CORRASION BY GRAVITY STREAMS. 227 



here of no appreciable work since at any depth below O it 

 would be forced to let its load fall out of the current. 

 However long the stream P P' acted, therefore, along this 

 grade it could not lower the point O until it had first suc- 

 ceeded in lowering the point B. 



Now suppose the stream P P' to become possessed of a 

 velocity eight times as great as it possessed when the basin 

 AOB was formed. What will be the new depth of the 

 basin ? The casual observer may answer that the new 

 basin will be twice as deep as the former one "since the 

 force is now eight times as great." That is, he imagines 

 the new basin will be twice as deep, twice as long, and 

 twice as broad as the former one. 



But (1) the laws of streams show that their power of 

 transportation varies probably as the sixth power of the 

 velocity and their corrasive strength exceeds the square 

 of the velocity. (See Appendix III.) 



(2) Under natural conditions increase of stream velocity 

 along a definite channel originates in increased stream 

 volume. 



Let us then suppose that a basin twice as deep and eight 

 times as large as the original one has been formed [Fig. 3 

 (c)], with depth O'Z = 2 O Z. The new stream P P' with 

 a velocity eight times increased descends the basin. 

 As its increased velocity is a result of increased volume 

 its transporting power is approximately now to be multiplied 

 by 8 6 , i.e. by 262, 144. Nevertheless, all that is required 

 of it in such a basin as we have assumed is to lift or trans- 

 port a burden eight times as large as its former one, the 

 great bulk of such material lying within the vertical limit 

 Z O, the dead work accomplished in lifting the debris from 

 the floor of the smaller excavation. On the other hand, 

 the stream has its transporting power increased 262, 144 

 times. 



O-Nov. 3, 1909. 



