222 E. C. ANDREWS. 



three times the velocity as compared with that of the point 

 acted on for the same time by the same stream when 

 possessed of its original velocity. The power of corrasion 

 by such a stream appears therefore to vary at least as the 

 square of the velocity. But this takes account only of 

 such material as the stream is enabled to transport with 

 the smaller velocity and does not take account of the 

 additional material which the accelerated stream is enabled 

 to transport. For mathematical proof see Appendix III. 



Similarly it may be shown that the transporting power 

 of gravity streams apparently varies as the sixth power of 

 the velocity when all other things are equal. (See Gilbert 

 also (a) pp. 89 — 90 for the case of water streams). Thus in 

 all streams we see that energy is not simply related to 

 increase of stream velocity, but that it rises in some high 

 geometrical ratio with increase of velocity. It will be 

 important to keep this principle continually in mind during 

 the present discussion as only by means of this can we 

 hope satisfactorily to explain some well known topographic 

 features. 



Stream strength as compared with channel structures. 

 — In this note we are concerned only with streams which 

 either exist to-day or which may have existed in recent 

 geological time. In nature, mobile streams never attain 

 enormous dimensions as compared with their topographic 

 surroundings. They have not the momentum necessary to 

 shatter the rock structures which they traverse, and thus 

 they are unable to tear out huge slabs along, or across, 

 dominant joint faces. They have power to drag loads over 

 the structures forming their channels and thus to scour 

 and strongly abrade, but their strength of impact is rarely 

 sufficient to overcome the coherence of the more important 

 rock structures. 



If now for the very mobile stream a crystalline solid be 

 substituted, which responds to gravity as flow only when 



