ON HYDRAULICS AS A BRANCH OF ENGINEERING. 161 



w = an abstract number, which was found by ex- 

 periment to be equal to 243*7. 



then V = ^^ngyd-0'\) _ ^.^ ^^^ _ 

 Hi/ s — log. V * + 1"6 



Such are some of the objects of M. Dubuat's work. But his 

 hypotheses are unfortunately founded upon assumptions which 

 render the applications of his theory of little use. It is evident 

 that the supposition of a constant and uniform velocity in rivers 

 cannot hold : nevertheless he has rendered great services to 

 the science by the solution of many important questions relating 

 to it ; and although he has left on some points a vast field open 

 to research, he is justly entitled to the merit of originahty and 

 accuracy. 



Contemporary with Dubuat was M. Chezy, one of the most 

 skilful engineers of his time : he was director of the Ecole des 

 Ponts et Chaussdes, and reported, conjointly with M. Perronet, 

 on the Canal Yvette. He endeavoured to assign, by experiment, 

 the relation existing between the inclination, length, trans- 

 versal section, and velocity of a canal. In the course of this 

 investigation he obtained a very simple expression of the velo- 

 city, involving three different variable quantities, and capable, 

 by means of a single experiment, of being applied to all cur- 

 rents whatever. He assimilates the resistance of the sides and 

 bottom of the canal to known resistances, which follow the law 

 of the square of the velocity, and he obtains the following sim- 

 ple formula : 



V — €^, where g is = 16*087 feet, the velocity acquired 

 z s 



by a heavy body after falling one second. 



d = hydraulic mean depth, equal to the area of the section 

 divided by the perimeter of the part of the canal in 

 contact with the water. 



s = the slope or declivity of the pipe. 



^ = an abstract number, to be determined by experiment. 



In the year 1784, M. Lespinasse published in the Memoirs 

 of the Academy of Sciences at Toulouse two papers, contain- 

 ing some interesting observations on the expenditure of water 

 through large orifices, and on the junction and separation of 

 rivers. The author had performed the experiments contained 

 in his last paper on the rivers Fresquel and Aude, and on that 

 part of the canal of Languedoc below the Fresquel lock, towards 

 its junction with that river. 



As we before stated, M. Dubuat had classified with much 

 18.33. M 



