DEVELOPMENT OF FORMULAE FOR FLOW 171 



character of the coefficients is an inconvenience peculiar to the 

 nature of the phenomena, and further progress in hydraulic 

 theory can never remove it. There are, moreover, very few 

 physical laws the formulated expression of which does not 

 include like inde terminates." 



The experiments of M. Bazin and the coefficients derived 

 from them are standards in hydraulic history, whose accuracy 

 has never been questioned, and are to-day used throughout 

 France in determining the velocity in open channels. Tables 

 based on this formula are given by Flynn in his Hydraulic 

 Tables (p. 180). 



About the same time that M. Bazin was making these 

 important experiments in France, Humphreys and Abbot were 

 making their well-known experiments on the velocity of flow 

 in the Mississippi River.* They deduced the following formula: 



v= \\o.oo8im-\- v 

 where m= ,ll-i= for small streams and m = 0.1856 for large 



streams. 



By experiments made more recently in which this formula 

 has been tested, it has been proved to be not generally applic- 

 able, both from the fact that the limits of m are not wide enough 

 and that the influence of slope as introduced is not accurate. 



The variation in the velocities of different laminae of the 

 stream were, however, well brought out by the work on the Mis- 

 sissippi River, and the earlier results of M. Bazin verified. It 

 appeared, especially from the later and more extensive work, 

 that the velocities in a longitudinal vertical plane would form 

 the abscissae of a parabolic curve with the axis parallel to the 

 surface and at the depth of maximum velocity. This depth, 

 when the air is still, is, according to the Mississippi work, 

 about fV of the entire depth below the surface. A wind blowing 



* Report on the Mississippi River, 1876. 



