^oS FOURTH REPORT — 1834. 



and that in consequence of the rolling and sliding motion they 

 acquire in their descent, there can be little or no abrasion of 

 the surface. Grandi, in considering the dam of Era, and com- 

 paring the specific gravities of the granite in the water, and of 

 the water itself, inferred that the transverse impetuosity of the 

 waters was sometimes sufficient to raise the gravels from the 

 bottom, and to throw them on the edges of the dykes. 



Besides his work on rivers and torrents, Frisi particularly 

 distinguished himself in the Bolognese and Ferrara controversy, 

 in which his plan for the rectification of the rivers of those 

 provinces in 1760 was approved of by all the mathematicians 

 then present. It was just at this period while Frisi was en- 

 gaged in the Bolognese controversy, that the Avork of M. Gen- 

 nete made its appearance ; and on comparing together the 

 observations made on rivers by both parties, it appeared to 

 Frisi that there was no sensible height even when there is a 

 considerable augmentation of water, and therefore, that the 

 velocity of the water increases sensibly in the same ratio as its 

 quantity. 



The propositions of Gennete were, 



let. If two rivers be added to another during the time of its 

 flood, the river will experience no sensible rise in its surface ; 



2ndly, That if from the same river two branches be taken, 

 its surface will not be sensibly lowered. 



These doctrines had been partly advanced with regard to ca- 

 nals by Castelli, Cassini, Guglielmini, and Corradi, but Gen- 

 nete was the first to apply them to rivers. It had been stated 

 by Frisi that the river Reno received the Samoggia without any 

 perceptible difference in the amplitude of its sections, and that 

 therefore it might receive other torrents without any sensible 

 augmentation. Doctrines so extraordinary, and at variance with 

 the received opinions on this subject, excited many discussions 

 in Italy. Gennete's experiments were tried at Ferrara in the 

 year 1762, and at Rome in the year following, and again repeated 

 at Feri'ara in the ^^ear 1766, but with results entirely different; 

 he, however, clearly proved that the dissimilarity was principally 

 owing to the different modes of experimenting, although the 

 apparatus used at Ferrara resembled Gennete's very nearly. 

 The recipient was 199 feet in length and 7 inches in width, 

 and the result was, that the first tributary stream (equal in sec- 

 tion to the recipient) occasioned an augmentation in height of 

 one half, and on introducing a second tributary of the same 

 section, the augmentation was double ; it Avas conceived, there- 

 fore, that Gennet^ had either erroneously stated his case, or 

 the effect was due to the increase of velocity occasioned by 



