DIFFERENT VELOCITIES IN A CROSS-SECTION. 213 



Focacci found that in a canal 5 feet deep, the maximum velocity 

 was from 2 to 2.5 feet below the surface. 



Defontaine states that in calm weather the velocity of the Rhine is 

 greatest at the surface. 



Raucourt made experiments upon the Neva where it is 900 feet wide 

 and of regular section, the maximum depth being 63 feet. When the 

 river was frozen over, the maximum velocity (2 feet 7 inches per sec- 

 ond) was found a litt'e below the middle of the deepest vertical, where 

 it was nearly double the velocity at the surface and bottom, which 

 were nearly equal to each other. In summer, he found the maximum 

 velocity was near the surface in calm weather ; but when a strong 

 wind was blowing up stream, the surface velocity was greatly dimin- 

 ished, so that it hardly exceeded that at the bottom. He considers the 

 law of diminution of velocity to be given by the ordinates of an ellipse 

 whose vertex is a little below the bottom, and whose minor axis is a 

 little below the surface. 



Hennocque found the maximum velocity in the Rhine to be, in calm 

 weather, or with a light wind, of the depth below the surface ; in a 

 strong wind up stream, it was a little below mid-depth ; in a strong 

 wind down stream, it was at the surface. 



Baumgarten found in the Garonne that the maximum velocity was 

 generally at the surface, but that in one section (about 325 feet wide) 

 it was always below the surface. 



D'Aubuisson considers that the velocity diminishes slowly at first, 

 as the depth increases, but that near the bottom it is more rapid. The 

 bottom velocity, however, is always more than half that of the surface. 

 Boileau found, by experiment in a small canal, that the maximum 

 velocity was \ to \ of the depth below the surface. Below this point, 

 the velocity diminished rapidly, and nearly in the ratio of the ordinates 

 of the parabola whose axis was at the surface. He decided, from a 

 discussion of the experiments of Defoutaine, Hennocque, and Baum- 

 garten, that in large rivers the maximum velocity is by no means al- 

 ways at the surface.* 



It will be seen from this synopsis that there is a great 

 diversity among the results obtained by different experi- 

 menters, and that no mathematical relation, of sufficiently 

 general application to constitute a practical law, has been 

 yet discovered. 



* See Report on the Hydraulics of the Mississippi River, by Humphreys and 

 Abbott, pp. aOO, etc. 



