VELOCITY OF CUB RE NTS. SQ5 



portions of the velocities at different depths, and it lias sometimes 

 been observed, perhaps on account of the resistance of the air, that 

 the velocity is a little less, immediately at the surface, than a few 

 inches below it. 



For similar reasons, the velocity of a river is also generally greater 

 in the middle than at the sides; and the motion of the particles iu 

 the middle must be retarded, not only by those which are below 

 them, but also by those on each side, while these, on the contrary, 

 are dragged on by the water in the middle : the middle parts tend, 

 therefore, to draw the sides towards them, which they cannot do, 

 without lowering the surface of the fluid next to the banks, in such 



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a, degree as to make the difference of level an equivalent to this 

 tf-ndency to approach the middle. This appears to be the reason, 

 why the surface of a lar<^e river :nay generally be observed to be 

 slightly convex, or a little elevated in the middle. 



The course of a river is sometimes interrupted by a is: ere or a 

 fall, natural or artificial; in such cases the velocity may be calcu- 

 lated in the same manner as when a fluid is discharged from a re- 

 servoir through an aperture of considerable height : supposing the 

 whole section of the were to be such an aperture, in a vessel so 

 much higher, that the velocity or" a fluid issuing from it at the 

 upper part of the aperture would be precisely equal to the actual 

 velocity of the river. The extent of the swell caused by a were, or 

 by any partial elevation thrown across t'.ie bed of a river, may also 

 be found by first determining the height at which the surface must 

 stand immediately above the were, and then calculating the inclina- 

 tion of the surface which will be required for producing the actual 

 velocity, in the river thus made deeper; which of course will deter- 

 mine the situation of the surface where the water approaches the 

 were ; and this surface, which is more nearly horizontal than the 

 general s-urface of the river, will be so joined to it as to have a cur- 

 vature nearly uniform throughout. , 



It appears from calculations of the effects of various changes in 

 the dimensions of rivers, as well as from immediate observation, 

 that a considerable diminution of the breadth of a river at a parti. 

 cular place, will often produce but a small elevation of its surface. 

 The velocity, however, may sometimes be considerably increased by 

 such a change, and where the bottom is of a loose nature, its par- 



