REPORT ON HYDRAULICS. PART II. 437 



vered that tlie reduced slope of the surface in the highest floods, 

 reckoning from the point to which the surface of the sea at low 

 water reaches to the mouth, was equal to the reduced slope of 

 the bottom or of the lower superficies of the river, beginnmg 

 from the same point, and proceeding to the opposite direction. 

 His observations generally on rivers are valuable ; but the most 

 estimable writer, after Guglielmini, on rivers and torrents is Paul 

 Frisi. 



The work of this author isdividedinto three parts ; inthefirst the 

 author investigates the phsenomena of rivers and. torrents which 

 flow over gravel ; the origin of rivers ; the substances brought 

 down by them; and the formation and rectification of their beds. 

 The 2nd chapter treats of the velocity of water from apertures 

 in vessels according to the theories of Torricelli, Newton, Michel- 

 lotti, &c. ; and the velocities of rivers and artificial canals whe- 

 ther united or divided; their declivities, and the distribution of 

 them according to the principles of Galileo, CasteUi, Grandi, 

 Guglielmini, Gennete and others : and the third part relates to 

 rivers which carry sands and mud ; the states of the old and 

 new beds of rivers, with reference to the projects which had 

 been advanced for improving the Tiber, Arno, and other rivers 

 of the Bolognese ; the resistances, whether natural or artificial, 

 opposed to the free flow of rivers ; the doctrines of different 

 authors upon this subject; the effects of regurgitations oc- 

 casioned by dams, weirs, and other obstructions thrown across 

 rivers ; and lastly, the phaenomena attendant on rivers entering 

 into the sea. An interesting essay on navigable canals com- 

 pletes the work. 



Frisi, after demonstrating that Guglielmini had been mistaken 

 in supposing that the formation of the smaller gravel and sand 

 in the beds of rivers was owing to the attrition of the larger 

 stones in the upper parts of the courses of rivers, maintained, 

 on the contrary, that gravel and sand are original bodies spread 

 over the earth through which the rivers traverse ; and, by expe- 

 riments, determined that the formation of sand in rivers is not 

 owing to the attrition of stones against each other, but to varia- 

 tions in the velocity of the current, which deposits the materials 

 according to the greater or less intensity of its force. 



Viviani and Belgrado were of the same opinion. Belgrado ob- 

 served that stones torn from the mountains are precipitated 

 down their declivities, turning for the greater part of the time 

 on their own centres ; that they continue to roll along in the 

 same manner in the beds of torrents, until, the slopes becoming 

 less, they afterwards slide along the bottom, rubbing against it, 

 and are scattered to and fro by the impetuosity of the torrent ; 



