RIV
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RIV
Parte having the Advantage of being prefs'd with half the Depth of the River, and of being free, at the lame Time, from the Friftion of the Bottom.
To find whether the Water of a River almoft Horizontal, flows by means of the Velocity acquired in it Defcent, or by the Preffure of its Depth ; fet up an Obftacle Perpendicular thereto ; and if the Water rife and fwell immediately againft fuch Obfta- cle, it runs in Virtue of its fall ; or if it flop a little while, in Vir- tue of its Preffion.
Rivers, according to this Author,almoft always make their own Beds— If the Bottom have originally been a large Declivity; the Water in Confequence hereof falling with a great deal of Force, will have fwept away the mod: elevated Parts of the Soil, and carrying them lower down, will gradually make the Bottom ho- rizontal; where the Stream is fwifteft, there will the Earth be tnoftdugup, and confequently there the greateft Cavity will be made.
The Water having made its Bed horizontal, becomes fo it felf, and confequently rakes with the lefs Force againft the Bot- tom ; till at length that Force is only equal to the Refiftancc of the Bottom. TheBottom is now arrived at a State of Permanen- cy, at leaft for a confiderable Time; and the longer, according to theQuality of the Soil ; Clay and Chalk refilling longer than Sand or Mud.
On the other Hand, the Water is continually gnawing and eat- ing off the Brims of its Channel ; and this with the more Force as by the Direction of its Stream it ftrikes more perpendicular- ly againft them. By this means it has a continual Tendency to render them parallel to its own Courle; and when it has arrived as near that as poffible, it ceafes to have any Effect in that Way. At the fame time that it has thus rectified its Edges, it has inlarged its own Bed ; that is, has loft of its Heigth, and confequently of its Force and Preffure : This it continues to do till there is an Equilibrium between the Force of the Water and the Rcfiftance of its Banks, upon which they will remain nVd. — And it is evident from Experience, that thefe Equilibriums are all reai; inafmuch as we find that Rivers only dig and widen to a certain Pitch.
The very reverfe of all thefe things does alfo happen — Rivers whofe Waters are thick and muddy, raife their Bed by letting Part of the heterogeneous Matters contain'd in them fall to the Bottom: They alfo contract their Banks by a continual Appor- tion of the fame Matter in brufliing over them. This Matter being thrown afide far from the Stream of Water, might even ferve, by reafon of theobfeurenefs of the Motion, to form new Banks.
Now, thefe oppofite Effects almoft always teem to meet to- gether, and are differently combined, according to the Circum- ilances; whence 'tis very difficult judging of the Refulr. Yet mufl this Combination be known very accurately, e're any Mea- fures can be taken about Rivers, efpecially as to the diverting their Courfes. — The Lamona, which emptied it felf into the Fo, being tunvd another Way to make ir difcharge it felf into the Adriatic, was fb alter'd, and its Force lb far dimtnifVd, now that its Waters were left to themfeives, that it rais'd its Bed a great Heighth, by continual Depofirions of Mud; 'till it became much higher than the Po, in its utmofl Accretions, and needed very high Banks or Dykes to keep it from overflowing. See Allu- vion.
A little River may be receiv'd into a large one, without either augmenting its Width or Depth. — This feeming Paradox arifes hence, that the Addition of the little River may only go to move the Waters before at reft near the Banks of the large one, and thus augment the Velocity of the Stream, in the fame Proporti- on as it does that of the Quantity of Water. — Thus theVeaetiati Branch of the Po fwallowed up the Ferrarefe Branch, and that of Papaya, without any inlargemcnt of its own Dimenfions. And the fame may be concluded proportionably of all other Acceili- ons to Rivers ; and in the general, of all new Augmentations of Water.
A River offering to enter into another, either perpendicularly, or in an oppofite Direction, will be diverted by Degrees from that Direction, and obliged to make it felf a new and more fa- vourable Bed next the Mouth.
The Union of two Rivers into one, makes it flow the fwifrer, by reafon in lieu of the Friction of four Shores, they have only two to furmount ; and that the Stream being further diftant from the Banks, goes on with the lefs Interruption ; befide that a greater Quantity of Water moving with a greater Velocity digs deeper in the Bed, and of Courfc retrenches of its former Width. —Hence alfo it is that Rivers, by being united, take up left Space on the Surface of the Earth are more advantageous to low Grounds ; which difcharge their fuperfluous Moiflurc into them, and have lefs Occafion for Dykes to prevent their overflowing.
Thefe Advantages are fo confiderable, that S. Gugliebmni thinks them worthy of Nature's having had a View to them in her contri- ving to make the Confluence of Rivers fo frequent as we find it.
To determine more precifely the general Laws of the Moti- on of Rivers, it may be obferved that a River is faid to remain in the fame State, or to be in a permanent State, when it flows uniformly, fo as to be always at the ia.m.9 Heighth \n the feme
Place. 2. Q i That a Plane, which cutting a River is perpendicular to the Bottom, as p n g, is call'd the Section of a River.
