430 FOURTH UEPORl' — 1834. 



3rdly, That if a river, flowing in a rectangular channel with a 

 certain velocity, be augmented by a flood to double its height, 

 the velocity of the water will be double ; a principle sub- 

 sequently adopted by Gennetd, and disputed so often by the 

 Italian philosophers. Castelli was well aware of the necessity 

 of removing the obstacles to the free flow of rivers ; but he 

 was wrong in his supposition of the effect of sluices, and 

 in attributing the velocity of the water near the mouths of 

 rivers to the pressure of the superior waters. His opinions 

 relative to the effect of rivers in purifying the air, and in pre- 

 venting the increase of the sea -shore opposite Venice, were con- 

 tradicted by Montanari and Guglielmini, who advised the di- 

 version of the rivers from their ancient channels ; and corrected 

 the evil for a time. 



Torricelli was the first who endeavoured to prove the analogy 

 subsisting between spouting fluids and rivers, and their accelera- 

 tion on account of the slope of the surface. 



The respect of Viviani for Galileo did not prevent him from 

 rejecting the ideas of his master as to the effect of shortening 

 the course of the Bisenzio *. Viviani added several useful ob- 

 servations on the subject. 



Zendrini, in his experiments with the pendulum, discovered 

 that the velocities in the different parts of the section of the 

 river Po were nearly proportional to the square roots of the 

 heights, when the velocities were not very great f. 



The truth of this law has been confirmed by all the experi- 

 ments which have been made with the hydrometrical flask 

 invented by the Bolognese in the year 1721, in which the quan- 

 tities of water entering in a given time by a small aperture left 

 open at the top, and collected by sinking the flask successively 

 to different depths in stagnant as well as running waters, were 

 at all times nearly in proportion to the square root of the 

 heights. Independently however of these experiments, the 

 parabolic law is sufiiciently ascertained ; so that in a parabola, 

 of which the abscisses represent the depth of a river, and a cor- 

 responding semiordinate represents the velocity, all the other 

 semiordinates will express velocities corresponding with the 

 heights of their respective abscisses. Again, the space run 



* Opinions are yet divided on the propriety of shortening the courses of 

 rivers ; but in rivers carrying gravel there can he no doubt. 



Viviani liad several striking examples before him of the evil consequences 

 which had resulted from shortening the course of the Arno, both above and 

 below Florence ; and his observations upon the rising of the bed of that river 

 are applicable to all rivers similarly situated. 



t Leggi, Fenomeni, Regolazioni ed Usi delle Acque Correnti, di Bernardo 

 Zendrini, (Firenze, 1770,) cap. v. part. ii. pag. 100. 



