268 N. S. SIIALER SPACING OF RIVERS 



tlie dilFerence does not affect the i)rincii)le involved, which is that tlie 

 effective angle oF the side slopes of the hasin goes far to determine the 

 limits of its Literal extension. 



Conditions of Torrents 

 relation of slope to down-cutting and basin area 



With the principle last noted, that the declivity of a basin's slopes de- 

 termines the range of its capturing, in mind, seeing also that the relative 

 rate of down-cutting of the channel established the condition of the stream 

 as winning or losing in drainage area, let us further consider the condi- 

 tions which determine this down-cutting. In the first stages of the exca- 

 vating work the miniature stream cuts very freely, the restraints of its 

 baselevel not being felt. In a word, it is a torrent. As its bed grows 

 deeper this influence begins to come in. The result is that the stream 

 soon passes the stage in which it is gaining in volume by capturing 

 drainage. Such augmentation as it receives in the later stages of down- 

 cutting are not likely to add much to its drainage area. Bearing in mind 

 the fact concerning this loss of power, namely, that the speed is about as 

 the square of the declivity and the efficient carrying energy as a higher 

 function of the speed, we may readily perceive that a very sudden arrest 

 is put to the capacity of the current to cut its bed deeper when it attains 

 a certain diminution of slope. 



It should now be possible to see why the rivulets on a considerably 

 eroded surface of an originally even slope, however irregular they may 

 be at the beginning, come to be rather evenly spaced in the course of 

 their development. This spacing is in effect determined b}^ the maximum 

 depth to which the beds of the streams can cut down in a given time. 

 Those channels which attain that depth do so because they manage to 

 carry their load of debris beyond the field. If the waste is fed in too 

 rapidly the cutting down is hindered. If they cut down to a certain 

 grade the}^ attain a critical point due to the diminished slope, beyond 

 which they can not well become deeper. The result of these several equa- 

 tions of action is the establishment of a somewhat definite maximum 

 area of basin, beyond the limits of which a stream can not effectively 

 compete with its neighbors. 



The conditions which make for the establishment of approximately 

 equal intervals between the drainage channels may be fairly well illus- 

 trated by pressing down V-shaped blocks of equal size into a sheet of 

 mud so as to make valleys of like dimensions. Imagine, now, that there 

 is an arrest of the down-sinking of any valley as it comes to a certain 

 critical plane the equivalent of the baselevel of erosion, and that the side 

 slopes of the trough have the same declivity ; it should at the same time 



