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The summits of the highest mountains are composed of rocks, of granite, free-stone, and other hard and vitrifiable matters, and this often as deep as two or three hundred fathoms; below which we often meet with quarries of marble, or hard stone, filled with fossil-shells, and whose matter is calcinable; as may be remarked at Great Chartreuse, in Dauphiny, and on Mount Cenis, where the stone and marble, which contains shells, are some hundred fathoms below the summits, points and peaks of high mountains; although these stones are more than a thousand fathom above the level of the sea. Thus mountains, whereon we see points or peaks, are generally vitrifiable rock, and those whose summits are flat, mostly contain marble and hard stones filled with marine productions. It is the same with respect to hills, for those containing granite, or free-stone, are mostly intersected with points, eminences, cavities, depths, and small intermediate valleys; on the contrary, those which are composed of calcinable stone are nearly equal in height, and are only interrupted by greater and more regular vallies, whose angles are correspondent; and they are crowned with rocks whose position is regular and level.

Whatever difference may appear at first between these two species of mountains, their forms proceed from the same cause, as we have already observed; only it may be remarked, that the calcinable stones have not undergone any alteration nor change since the formation of the horizontal strata; whereas those of vitrifiable sand have been changed and interrupted by the posterior production of rocks and angular blocks formed within this sand. These two kinds of mountains have cracks which are almost always perpendicular in those of calcinable stones; but those of granite and free-stone appear to be a little more irregular in their direction. It is in these cracks metal, minerals, crystals, sulphurs, and all matters of the second class are found, and it is below these cracks that the water collects to penetrate the earth, and form those veins of water which are every where found below the surface.

ARTICLE X.
OF RIVERS

We have before said that, generally speaking, the greatest mountains are in islands and in the projections in the sea. That in the old continent the greatest chains of mountains are directed from west to east, and that those which incline towards the north or south are only branches of these principal chains; we shall likewise find that the greatest rivers are directed as the greatest mountains, and that there are but few which follow the course of the branches of those mountains. To be assured of this, we have only to look on a common globe, and trace the old continent from Spain to China. We shall find, by beginning at Spain, that the Vigo, Douro, Tagos, and Guadiana run from east to west, and the Ebro from west to east, and that there is not one remarkable river whose course is directed from south to north, or from north to south, although Spain is entirely surrounded by the sea on the west side, and almost so on the north. This observation on the directions of rivers in Spain not only proves that the mountains in this country are directed from west to east, but also that the southern lands, which border on the straits, are higher than the coasts of Portugal; and on the northern coast, that the mountains of Galicia, the Asturias, &c. are only a continuation of the Pyrennees, and that it is this elevation of the country, as well north as south, which does not permit the rivers to run into the sea that way.

It will also be seen, by looking on the map of France, that there is only the Rhone which runs from north to south, and nearly half its course, from the mountains to Lyons, is directed from the east towards the west; but that on the contrary all the other great rivers, as the Loir, the Charantee, the Garonne, and even the Seine, have a direction from east to west.

It will be likewise perceived, that in Germany there is only the Rhine, which like the Rhone shapes the greatest part of its course from north to south, but that the others, as the Danube, the Drave, and all the great rivers which fall into them, flow from the west to east into the Black Sea.

It will be perceived that this Black Sea, which should rather be considered as a great lake, has almost three times more extent from east to west than from north to south, and consequently its direction is similar to the rivers in general. It is the same with the Mediterranean, whose length from east to west is about six times greater than from north to south.

The Caspian Sea, according to the chart drawn by the order of Czar Peter I. has more extent from the south to the north than from east to west; whereas in the ancient charts it appears almost round, or rather more broad from east to west than from south to north; but if we consider the lake Aral as a part of the Caspian Sea, from which it is separated only by plains of sand, we shall find the length is from the western coast of the Caspian Sea as far as the greatest border of Lake Aral.

So likewise the Euphrates, the Persian gulph, and almost all the rivers in China run from west to east; all the rivers in Africa beyond Barbary flow from east to west, or from west to east, and there are only the rivers of Barbary and the Nile which flow from south to north. There are, in fact, great rivers in Asia which partly run from north to south, as the Wolga, the Don, &c. but by taking the whole length of their course, we find, that they only turn from the south to run into the Black and Caspian seas, which are only inland lakes.