Hence, when a River is terminated by flat Sides, parallel to each other, and perpendicular to the Horizon, and the Bottom alfo is a Plane, either horizontal, or inclined, the Section of the River with thefe three Planes makes Right Angles, and is a Pa- rallelogram.
Now in every River that is in a permanent State, the fame Quantity of Water flows in the fame Time through every Secti- on; for unlcfs there be in every Place as great a Supply of Wa- ter, as what runs from it, the River will not remain in the fame State. This will hold good, whatever be the Irregularity of the Bed, or Channel, from which in another refpect feveral Changes in the Motion of the River may arife : For Example, a grea- ter Friction, in Proportion to the Inequality of the Channel.
The Irregularities in the Motion of a River may be infinitely varied, nor can any Rules be given to fettle them. All Irregula- rities muft be fet aiide ; and only the general Tenor or Flux be confidered to examine the general Courfe of Rivers.
Suppofe, "then, the Water to run in a regular Channel, with- out any fenfible Friction, and that the Channel is terminated with Plane Sides, parallel to one another, and Vertical; and aifo that the Bottom is a Plane, and inclined to the Horizon. — Let AE be the Channel, into which the Water runs from a greater Re- ceptacle or Head ; and let the Water always remain in the fame Heighth at the Head, fo that the River may be in a permanent State: The Water here defcends along an inclined Plane, and is accelerated; whereby, becaufe the fame Quantity of Water flows through every Section, the Heighth of the Water, as you recede from the Head of the River, is continually diminifhed, and its Surface will acquire the Figure, i a v.
To determine the Velocity of the Water in different Places; fuppofe the hollow of the Channel ADCB to be fhut up with a Plane; if there be an Hole made in the Plane, the Water will fpout the fafler through the Hole, as the Hole is more diftant from the Surface of the Water HI; and the Water will have the fame Celerity that a Body failing from ihe Surface of the Water to the Depth of the Hole below it, would acquire : All which arifes from the Preffure of the fuperinciimbcnt Water.— There is the fame Preffure, that is, the fame moving Force, when the Obftacle at AC is taken away, upon which every Particle of Water enters into the Channel with the Celerity a Body would acquire in falling from the Surface of the Water to the Depth of that Particle. This Particle is moved along in an inclined Plane in the Channel, with an accelerated Motion ; and that in the fame manner, as if in falling vertically, it had continued its Motion to the fame Depth below the Surface of the Water in the Head of the River.
So, if you draw the horizontal Line ;/, the Particle at r will have the fame Celerity as a Body falling the length ;' C, and run- ning down Cr, can acquire; which is the Celerity acquired by the Body in falling down t r. Therefore the Celerity of a Par- ticle may be every where meafured, by drawing from it a Per- pendicular to the horizontal Plane, which is conceived to run a- long the Surface of the Water in the Head of the River ; and the Velocity which a Body acquires in falling down that Perpen- dicular, will be the Celerity of the Particle; which is greater, the longer the Perpendicular is. From any Point, as r, draw RS perpendicular to the Bottom of the River, this will meafure the Heighth or Depth of the River. Since r s is inclined to the Horizon, if from the feveral Points of that Line, you draw Perpendiculars to it, they wilt befhorter, the more diftant they are from r, and the fhortefl of them alfo will befv: There- fore the Celerities of the Particles in the Line r s, are fo much the lefs, the nearer they are to the Surface of the River-, and the lower Water is moved fafler than the upper Water.
Yet the Celerities of thofe Waters, as the River runs on, con- tinually approach nearer and nearer to an Equality : For the Squares of thofe Celerities are as r t to r v, the Difference of which Lines, as you recede from the Head of the River is continually leffcned, becaufe of the Heighth r s, which is alfo continually diminifhed as the Lines themfeives are lengthened. Now as this obtains in the Squares, it will much more obtain in the Celerities themfeives, whole Difference therefore is diminifhed as they in- creafe.
If the Inclination of the Bottom be changed up to the Head of the River, fo as to become^ z 3 and a greater Quantity of Wa- ter flow into the Channel, it will be higher every where in the River* but the Celerity of the Water will not be changed.— For this Celerity does not depend on the Heighth of the Wa- ter in the River, bur, on the Diftance of the moved Particle from the horizontal Plane of the Surface at the Head continued over the faid Particle; which Diftance is meafured by the Per- pendicular r t, or fv ; but thefe Lines, are not changed by the Afflux of Water, provided the Water remain at the fame Heighth in the Bafon or Head.
Suppofe the upper Part of the Channel ftop'd by an Obftacle, as X, which defcends a little way below the Surface of the Water ; here, the whole Water which comes cannot run through, there- fore it muft rife : But the Celerity of the Water below this Ca- taract is not increafed; and the Water that comes on, is conti- nually
