HYDRAULIC INVESTIGATIONS. 10J 



Mv. de St. Honore, who assisted him in the construction of 

 his expressions. I am by no means disposed to dissent from 

 this encomium ; and I a^ree with Professor llobison, and 

 with all other late authors on hydraulics, in applauding the 

 unusually accurate coincidence between these theorems and 

 the experiments from which they were deduced. But I The form of 

 have already taken the liberty of remarking, in my lecture not very con „ 

 on the history of hydraulics, that the form of these expres- venient for 

 sions is by no means so convenient for practice as it might 

 have been rendered; and they are also liable to still greater 

 objections in particular cases, since, when the pipe is either 

 extremely narrow, or extremely long, they become com- \ n somc cases 

 pletely .erroneous : for notwithstanding Mr. Dubuat seems erroneous « 

 to be of opinion, that a canal may have a finite inclination, 

 and yet the water contained in it may remain perfectly at 

 rest, and that no farce can be sufficient, to make water flow 

 in any finite quantity through a tube less than one twenty- 

 fifth of an inch in diameter; it can scarcely require an ar- 

 gument to show, that he is mistaken in both these respects. 

 It was therefore necessary for my purpose to substitute, for 

 the formula? of Mr. Dubuat, others of a totally different 

 nature; and I could follow Dubuat in nothing but in his 

 general mode of considering a part of the pressure, or of 

 the height of a given reservoir, as employed in overcoming 

 the friction of the pipe through which the water flows out of 

 it; a principle, which, if not of his original invention, was 

 certainly first reduced by him into a practical form. By A formula <hs- 

 comparing the experiments, which he has collected, with hal^d vantage 

 some of Gerstner, and some of my own, I have ultimately over Dnbuat**. 

 discovered a formula, which appears to agree fully as well 

 as Dubuat's with the experiments from which his rules were 

 deduced, which accords better with Gerstner's experiments, 

 which extends to all the extreme cases with equal accuracy, 

 which seems to represent more simply the actual operation 

 of the forces concerned, and which is direct in its appli- 

 cation to practice, without the necessity of any successive 

 approximations. 



I began by examining the velocities of the water dis- Velocities of 

 charged thrpugh pipes of a given diameter with different water discharg. 



degrees 