It may therefore in general be said, that in Europe, Asia, and Africa, the rivers, and other mediterranean waters, extend more from east to west than from north to south, which proceeds from the chains of mountains being for the most part so directed, and that the whole continent of Europe and Asia is broader in this direction than the other; for there are two modes of considering the direction of mountains. In a long and narrow continent like South America, in which there is only one principal chain of mountains which stretches from south to north, the river not being confined by any parallel range, necessarily runs perpendicular to the course of the mountains, that is from east to west, or from west to east; in fact, it is in this direction all the rivers of America flow. In the old as well as the new continent most of the waters have their greatest extent from west to east, and most of the rivers flow in this direction; but yet this similar direction is produced by different causes; for instance, those in the old continent flow from east to west, because they are bounded by mountains whose direction is from west to east; whereas those in America preserve the same course from there being only one chain of mountains that extends from north to south.

In general, rivers run through the centre of vallies, or rather the lowest ground betwixt two opposite hills or mountains; if the two hills have nearly an equal inclination, the river will be nearly in the middle of the intermediate valley, let the valley be broad or narrow. On the contrary, if one of the hills has a more steep inclination than the other, the river will not be in the middle of the valley, but much nearer the hill whose inclination is greatest, and that too in proportion to the superiority of its declivity: in this case, the lowest ground is not in the middle of the valley, but inclines towards the highest hill, and which the river must necessarily occupy. In all places where there is any considerable difference in the height of the mountains, the rivers flow at the foot of the steepest hills, and follow them throughout all their directions, never quitting their course while they maintain the superiority of height. In the length of time, however, the steepest hills are diminished by the rain acting upon them with a greater degree of force, proportionate to their height, and consequently carry away the sand and gravel in more considerable quantities, and with greater violence; the river is then constrained to change its bed, and seek the lowest part of the valley: to this may be added, that as all rivers overflow at times, they transport and deposit mud and sand in different places, and that sands often accumulate in their own beds, and cause a swell of the water, which changes the direction of its course. It is very common to meet in vallies with a great number of old channels of the river, particularly if it is subject to frequent inundations, and carries off much sand and mud.

In plains and large vallies, where there are great rivers, the beds are generally the lowest part of the valley, but the surface of the water is very often higher than the ground adjacent. For example, when a river begins to overflow, the plain will presently be inundated to a considerable breadth, and it will be observed that the borders of the river will be covered the last; which proves that they are higher than the rest of the ground, and that from the banks to a certain part of the plain, there is an insensible inclination, so that the surface of the water must be higher than the plain when the river is full. This elevation on the banks of rivers proceeds from the deposit of the mud and sand at the time of inundations. The water is commonly very muddy in the great swellings of rivers; when it begins to overflow, it runs very gently over the banks, and by depositing the mud and sand purifies itself as it advances into the plain; so that all the soil which the currents of the river does not carry along, is deposited on the banks, which raises them by degrees above the rest of the plain.

Rivers are always broadest at their mouths; in proportion as we advance in the country, and are more remote from the sea, their breadth diminishes; but what is more remarkable, in the inland parts they flow in a direct line, and in proportion as they approach their mouths the windings of their course increase. I have been informed by M. Fabry, a sensible traveller, who went several times by land into the western part of North America, that travellers, and even the savages, are seldom deceived in the distance they are from the sea if they follow the bank of a large river; when the direction of the river is straight for 15 or 20 leagues, they know themselves to be a great distance from the coast; but, on the contrary, if the river winds, and often changes its direction, they are certain of not being far from the sea. M. Fabry himself verified this remark in his travels over that unknown and almost uninhabited country. In large rivers there is a considerable eddy along the banks, which is so much the more considerable as the river is less remote from the sea, which may also serve as a guide to judge whether we are at a great or short distance from the mouth; and as the windings of rivers increase in proportion as they approach the sea, it is not surprising that some of them should give way to the water, and be one reason why great rivers generally divide into many arms before they gain the sea.

The motion of the waters in rivers is quite different from that supposed by authors who attempt to give mathematical theories on this subject; the surface of a river in motion is not level when taken from one bank to the other, but according to circumstances the current in the middle is considerably higher or lower than the water close to the banks; when a river swells by a sudden melting of snow, or when by some other cause its rapidity is augmented, if the direction of the river is straight, the middle of the water where the current is rises, and the river forms a convex curve, of a very sensible elevation. This elevation is sometimes very considerable; M. Hupeau, an able engineer of bridges, once measured the river Avieron, and found the middle was three feet higher than near the bank. This, in fact, must happen every time the water has a very great rapidity; the velocity with which it is carried, diminishing the action of its weight in the middle of the current, so that it has not time to sink to a level with that near shore, and therefore remains higher. On the other hand, near the mouths, it often happens that the water which is near the banks is higher than that of the middle, although the current be ever so rapid. This happens wherever the action of the tides is felt in a river, which in great ones often sensibly extends as far as one or two hundred leagues from the sea; it is also a well known fact that the current of a river preserves its motion in the sea to a considerable distance; there is, in this case, therefore, two contrary motions in a river; the middle, which forms the current, precipitates itself towards the sea, and the action of the tide forms a counter-current, which causes the water near the banks to ascend, while that in the middle descends, and as then all the water must be carried down by the current in the middle, that of the banks continually descends thereto, and descends so much the more as it is higher, and counteracted with more force by the tide.

