REPORT ON HYDRAULICS. — PART 11. 445 



In the year 1823 a new collection, or rather continuation, of 

 the Trattato was published at Bologna, in six volumes, in which 

 the papers relating to rivers, are, first, An elegant dissertation 

 on the Natui'al Phaenomena of Rivers, by Count Mengiottij and 

 secondly. An Exposition of the Experiments which have been 

 made by different authors to arrive at the true theory of running 

 waters, by means of various instruments, such as the float, the 

 pendulum, the wheel, &c. Thirdly, A confirmation of the doc- 

 trines of Castelli with regard to the ratio of Increase by Tribu- 

 taries : and remarks on the inutility of diversions in rivers, as ad- 

 duced by the diversions from the Po, the Rhine, and other rivers, 

 by Guglielmini and Gennet^. The effects of regurgitations 

 in obstructing the free flow of rivers are quoted from different 

 authors and illustrated by experiment, more or less confirmatory 

 of the opinions of Guglielmini. 



Volume the second, contains papers by De Lorgna on the In- 

 undation of the River Adige ; the prolongation of Rivers into the 

 Sea, and the confining of their channels ; the effects of Affluents 

 and Diversions. — A paper, by Zuliani, on the advantages and 

 disadvantages attending the expansion of rivers at their embou- 

 chures ; the number and direction of the streams necessary to 

 maintain the water in its proper channel, and to resist the oppo- 

 sition of winds and waves. The author quotes many examples 

 in illustration of his theory, but concludes that the determination 

 of the question in a mathematical point of view is beyond the 

 reach of science. — Also, a learned paper on the motion and 

 measure of running water, by Tadini. The author adopts the 

 usually received theory of the velocity of running water, which 

 he reduces to expressions, and makes the relation of the velo- 

 city at the surface and bottom of a torrent to be as 1 : + 0*0016 j 

 he states that in the case of a river such as the Po, of which the 

 inclination, when the experiment was made, was as 0*0002 14 

 metre per metre, the velocity at the surface and bottom is very 

 nearly alike, and that in similar cases the velocity is small and 

 the surface nearly parallel to the bed. The notion, therefore, that 

 the velocity of a river increases from the surface to the bottom 

 as the square roots of the depths, is erroneous. 



The remaining chapters of Tadini' s treatise are devoted to an 

 examination of the theory of the measurement of running water 

 through close and open channels according to the velocity and 

 amplitude of the sections, with due allowance for obstacles ; he 

 shows also the modes adopted by the different provinces in Italy, 

 in the measurement of running water, and the discrepancies 

 resulting therefrom, and concludes with a variety of experi- 

 ments on the expenditures of orifices and rectangular channels. 



