirely kept up and hindered from running off in proportion thereto. Now as the waters must continue to come down from their sources, if their free running off is hindered by any obstacles whatever, their relative height back from them must necessarily be increased until their elevation, combined with the velocity of their current proceeding from it, be arrived to such a pitch at the point where the obstacles exist, as to counterbalance the quantity of opposition or impediment proceeding from thence, which frequently does not happen until all the lower parts of the country round about are laid under water.

Now it is certain from all experience, that the beds of rivers and canals in general are subject to some or others of the obstacles above-mentioned. If rocks or trees do not bar their channels, at least the quantity of sand, earth, and mud, which their streams never fail to bring down, particularly in floods, and which are unequally deposited according to the various windings and degrees of swiftness in the current, must unavoidably, in course of time, fill up, in part, different places in the channel, and thereby hinder the free running off of the back-waters. This is certainly the case, more or less, in all rivers, and in all canals of long standing, as is notorious to all those well acquainted with them. Hence, if these accidents are not carefully and with a constant attention prevented, come inundations, which sometimes lay waste whole districts, and ruin the finest tracts of ground, by covering them with sand; hence rivers become unnavigable, and canals useless for the purposes for which they were constructed. Canals, in particular, by reason that their waters for the most part remain stagnant in them, are still more liable than rivers to have their beds fill up by the subiding of mud, and that especially for some distance above each of their sluices; insomuch, that if continual care be not taken to prevent it, or remedy it as often as it happens, they will soon become incapable of receiving and passing the same vessels as formerly. Nay, the very sluices themselves, if the floors of their bottoms are not of a depth conformable to the bed of the canal, will produce the same accidents as those we have been speaking of; for if they are placed too low, they will be continually filling up with sand or mud; if too high, they have the same effect as banks or bars in the bed of a river, that is, they hinder all the back-waters under their level from running off, and soon fill up the bed to that height by the subiding of mud. This effect is much accelerated by the shutting of the lower sluices, which makes a great volume of water flow back to those next above them, till the whole is filled and becomes stagnant. Now it is evident, that this state of things must contribute far more to the subidence of mud and all other matters brought down by the waters in canals, than can be the case in rivers whose currents constantly flow.

The waters of all rivers and canals are from time to time muddy; their streams, particularly during rains and floods, carry along with them earth and other substances which subside in those places where their currents are the least, whereby their beds are continually raised; so that the successive increase of inundations in rivers, and of unfitness for navigation in canals, when they are neglected and left to themselves, is a natural and necessary consequence of the state of things, which no intelligent person can be at a loss to account for; and yet whole countries remain in this habitual state of negligence, to their very great detriment.

Having thus shown the principal accidents which rivers and canals are liable to, with the causes of them, our author proceeds to point out the most efficacious methods of preventing them, or at least of diminishing their effects. They flow immediately from the principles laid down in his essay, and do not need many words to make them completely understood. A work of this kind, he observes, if it is properly conducted, must be begun at the lower end of the river or canal; that is to say, at that end where their waters are discharged into the sea, or where they fall into some other greater river or canal, from whence their waters are carried off without farther hindrance. If it is a river whose bed, by being filled up with mud, sand, or other obstructions, and by being otherwise become irregular in its course, is thereby often subject to inundations, and incapable of internal navigation, the point, from which the work must be begun and directed throughout all the rest of the channel, is from the lowest water-mark of spring-tides on the shore at the mouth of the river; or even something below it, if it can be done; though this part will soon fill up again by the sand, mud, &c., which the tides cease not to roll in.

If it is a canal whose bed is to be dug anew, or one already made, which is to be cleaned and deepened from the sea-shore or some large river back into the country, and where no declivity is to be lost, as is the case in all flat countries; the work must be begun, and the depth of the whole channel directed, from the low water-mark of spring tides, if the mouth is to the sea, or from such a depth in the channel of the river, if the canal falls into one, that there may be such a communication of water from the canal to the river, in all situations of the current, as may let boats freely pass from one to the other. This, of course, must also direct the depth of the floor of the last sluice towards the mouth of the canal, be it to the sea or into a river. If the bottom or floor of a sluice already constructed be too low, it will soon fill up with sand or mud, and thereby hinder the gates from opening; unless it be continually cleaned out; if, on the contrary, this floor be too high, and in a canal whose natural declivity is too little for the free current of the water, as is generally the case in Holland and Flanders, all depth of the bed of the canal below the horizontal level of the bottom of the sluice will serve to no manner of purpose, either for navigation, or for carrying off the back-waters, but will soon fill up with mud, in spite of all means used to the contrary, except that of digging it continually anew to no manner of purpose.

