ON THE I'-RICTIOV OF FLUIDS. 295 



water; the surface being retarded by the particles immediately below it, 

 those particles i)y the next inferior stratum, and each stratum being actuated, 

 besides its OM'n relative weight, by the friction of the water above, tending 

 to draw it forwards, and by that of the water below, tending still more to 

 retard it; the retardation being communicated, from below upwards, isi 

 such a manner as to be every where equivalent to the relative weight of 

 the water above the part considered. It appears from observation, that when 

 we have determined the mean velocity in English inches, we may find the 

 superficial velocity, very nearly, by adding to it its square root, and the ve- 

 locity at the bottom, by subtracting from it the same number: thus the square 

 root of 48^- being nearly T, the superficial velocity of the Ganges will be about 

 55 inches, or 4 feet 7 inches in a second, and the velocity at the bottom 41-}. 

 There are, however, frequent irregularities in the proportions of the velocities 

 at different depths, and it has 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 in 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 tliem, which they 

 cannot do, without lowering the surface of the fluid next to the banks, in 

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

 to approach the middle. This appears to be the reason, that the surface of a 

 large river may generally be observed to be slightly convex, or a little ele- 

 vated in the middle. 



The course of a river is sometimes interrupted by a were or a fall, natural 

 or artificial; in such cases the velocity may be calculated in the same manner 

 as when a fluid is discharged from a reservoir through an aperture of consi- 

 derable height; supposing the whole section of the were to be such an aper- 

 ture, in a vessel so much higher, that the velocity of a fluid issuing from it 

 at the upper part of the aperture would be precisely equal to the actual velo- 

 city of the river. The extent of the swell caused by a were, or by any par- 

 tial elevation thrown acj-oss the bed of a river, may also be found by first 



