394 lECTURE XXIV. 



From considering the effect of the magnitude of the surface exposed to the 

 friction of the water, in comparison with the whole quantity contained in 

 the river, together with the degree in which the river is inclined to the ho- 

 rizon, we may determine, by following the methods adopted by Mr. Buat, 

 the velocity of any river of which we know the dimensions and the inclinar 

 tion. Supposing the whole quantity of water to be spread on a horizontal 

 surface, equal in extent to the bottom and sides of the river, the height, at 

 which it would stand, is called the hydraulic mean depth ; and it may be 

 shown that the square of the velocity must be jointly proportional to the 

 hydraulic mean depth, and to the fall in a given length. If we measure 

 the inclination by the fall in 2800 yards, the square of the velocity in a se- 

 cond will be nearly equal to the product of this fall multiplied by the hydraulic 

 mean depth. For example, in the Ganges, and in some other great rivers, 

 the mean depth being about 30 feet, and the fall 4 inches in a mile, the 

 fall in £800 yards will be about 6~ inches, which, multiplied by 360 inches, 

 gives 2340 inches for the square of the mean velocity, and 48^ 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 rapid. 

 If, however, great precision were required in the determination, some fur- 

 ther corrections would be necessary, on account of the deviation of the resist- 

 ance 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 the surface of a solid 

 alone, would not produce any material retardation of its motion, if the par- 

 ticles of the 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, how- 

 ever, that the water in contact with the bottom of a river moves with a very 

 considerable velocity, and the v/ater next above this only a little faster, so 

 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 sur- 

 face of a solid. This internal friction operates gradually throughout the 



