VELOCITY OP CURRENTS. 



ter issuing from a simple orifice, which constitutes the contraction 

 already described, is very nearly the same, whatever the velocity 

 may be: nor does the friction increase with the pressure, as is de- 

 monstrated by an experiment of Professor Robisou on the oscilla*. 

 tion of a fluid through a bent tube, terminated by two bulbs, which 

 were performed in the same time, whether the tube was in a hoii- 

 ontal or in a vertical position. Mr. Coulomb has also proved the 

 same fact by experiments on the vibrations of bodies immersed in 

 fluids, and suspended by twisted wires ; he finds that precisely at 

 the surface, the friction is somewhat greater than at any depth be. 

 low it : he also considers a certain part of the friction as simply 

 proportional to the velocity, and a small portion only, in common 

 fluids, as perfectly independent of it.- 



It is obvious that wherever the friction varies as the square of the 

 velocity, or even when it increases in any degree with the velocity, 

 there must always be a limit, which the velocity can never exceed, 

 by means of any constant force, and this limit must be the velocity 

 at which the resistance would become equal to the force. It is for 

 Ihis reason that a light body, descending through the air, soon ac. 

 quires a velocity nearly uniform j and if it be caused, by any exter- 

 nal force, to move fora time more rapidly, it will again be speedily 

 retarded, until its velocity be restored very nearly to its original 

 state. In the same manner the weight of the water in a river, 

 which has once acquired a stationary velocity, is wholly employed 

 in overcoming the friction produced by the bottom and the banks. 



From considering the effect of the magnitude of the surface ex- 

 posed 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 horizon, we may determine, by following 

 the methods adopted by Mr. Buat, the velocity of any river of which 

 we know the dimensions and the inclination. Supposing the whole 

 quantity of water to be spread on a horizontal surface, equal in ex- 

 tent 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 <?800 yards, the square of 

 the velocity in a second will be nearly equal to the product of this 

 fall multiplied by the hydraulic mean depth. For example, in the 



