ON THE FRICTION AND 



Ganges, and in sonic other great rivers, the mean depth being about 

 30 feet, and the fall four inches in a mile, the fall in 2 SCO yards will 

 be about 6| inches, which, multiplied by 36O incites, gives 2340 

 inches for the square of the mean velocity, and 4Si inches, or about 

 four feet for the mean velocity in a second, that is, not quite three 

 miles an hour, which is the usual velocity of rivers moderately ra- 

 pid. If, however, great precision were required in the determina- 

 tion, some further corrections would be necessary, on account of 

 the deviation of the resistance from the exact proportion of the 

 squares of the velocities : since the friction, as we have already seen, 

 does not increase quite so fast as this. 



It is obvious that the friction of a fluid, moving on tht surface of 

 a solid alone, would not produce any material retardation of its 

 motion, if the particles of Hie fluid themselves were capable of 

 moving on each other, without the least resistance ; for in this case a 

 small portion of the fluid, in immediate contact with the solid, might 

 remain at rest, and the remaining mass of the fluid might slide over 

 this portion without any retardation. It appears, however, that the 

 water in contact with the bottom of a river moves with a very con. 

 siderable velocity, arid the water next above this only a little faster, 

 :>o that the velocity increases almost uniformly as we ascend towards 

 the surface. It follows, therefore, that the resistance must be much 

 greater where the particles of water slide on each other, than where 

 they glide along the surface of a solid. This internal friction ope- 

 rates gradually throughout the water; the surface being retarded by 

 the particles immediately below it, those particles by the next infe- 

 rior stratum, and each stratum being actuated, besides its own re- 

 lative 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 up- 

 wards, in such a manner as to be every where equivalent to the re- 

 lative 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 velocity at bottom, by sub. 

 trading from it the same number ; thus the square root of48j 

 being nearly 7, 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 f. There are, however, frequent irregularies in the pro. 



