174 THIRD REPORT 1833. 



and pumps of different descriptions, horizontal and inclined 

 helices, bucket-wheels, throwing-wheels, and lastly, on instru- 

 ments for measuring the velocity of streams of water. A very 

 detailed account of the work was given in the Journal of the 

 Royal Institution, by the late Dr. Young. But it is due to 

 MM. Dubuat and Prony to state, that M. Eytelwein has 

 exactly followed the steps of these gentlemen in his Theory of 

 the Motion of Water 171 open Channels. 



In the year 1809 a valuable series of experiments upon the 

 motions of waters through pipes, was made by MM. Mallet 

 and Vici at Rome, and afterwards by M. Prony*. 



It had been proved, by experiments made with great care, 

 that the diminution of velocity, and consequent expenditure in 

 pipes, was not in the ratio of the capacity of the pipes, as Fron- 

 tinus had supposed in his valuation of the product of the an- 

 cient module or calice ; and as it was desirable to ascertain the 

 actual product of the three fountains now used at Rome, a se- 

 ries of experiments was undertaken by these gentlemen ; the 

 principal result of which was, that a pipe, of which the gauge 

 was five oncesf, furnished |th more water than five pipes of 

 one once, on account of the diminution of the velocity by 

 friction in the ratio of the perimeters of the orifices as com- 

 pared with their areas. 



M. Mallet also made a great many researches relative to the 

 distribution of water in the different cities and towns of En- 

 gland and France, with a view to their application at Paris; of 

 all of which he has published an account. 



The researches that had been made hitherto on the expendi- 

 ture of water through orifices, had for their object the deter- 

 mination of the velocity and magnitude of the section, by which 

 it is necessary to multiply the velocity to obtain the expense. 

 But although these be the first elements for consideration, they 

 are not sufficient ; for the fluid vein presents other phasnomena 

 equally important, both in the theory and its application, 

 namely, the form and direction of the vein after it has issued 

 from the orifice. The former phaenomena, as we before stated, 

 had been long noticed by Michelotti and others, but nothing 

 precise had been established on the forms and remarkable phae- 

 nomena of the fluid vein itself. Venturi had given three ex- 

 amples. 



M. Hachette, in two memoirs presented to the Academie 

 Royale des Sciences in 1815 and 1816, also considered the 



• Notices Historiques, par M. Mallet. Paris 1830. 

 t French measure, or 0-03059 French kilolitres. 



