ON THE FRICTION OF FLUIDS. 225 



surface which will be required for producing the actual velocity in the 

 river thus made deeper ; which of course will determine the situation of 

 the surface where the water approaches the were ; and this surface, which 

 is more nearly horizontal than the general surface of the river, will be so 

 joined to it as to have a curvature 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 con- 

 siderable diminution of the breadth of a river at a particular 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 particles may be carried away by means of 

 the increased velocity, and the bed of the river may be deepened. 



Where a river bends in a considerable degree, it is generally remarked 

 that the velocity of the water is greater near the concave than the convex 

 side of the flexure, that is, at the greatest distance from the centre of its 

 curvature. This effect is probably occasioned by the centrifugal force, 

 which accumulates the water on that side ; so that the banks are under- 

 mined, and the channel is deepened by its friction. Some authors have 

 been led to expect that the velocity would be greater nearest to the convex 

 bank, because the inclination of the surface must be a little greater there ; 

 but the effect of the accelerating force in any short distance is inconsiderable, 

 and it is more than compensated by the want of depth. It may easily be 

 understood, that all angles and flexures must diminish the general velocity 

 of the river's motion, and the more as they are more abrupt. 



It has sometimes been imagined, that because the pressure of fluids is 

 propagated equally in all directions, their motions ought also to diverge in 

 a similar manner ; but this opinion is by no means well founded, even 

 with respect to those particles which receive their motions in an unlimited 

 reservoir from the impulse of a stream which enters it. An experi- 

 ment, which sets this fact in a clear point of view, was made long ago 

 by Hauksbee. * He produced a very rapid current of air, by means of a 

 vessel, into which three or four times as much air as it naturally con- 

 tained had been condensed by means of a syringe, and causing the current 

 to pass through a small box, in which the bason of a barometer was 

 placed, the mercury was depressed more than two inches, in consequence 

 of the rarefaction which the current produced in the air of the box. (Plate 

 XXI. Fig. 268.) 



Professor Venturi has also made several experiments of a similar nature 

 on the motion of water : he observes that not only the water in contact with 

 a stream is drawn along by it, but that the air in the neighbourhood of a jet 

 is also made to partake of its motion. When the mouth of a pipe through 

 which a stream of water is discharged, is introduced into a vessel a little 

 below the surface of the water which it contains, and is allowed to escape 

 by ascending an inclined surface placed opposite to the pipe and leading 

 over the side of the vessel, the stream not only ascends this surface without 

 leaving any portion of itself behind, but carries also with it the whole of 



* Hauksbee, Physico- Mechanical Experiments, 4to, Lond. 1709, p. 89. See 

 Leslie's examination of the experiment, art. Barometer. Supp. Encyc. Brit. p. 129. 



