fi^5 LECTURE XXIV. 



determining the height at which the surface must stand immediately above 

 the were, and then calculating the inclination of the 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 dimen- 

 sions of rivers, as well as from immediate observation, that a considerable 

 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 sometime* 

 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 ve- 

 locity, 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 curva- 

 ture. This effect is probably occasioned by the centrifugal force, which ac- 

 cumulates the water on that side; so that the banks are undermined, 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 efJect 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 pf the river's motion, 

 and the more as they are more abrupt. 



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

 pagated equally in all directions, their motions ought also to diverge in a si- 

 milar manner; but this opinion is by no means well founded, even with 

 respect to those particles which receive their motions in an unlimited reser- 

 voir from the impulse of a stream which enters it. An experiment, 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 



