REPORT ON HYDRAULICS. — PART II. 429 



and Viviani to confine the Chiana by banks, and so conduct it 

 to the Arno. In a subsequent meeting, at which Torricelli was 

 present, the same system was recommended, on the ground that 

 the rivers Arno, Tiber, and Po were confined by the same means. 



Although nothing important had arisen out of the proceed- 

 ings of the congress of Florence, the attention of philosophers 

 was excited to discover the true causes of these evils. Much 

 had been said and written on the rivers of Lombardy, Ferrara, 

 Bologna *, Tuscany, and other provinces of Italy ; but no one 

 had undertaken to combine together the facts elicited, by a 

 careful observation on the rivers themselves, until the meeting 

 of a second congress at Bologna in the year 1681. 



The Po and the Reno were the rivers that excited the greatest 

 interest, on account of the absorption of the river Primaro by 

 the Po, and the blocking up of the Reno by the depositions of 

 the Ferrara branch, by which the Reno was raised so high as to 

 cause the bursting of the banks, and the consequent inundation 

 of the most fertile provinces of the Bolognese. This evil was 

 greatly increased by the addition of five other torrents to the 

 mass. Such a scene was well calculated to increase the interest 

 upon this subject ; hence may be dated the rise of the science 

 of hydrometry in Italy. 



The discovery of the law of falling bodies by Galileo, and the 

 subsequent misapplication of this law to the rivers Bisenzio and 

 Arnof in opposition to the opinion of Bartolotti, paved the way 

 to several very important investigations by Castelli, who in- 

 troduced the element of velocity, arising from pressure, into 

 the calculation of the quantities of water which flow in the beds 

 of rirers. Castelli proved, — 



1st, That in a river reduced to a state of permanence, the 

 quantity of water which passes through all its sections in equal 

 spaces of time will be equal : 



2ndly, That the medium velocities in the different sections will 

 be reciprocally proportional to the amplitude of the sections : 



• Delia Salveazione de' Fiume del Bolognese e della Romagna, del M. R. P. 

 Leonardo Ximenes e del Pietro Paolo Conti : Roma, 1776. Also, Trattala de' 

 Canali Navigabili &e\ Ah. h-nionioljecclri: Milano, 1776. A\so, De' Canali 

 Navigabili di P. D. Paoli Frisi, 1770. 



f Lettera di Galileo Galilei sopra il Fiume Bisenzio, a Raffaello Sfaccoli. 



Bartolotti, an engineer, having projected to shorten the course of the river 

 Bisenzio by means of a cut or canal, Galileo opposed it for the following rea- 

 sons : — 1st, That in two canals of equal height, but of unequal lengths, the 

 velocity of the stream would be the same in both of them. 2ndly, That it is 

 not the inclination of the bed of the canal, but the surface, that regulates the mo- 

 tion of the water. Srdly, That the velocities do not follow the ratio of inclination 

 as Bartolotti asserted, but differ in a variety of ways in similar inclinations. 



