REPORT ON HYDRAULICS. PART II. 



471 



the dam. The height of the river above the dam will be the 

 quantity designated by H in the formula, now adopted by 

 Messrs. Poncelet and Lesbros, for the expenditure through 

 notches in dams, where « = 1*80 ZHVH, where 1-80 is the 

 value of m in the expression of f m v' 2 jg- = 0-610 ; if therefore 

 b be the height of the dam from the bottom of the river, and b' 

 the depth of the water before the erection of the dam, the height 

 of the swelUng of the water will be H + A — Z» /, as we before 

 stated. The merit of having discovered the true law of the 

 expenditui-e of water through notches in dams belongs to 

 M. Bidone*, but he has carried his researches still further by 

 his valuable experiments on the eflPects of dams and other ob- 

 structions in raising the surface of running waters. 

 The following Table gives the results : 



Dubuat was the first who turned his attention to the forms 



and extent of swellings. Observing that the depth of the water 



towards the dam increased, whilst the velocity decreased in the 



same proportion, he concluded that the surface was a concave, 



similar to an arc of a circle, and calling H the height of the 



swelling, /> the inclinationof the current before the erection of the 



dam, and />' the inclination of the swelling immediately in front 



l'*9H H 

 of the culminating point, which he makes equal to ^, — 



torn 



" Experiences sur la Depense des Reservoirs," par George Bidone, 1824, 

 . xxviii. des Memoires de I'Academie des Sciences de Turin. 