There are two kinds of ebbings in rivers; the first above-mentioned is a strong power occasioned by the tide, which not only opposes the natural motion of the river, but even forces a contrary and opposite current. The other arises from an inactive cause, such as a projection of land, an island, &c. This does not commonly occasion a very sensible counter-current, yet it is sufficient to impede the progress of boats and craft, and necessarily produces what is called a dead water, which does not flow like the rest of the river, but whirls about in such a manner that when boats are drawn therein they require great strength to get them out. These dead waters are very perceptible at the arches of bridges in rapid rivers. The velocity of the water increases in proportion as the diameter of the channel through which it passes diminishes, the impelling force being the same; the velocity of a river, therefore, increases at the passage of a bridge, in an inverse proportion of the breadth of the arches to the whole breadth of the river; the rapidity being very considerable in coming through the arch, it forces the water against the banks, from whence it is reflected with such violence as to form dangerous eddies and whirlpools. In going through the bridge St. Esprit, the men are forced to be careful not to lose the stream, even after they are past the bridge, for if they suffer the boat to go either to the right or left, it might be driven against the shore, or forced into the whirling waters, which would be attended with great danger. When this eddy is very considerable, it forms a kind of small gulph, the middle of which appears hollow and to form a kind of cylindrical cavity, around which the water whirls with rapidity: this appearance of a cylindrical cavity is produced by the centrifugal force, which causes the water to endeavour to remove itself from the centre of the whirlpool. When a great swell of water happens, the watermen know it by a particular motion; they then say the water at the bottom flows quicker than common: this augmentation of rapidity at the bottom, according to them, always announces a sudden rise of the water. The motion and weight of the upper water communicates this motion to them; for in certain respects we must consider a river as a pillar of water contained in a tube, and the whole channel as a very long canal where every motion must be communicated from one end to the other. Now, independent of the motion of the upper waters, their weight alone might cause the rapidity of the river to increase, and perhaps move it at bottom; for it is known, that by putting many boats at one time into the water, at that instant we increase the rapidity of the under part of the river, as well as retard that of the upper.

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 Ferrara³³.

On the whole, the theory of the motion of running waters is still subject to many difficulties, nor is it easy to lay down rules which might be applied to every particular case. Experience is here more useful than speculation. We must not only know the general effects of rivers, but we must also know in particular the river we have to do with, if we would reason justly, make useful observations, and draw stable conclusions. The remarks I have above given are mostly new; it is to be wished that others may be collected, and then, possibly, in time, we may obtain a sufficient knowledge of the subject to lay down certain rules to confine and direct rivers, and prevent the ruin of bridges, banks, and other damages which the violent impetuosity of the water occasions.

The greatest rivers in Europe are the Wolga, which is about 650 leagues in its course from Reschow to Astracan, on the Caspian Sea; the Danube, whose course is about 450 leagues from the mountains of Switzerland to the Black Sea; the Don, which is 400 leagues in its course from the source of the Sosnia, which it receives, to its mouth in the Black Sea; the Dnieper, whose course is about 350 leagues, and which also runs into the Black Sea; the Duine is about 400 leagues in its course, and empties itself into the White Sea, &c.

The greatest rivers in Asia are the Hoanho of China, whose course is 850 leagues, taking its source at Raja-Ribron, and falls into the sea of China, in the middle of the gulph Changi: the Jenisca of Tartary, which is about 800 leagues in extent, from the lake Seligna to the northern sea of Tartary; the river Oby, which is about 600 leagues from Lake Kila, to the Northern Sea, beyond the Strait of Waigats. The river Amour, of eastern Tartary, which is about 575 leagues in its course, reckoning it from the source of the river Kerlon, to the sea of Kamschatka. The river Menan, whose mouth is at Poulo Condor, may be measured from the surface of the Longmu which falls into it; the Kian, whose course is about 550 leagues from the source of the river Kinxa, which it receives, to its mouth in the China Sea; the Ganges is also about 550 leagues, and the Euphrates 500, taking it from the source of Irma, which it receives. The Indus about 400 leagues, and which falls into the Arabian Sea, on the east of Guzarat. The Sirderious, which is about 400 leagues long, and falls into Lake Aral.

