REPORT ON HYDRAULICS. PART II. 421 



a and b, two constant quantities to be determined by experi- 

 ment*. 



From these, and additional notations, M. Belanger arrives at 

 a general expression for the permanent and uniform motion of 

 the current similar in some respects to that of M. Prony, whose 

 formula for canals is 



av + Of = — . 



The values of a and b, which represent the constant coefficient 

 of the first and second powers of the velocity, were determined 

 by M. Prony from thirty experiments deduced from the mean 

 and superficial velocities of the current : 



thus a = 0-000444499 

 b =0-00030931401. 



Eytelwein has exactly followed M. Prony, but from a greater 

 number of experiments. 



a = 0-000242651 

 b = 0-0003655430. 



The difference between these respective coefficients does not 

 much affect the results for calculations in the formulae for the 

 relations between the velocity of the water in a canal, and its 

 length, inclination, and section, as they appear in M. Prony's 

 Five Tables J. 



If the form of the channel and the volume of water expended 

 remain the same, uniformity of motion can only take place when 

 the canal has one inclination and a proportionate depth through- 

 out its length. 



The true principle, therefore, for regulating the inclination of 

 a canal, consists in establishing a relation between the ordinates 

 of the height and the horizontal distances, always considering 

 that for every volume of water contained in a given inclination, 

 there must be a depth corresponding to the uniform regimen. 

 M.Genieys§, who has investigated these principles with a view to 

 render them applicable to canals and aqueducts, has endeavoured 

 to find the velocity best suited to the nature of the soil, but al- 

 ways with reference to the velocity necessary to maintain tlie 

 salubrity of the water, which has been determined to be 35 centi- 

 metres, or about 13f English inches, per second for the minimum 

 velocity ; whereas M. Girard adopted a less velocity in the canal 

 deL'Ourcq. M. Girard at first proposed to lay out the inclination 



• Recherches Physiques et Mathematiques sur la Theorie desEaux Courantes: 

 par M. de Prony. Paris, 1804. 



t Rectteil de cinq Tables : par M. Prony. Paris, 1825. 



J Memoiresde I'Academie de Berlin (Annees 1814 etl815). 



§ Essais sur les Moyens de conduire, d'elever et de distribuer les Eaux : par 

 M. Genieys. 



