RIVER. 



where they are more deprefled with refpedl to the elevation 

 of their common fource or fpring. 



The upper parts of the water of a river, and thofe at a 

 diftance from the banks, may continue to flow, from the 

 fingle caufe, or principle of declivity, how fmall foever it 

 be ; for, not being detained by any oneobitacle, the minuteft 

 difference of level will have its effect ; but the lower parts, 

 which roll along the bottom, will fcarcely be fenfible of fo 

 fmall a declivity ; and will only have what motion they 

 receive from the preffion of the fuperincumbent waters. 



The natural cohefion of the particles of water, and their 

 implication, as it were, with one another, make the lower, 

 which are moved by means of the depth, carry along with 

 them the upper, which, in an horizontal channel, would have 

 no motion at all : or, in a channel very little inclined, next to 

 none ; fo that the lower, in this cafe, communicate to the 

 upper a part of the motion they have received from the 

 prefiure of it. Hence, from the prefiure, it frequently 

 happens that the greateil velocity of a river is about the 

 middle of its depth, or that point, which is the f.irtheft pol- 

 fible from the furface of the water, and from the bottom 

 and fides of the bed ; fuch middle parts having the advan- 

 tage of being prefled with half the depth of the river, and 

 of being free, at the fame time, from the friction ot the 

 bottom ; whereas, on the contrary, the leaft velocity of the 

 water is at the bottom and fides of the bed, becaufe there 

 the refiftance refulting from friction is the greateft, which 

 is communicated to the other parts of the fedtion of the 

 river, in an inverfe duplicate proportion of the diftances 

 from the bottom and fides combined together. 



To find whether the water of a river, almoft horizontal, 

 flows by means of the velocity acquired in its defcent, or 

 by the prefiure of its depth, fet up an obftacle perpen- 

 dicular to it ; if the water rife and fwell immediately againft 

 fuch obftacle, it runs in virtue of its fall ; or, if it ftop a 

 little while firft, in virtue 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 of it, falling 

 with a great deal of force, will have fwept away the moil 

 elevated parts of the foil, and carrying them lower down, 

 will gradually render the bottom horizontal ; where the 

 ftream is fwifteft, there will the earth be moft dug up ; 

 and, confequently, there the greateft cavity will be made. 



The water having made its bed horizontal becomes fo 

 itfelf, and confequently rakes with the lefs force againft 

 the bottom, till at length that force becomes only equal to 

 the refiitance of the bottom. The bottom is now arrived 

 at a ftate of permanency, at leaft for a confiderable time : 

 and the longer, according to the quality of the foil, clay 

 and chalk refilling longer than fand or mud. 



On the other hand, the water is continually wearing away 

 the brims of its channel, and this with the more force, as, 

 by the direction of its ftream, it impinges more perpen- 

 dicularly againft them. By this means it has a continual 

 tendency to render them parallel to its own courfe ; and 

 when it has arrived as near that as poffible, it ceafes to have 

 any effect that way. At the fame time that it has thus 

 rectified its edges, it has enlarged its own bed ; that is, it 

 has loft of its depth, and confequently of its force and 

 prefiure : this it continues to do till there is an equilibrium 

 between the force of the water and the refiftance of its 

 banks, upon which they will remain without farther muta- 

 tion. And it is evident, from experience, that thefe equi- 

 libriums are all real, inafmuch as we find that rivers only 

 dig and widen to a certain pitch. 



The very reverfe of all thefe things happens on other oc- 



cafions. Rivers, whofe waters are thick and muddy, raife 

 their bed, by letting part of the heterogeneous matters 

 contained in them fall to the bottom : they alfo contract 

 their banks, by a continual appofition of the fame matter, in 

 bruihing over them. This matter, being thrown afide far 

 from the ftream of water, might even ferve, by reafon of 

 the obfeurenefs of the motion, to form new banks. 



Now thefe oppofite effects feem almoft always to concur, 

 and are differently combined, according to the circumltances, 

 whence it is very difficult to judge of the refult ; yet mull 

 this combination be known very accurately, before any 

 meafures can be taken about rivers, elpecially as to the 

 diverting of their courfes. The Lamona, which emptied 

 itfelf into the Po, being turned another way, to make it 

 difcharge itfelf into the Adriatic, was fo altered, and its 

 force fo far diminifhed, after its waters were left to them- 

 felves, that it raifed its bed a great height, by continual 

 depofitions of mud, till it became much higher than the 

 Po, in its utmoft accretions, and needed very high banks, 

 or dykes, to keep it from overflowing. 



If various caufes of refiftance to the motion of flowing 

 waters did not exift, fuch as the attraction and continual 

 friction of the bottom and fides, the inequalities in both, 

 the windings and angles that occur in their courfe, and the 

 diminution of their declivity the farther they recede from 

 their fprings, the velocities of their currents would be ac- 

 celerated to twelve, fifteen, and, in fome cafes, even to twenty 

 times more than they are at prefent in the fame rivers, by 

 which they would became abfolutely unnavigable. 



A little river may be received into a large one, without 

 either augmenting its width or depth. This feeming pa- 

 radox ariies hence, that the addition of the little river may 

 only go towards moving the waters, before at reft near the 

 banks of the large one, and thus augmenting the velocity 

 of the ftream, in the fame proportion as it does that of the 

 quantity of water. Thus the Venetian branch of the Po 

 fwallowed up the Ferrarefe branch, and that of Panaro, 

 without any enlargement of its own dimenfions. And the 

 fame may be concluded proportionably of all other accef- 

 fions to rivers, and, in the general, of all new augmentations 

 of water. 



A river offering to enter into another, either perpendi- 

 cularly, or in an oppofite direction, will be diverted by 

 degrees from that direction, and obliged to make itfelf a 

 new and more favourable bed towards the mouth. 



The union of two rivers into one makes the whole flow 

 the fwifter, becaufe, in lieu of the friction of four fhores, 

 they have only two to furmount ; and that the ftream, 

 being farther diftant from the banks, goes on with the lefs 

 interruption ; beiides, that a greater quantity of water, 

 moving with a greater velocity, digs deeper in the bed, 

 and of courfe retrenches of its former width. Hence alfo 

 it is that rivers, by being united, take up lefs fpace on the 

 furface of the earth, and are more advantageous to low 

 grounds, which difcharge their fuperfluous moifture into 

 them, and have likewife lefs occafion for dykes to prevent 

 their overflowing. 



Thefe advantages are fo confiderable, that S. Guglielmini 

 thinks them worthy of nature's having had a view to them 

 in her contriving to make the confluences of rivers io fre- 

 quent as we find them. 



Such were the views and deductions of this author, in 

 which he has been followed by feveral mathematicians of 

 the firft eminence ; but certainly without coming to any 

 very accurate and eftablifhed principles, on which to found 

 a computation of the quantity of water that would be dif- 

 charged, in any new cafe that prefented itfelf for determina- 

 tion ; 



