1878.] Uniform Regime in Rivers and other Open Channels. 115 



under the laminar theory, the forward velocity of the water in rivers is, 

 in actual fact, sometimes or usually not greatest at the surface with 

 gradual abatement from the surface to the bottom; but that when the 

 different forward velocities are compared which are met with at suc- 

 cessive points along a vertical line traversing the water from the 

 surface to the bottom, it may often be found that the velocity increases 

 with descent from the surface downwards through some part of the 

 whole depth, until a place of maximum velocity is reached, beyond 

 which the velocity diminishes with further descent towards the resist- 

 ing bottom. 



That the superficial stratum of water flowing downhill under the 

 influence of the earth's attraction should not have its forward velocity 

 continually accelerated until, by its moving quicker than the bed of 

 water on which it lies, a frictional drag would be communicated to it 

 from below, by that supporting bed of water, sufficient to hold it back 

 against further acceleration, has appeared very paradoxical. In various 

 cases, during a long period of time, the alleged result appeared so 

 incredible that the experimental evidence was doubted, or was dis- 

 missed as untrustworthy. In some cases the phenomenon was 

 admitted as a fact, but was attributed to a frictional drag or resist- 

 ance applied to the surface of the water by the superincumbent air, 

 even in case of the air being at rest with the water flowing below, 

 or more strongly so when the wind might be blowing contrary to the 

 motion of the river. 



Omitting to touch on the experimental resuHs, and the opinions of 

 various investigators in the older times, as 1 have not had sufficient 

 opportunity to scrutinise them in detail, I have to refer to the investi- 

 gations conducted at about the year 1850 by Ellet on the Mississippi 

 and Ohio Rivers.* He was led to the conclusionf from his own expe- 

 riments on the Mississippi, that the mean velocity of that river (or at 

 least the mean velocity of the great body of its current, as the part 

 near the bottom or bed of the river had not been definitely included in 

 his researches) instead of being less, is in fact greater than the mean 

 surface velocity. He attributed this phenomenon, which he regarded 

 as indubitably proved, and which if true must certainly be very 

 remarkable, to a frictional drag or resistance, against the forward 

 motion, applied to the surface of the water by the atmosphere in 

 contact with the surface. Like suppositions had previously been 

 made by some observers and theoretical investigators in Europe, as 

 may be gathered from D'Aubuisson " Traite d'Hydraulique," 2nd 

 edition, 1840, p. 176, and from other sources of information. 



* Ellet on the " Mississippi and Ohio Rivers." Philadelphia : 1853. This is a 

 republished edition of a Report to the American War Department by Ellet on his 

 investigations, which were made under axxthority of an Act of Congress. 



f Pages 37 and 38 of the book referred to in the preceding note. 