Setting off from this determinate point, at the mouth of a river, or at the bottom of the last sluice upon a canal, which are to be cleaned and deepened; the work must be carried on, in consequence, uniformly throughout their whole course backwards into the country as far as is found necessary for the purposes intended. This is to be done after the following manner:

1st, One must dig up and carry away all irregularities in the bottom and sides of the bed, such as banks of sand and mud, rocks, stumps or trunks of trees, and whatever else may cause an obstacle to the regular motion of the water, and to the free passage of vessels upon it.

2dly, If the declivity of the bed should be still too little to give a sufficient current to carry off the water as often and as fast as is necessary, the whole bed itself must be regularly deepened, and what is dug out from the bottom must be laid upon the sides, to render it narrower in proportion to its depth.

3dly, Wherever the banks are too low to contain the stream in all its situations, they must be sufficiently raised; which may be conveniently done with what is dug out from the bed; and the whole being covered with green turf will render these banks firm and solid against the corrosion of the water. It is proper at all times to lay upon the banks what is dug from the bed, by which they are continually strengthened against the force of the current.

4thly, It is often necessary to diminish the windings and sinuosities in the channel as much as possible, by making new cuts whereby its course may approach towards a right line. This is a great resource in flat countries subject to inundations; because thereby all the declivity of a great extent of the river, through its turns and windings, may be thrown into a small space by cutting a new channel in a straight line; as may generally be done without obstacle in such countries as we are speaking of, and hereby the velocity of the current will be very greatly augmented, and the back-waters carried off to a surprising degree.

5thly, Wherever there is a confluence of rivers or canals, the angle of their junction must be made as acute as possible, or else the worst of consequences will arise from the corrosion of their respective streams; what they carry of from the sides will be thrown into irregular banks in the bottom of the bed. This acute angle of the junction may always be procured by taking the direction at some distance from the point of confluence.

6thly, Wherever the sides or banks of a river are liable to a more particular corrosion, either from the confluence of streams, or from irremediable windings and turns in the channel, they must be secured against it as much as possible by weirs: for this corrosion not only destroys the banks, and alters by degrees the course of the river, but also fills up the bed, and thereby produces all the bad effects we have spoken of above.

7thly, But the principal and greatest attention in digging the beds of rivers and canals must be had to the quantity and form of their declivity. This must be done uniformly throughout their whole extent, or so much of it as is necessary for the purposes in hand, according to the principles laid down. Conformable thereto, the depths of their beds, and of the floors of their sluices, at the mouths whereby they discharge their waters, being fixed, the depth of the rest of the beds, and the quantity of declivity therein, must be regulated in consequence thereof, so as to increase regularly the quantity of the declivity in equal spaces the farther we recede from their mouths, and proceed towards their sources or to the part where the regular current is to take place.

If the depth and volume of water in a river or canal is considerable, it will suffice, in the part next the mouth, mouth, to allow one foot perpendicular of declivity through six, eight, or even, according to Defchales, ten thousand feet in horizontal extent; at most it must not be above one in six or seven 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 four thousand feet of horizontal extent. If it be made greater than that in a regular bed containing a considerable volume of water, the current will be so strong as to be found very unfit for the purposes of navigation.

I dare boldly affirm, says Mr Mann, from the certain principles of hydrodynamics laid down in this essay, that if the abovementioned things were carried into execution in a proper manner, the velocity of currents, and the acceleration of motion of the waters in rivers, and in canals when their sluices are open, might be increased to any degree that can be required for opening their beds, and for preventing inundations during great rains or sudden floods; by carrying off more swiftly the great accretion of water which then takes place. It would not be difficult, by these means, to increase the velocity of the current to double and triple what it is in rivers and canals, whose beds for a long space of time have been left to themselves. There is not, perhaps, a country on earth but what might be freed from inundations by these means. But it may be objected, that if all I have advised were put in execution, even in the flattest countries, the currents of rivers (for canals shut up with sluices are here out of the question) would become inconvenient, if not unfit for navigation, especially against their streams. This objection would be of weight, if it were not evident that the various means which I have pointed out may be executed in whole or in part, to a certain degree, and no farther than necessary for the purposes required. But, as it is certain that a strong and regular current in a river is the best of all means for keeping it open and deep, and for preventing the formation of banks in the bed, by the subsidence of mud, &c. which it does not allow time to precipitate; I leave it to be considered, whether it is better to have a free and open navigation something incommodeed by the strength of the current, or soon to have no navigation at all, without repeatedly digging the bed anew.