634 DYNAMICAL GEOLOGY. 



the waters above the entrance of the gorge are partially held back, 

 and have less slope during freshets than at low water ; and conse- 

 quently the pitch through the course of the gorge is increased. 



3. Flow of a stream. — The above causes affect directly the velocity 

 of the stream, as this varies with the pitch and depth of water. 

 The sudden expansion in size and depth of a river-channel, as 

 when a lake intervenes, also affects the velocity, often producing 

 seemingly a state of nearly perfect quiet. The water-level becomes 

 for the interval nearly horizontal. K. Bakewell, Jr., accounts for 

 the quiet at the whirlpool in the rapids below the Falls of Niagara 

 on the ground of the great increase of depth and the abrupt expan- 

 sion in breadth. 



The movement of a stream is most rapid near the surface above 

 the line of deepest water. The bottom, sides, and air retard by 

 friction the layer in contact with them, and other adjoining layers 

 are retarded through the cohesion between the particles of the 

 water. The velocity is greater the less the extent of the upper 

 (or air) and bottom surfaces, — the surfaces of friction. When two 

 streams unite, the waters have the surfaces of friction of one 

 stream instead of two, and there is consequently an increased rate 

 of flow ; besides, owing to the greater velocity, the united waters 

 do not occupy a space equal to the sum of those which they occu- 

 pied before the union. 



The velocities at different depths from the surface to the bottom being repre- 

 sented by parallel lines drawn from a given base-line, 

 if the extremities of these lines be connected the curve Fig. 937. 



obtained is a parabola whose axis is parallel to the 

 water's surface and may be some distance below it, 

 and whose abscissa? vary as the velocities, — a princi- 

 ple first established by Humphreys & Abbot. The 

 form of the parabola changes with the changing 

 depth and other conditions of a river. Fig. 937, from 

 the Report of these authors, shows the curve deduced 

 for the Mississippi at mean height, from observations 

 made in 1851 at Carrollton and Baton Rouge; s is the 

 surface ; b, the bottom ; a x, the axis of the parabola. 

 They give other figures, representing the curve for 



low and high water, and others also as deductions from each set of observa- 

 tions. The axis, or line of greatest velocity, is nearest the surface at low water. 

 For the methods of experiment in determining the velocities, and for all details 

 on this important subject, and mathematical formulas connected with it, refer- 

 ence should be made to the admirable " Report on the Physics and Hydraulics 

 of the Mississippi River," by Captain Humphreys and Lieutenant Abbot, 

 4to, 1861, based upon surveys and investigations made under acts of Congress, 

 directing the topographical and hydrographical survey of the Delta, &c. 



