214 DIFFERENT VELOCITIES IN A CROSS-SECTION. 



The velocities observed on any given longitudinal section, at any 

 given moment, do not form, when plotted, any regular curve. But if 

 a series of observations are taken at each depth, and the results aver- 

 aged, the mean velocities at each depth, when plotted, give a regular 

 curve agreeing very fairly with a parabola whose axis is horizontal, cor- 

 responding to the position of the filament of maximum velocity. All 

 the best observations show that the maximum velocity is to be found 

 at some distance below the free surface. 



In the experiments on the Mississippi River, the velocities on any 

 longitudinal section, in calm weather, were found to be represented 

 very fairly by a parabola, the greatest velocity being at T s ff of the depth 

 of the stream from the surface. With a wind blowing down stream, 

 the surface velocity is increased and the axis of the parabola approaches 

 the surface. With a wind blowing up stream, the surface velocity is 

 diminished and the axis of the parabola is lowered, sometimes to half 

 the depth of the stream. The observers on the Mississippi drew from 

 their observations the conclusion that there was an energetic retarding 

 action at the surface of a stream, like that at the bottom and sides. If 

 there were such a retarding action, the position of the filament of max- 

 imum velocity below the surface would be explained. If there were 

 no such resistance, the maximum velocity should be at the sur- 

 face. 



It is not difficult to understand that a wind, acting on surface rip- 

 ples, should accelerate or retard the surface motion of the stream, and 

 the Mississippi results may be accepted so far as showing that the sur- 

 face velocity of a stream is variable when the mean velocity of the 

 stream is constant. Hence observations of surface velocity, by floats 

 or otherwise, should only be made in very calm weather. But it is 

 very difficult to suppose that, in still air, there is a resistance at the 

 free surface of the stream at all analogous to that at the sides and 

 bottom. In very careful experiments, Boileau found the maximum 

 velocity, though raised a little above its position for calm weather, 

 still at a considerable distance below the surface, even when the wind 

 was blowing down stream with a velocity greater than that of the 

 stream, and when the action of the air must have been an accelerating 

 and not a retarding action. Prof. James Thomson has given a much 

 more probable explanation of the diminution of the velocity at and 

 near the free surface. He points out that portions of water, with a 

 diminished velocity from retardation by the sides or bottom, are thrown 

 off in eddying masses and mingle with the rest of the stream. These 

 eddying masses modify the velocity in all parts of the stream, but 

 have their greatest influence at the free surface. Reaching the free 



