424 FOURTH REPORT — 1834. 



Seine at Paris above the level of the sea is 127 French feet, 

 which divided over the length of that river to Havre is one in 

 4252. By similar observations made on the river Loire by 

 MM. Pi card and Pitot, the declivity in proportion to its length 

 was found to be ^^-^Vt* 



The Rhone gives the proportion g^V^j which is double the 

 mean declivity of the rivers in Flanders. 



0)i the mean Velocity of Water running in artijicial Canals. 



We have seen, that the resistance of the sides of the channel 

 causes a diminution in the velocity of the water which is com- 

 municated to parts remote from the periphery ; fnmi which it 

 follows that when the section is a semicircle the greatest velocity 

 is in the middle of the surface ; and that in a channel of any 

 other shape this maximum velocity is in the most distant point 

 from the periphery ; and that, vice versa, the velocity decreases 

 towards the periphery. A knowledge of this progression has 

 always been considered of great importance, and many experi- 

 ments have been made for that purpose. 



Dubuat has perhaps made the most accurate experiments on 

 the subject ; and having performed them on a scale of consider- 

 able magnitude, he concluded that the relation between the velo- 

 city at the surface and the bottom was independent of the depth, 

 and greater in proportion as the velocity was smaller ; he ob- 

 served also, that the mean velocity is a mean proportional be- 

 tween the superficial and bottom velocity, that is, calling 



V the velocity at the bottom, 



V the velocity at the surface, 

 u the mean velocity, 



the result of these observations may be represented by the 



equations 



?; = (-v/V^0-165)3and«=l(V + i) = (\/V-0-082f + 0-00677. 

 M. Prony*, in discussing these observations of Dubuat, adopts 

 ^- V + 2-372 . 



Jangca(>e des Eaii.c Cviiranlef, 1802. 



