216 



E. C. ANDREWS. 



Channel Slope. — All other things being equal, stream 

 velocity is increased in proportion to the increase of slope 

 of channel base. 



Increase of Stream Volume. — From considerations of 

 pressure this implies increase of velocity. 



Path of a Stream Particle. — The descending stream is 



always tending to parabolic motion from a consideration 



of the dual action on a stream particle at any point. 



Gravity attempts to impart a vertical motion to the particle 



but is prevented, as a rule, from doing so owing to the 



resistance offered by the earth. The motion of the particle 



is thus deflected at some angle to the vertical. This again 



tends to hold the particle in the new direction, but as 



opportunity offers, gravity again tends to impart a vertical 



motion to it. Thus the result is a compromise between 



a motion possessing a more or less horizontal value with 



one possessing a constant vertical value. The tendency is 



thus to parabolic motion. (See mathematical proof in 



appendix). 



Fig. 1. 



Path of a Stream Particle. 



In the figure the path of 



the particle is shown as a 



curve convex to the sky. 



This is the path when 



the particle is free to 



move in all directions. In 



nature the resistance of 



^ the earth's crust comes 



into play, and the path 



becomes more or less 



parabolic by the aid of corrasion or aggradation. 



The corraded path is concave to the sky, i.e. an approximation 



to the axis (y). The aggraded path is convex to the sky, i.e. an 



approximation to the axis (x). 