The greatest rivers in Africa are Senegal, which is 1125 leagues long, comprehending the Niger, which in fact is a continuation of it, and the source of Gombarou, which falls into the Niger. The Nile 970 leagues long, and which derives its source in Upper Ethiopia, where it makes many windings. There are also the Zaira, the Coanza, and the Couma, which are known as far as 400 leagues, but extend much farther; the Quilmanci, whose course is 400 leagues, and which derives its source in the kingdom of Gingiro.

The greatest rivers of America, and which are also the greatest in the world, are the river Amazons, whose course is 1200 leagues, if we go up as far as the Lake near Guanuco, 30 leagues from Lima, where the Maragnon takes its source; and even reckoning from the source of the river Napo, some distance from Quito, the course of the river Amazons is more than a thousand leagues.

It might be said that the course of the river St. Lawrence, in Canada, is more than 900 leagues from its mouth to the lake Ontaro, from thence to lake Huron, afterwards to the lake Alemipigo, and to the lake Assiniboils; the waters of these lakes falling one into another, and at last into St. Lawrence.

The river Mississippi more than 700 leagues long from its mouth to any of its sources, which are not remote from the lake of the Assiniboils.

The river de la Plata is more than 800 leagues long, from the source of the river Parana, which it receives.

The river Oroonoko runs more than 575 leagues, reckoning from the source of the river Caketa, near Pasto, part of which falls into the Oroonoko, and part flows also towards the river Amazons.

The river Madera, which falls into the Amazons, is more than 660 leagues.

To know nearly the quantity of water the sea receives by all the rivers which fall into it, let us suppose that one half of the globe is covered by the sea, and that the other half is land, which is nearly the fact; let us suppose also, that the mediate depth of the sea is 230 fathom. The surface of all the earth being 170,981,012 square miles; and that of the sea 85,490,506 square miles, which being multiplied by 1/4, the depth of the sea gives 21,372,626, cubical miles for the quantity of water contained in the ocean. Now, to calculate the quantity of water which the ocean receives from the rivers, let us take some great river, whose rapidity and quantity of waters are known; for example, the Po, which runs through Lombardy, and waters a tract of land 380 miles long; according to Riccioli, its breadth, before it divides into many trenches, is 100 perches of Boulogne, or 1000 feet, its depth 10 feet, and it runs four miles an hour; therefore the Po supplies the sea with 200,000 cubical perches of water in an hour, or 4 millions 800 thousand in a day; but a cubical mile contains 125 millions cubical perches; therefore 26 days is required to convey a cubical mile of water to the sea: it remains therefore only to determine the proportion between the river Po and all the rivers of the earth taken together, which is impossible to do precisely. But to know it pretty exactly, let us suppose that the quantity of water which the sea receives by the large rivers in all countries is proportional to the extent and surface of these countries, and that consequently the country watered by the Po, and other rivers which fall therein, is in the same proportion on the surface of the whole earth, as the Po is to all the rivers of the earth. Now by the most correct charts, the Po, from its source to its mouth, traverses a tract 380 miles long, and the rivers which fall therein, on each side, proceed from the springs and rivers 60 miles distant from the Po; therefore this great river, and the others it receives, waters a tract 380 miles long, and 120 miles broad, which makes 450,600 square miles, but the surface of all the dry land is 85,490,506 square miles; consequently all the water which the rivers carry to the sea, will be 1974 times greater than the quantity which the Po furnishes; but as 26 rivers equal to the Po furnish a cubical mile of water to the sea in a day, of course 1874 rivers like the Po would supply the sea with 26,308 cubical miles of water in a year, and that in the space of 812 years all the rivers would supply the sea with 21,372,626 cubical miles of water; that is to say, as much as there is in the ocean, and therefore 812 years is only required to fill it.³⁴

The result of this calculation is, that the quantity of water evaporated from the sea, and which the winds convey on the earth, is about 245 lines, or from 20 to 21 inches a year, or about two thirds of a line each day: this is a very trifling evaporation even when trebled, in order to estimate the water which refalls in the sea, and which is not conveyed over the earth. Mr. Halley, in the Phil. Transactions, page 192, evidently shews, that the vapours which rise above the sea, and which the winds convey over all the earth, are sufficient to supply all the rivers in the world.