238 E. C. ANDREWS. 



the stream material to become stagnant if unaltered in 

 volume. This slope will vary with all streams, being flatter 

 in the cases of more mobile or more voluminous streams 

 and steeper as the mobility or the volume of stream is 

 decreased. Commencing then with this limiting slope of 

 channel bed it is evident that any increase of such will be 

 productive of increase of velocity. 



In addition to this general increase of stream velocity by 

 steepening of the slope of the channel bed there may also be 

 local increase of velocity arising either from channel con- 

 strictions or from variable strengths of the channel struc- 

 tures. At all such points stream corrasion will be much 

 more strongly emphasised than is the increase of velocity 

 and here excavations will tend to form in the channel 

 base. 



Now at every point on a channel declivity gravity is 

 tending to induce a vertical motion in the sliding, rolling 

 and flowing mass. With this motion also at any point, 

 there is the more or less horizontal motion of the stream 

 mass, caused by the opposition which the channel base sets 

 up to a "free falling" motion. Consequently the path of 

 the stream is inclined at some angle to the vertical (ten- 

 dency to parabolic motion). The declivity then will not 

 experience the total energy of the stream, and in propor- 

 tion to the increase of declivity so will the channel declivity 

 experience a less percentage of the total energy of the 

 stream. This has nothing to do with the absolute energy 

 expended on the declivity, but merely with the relative 

 percentage of stream energy so expended. 



But at all points where the angular value of the slope is 

 rapidly changed from higher to lower, there the percentage 

 of stream strength expended as corrasion rapidly increases. 

 At such abrupt changes from declivity to flats the net 

 result is loss of stream energy which is expressed by inten- 



