12 GRAVITY, AND ITS RESULTS. 



stream increases, if the fall becomes greater. 

 Those rivers are therefore the swiftest that have 

 the greatest fall. The latter, however, as I have 

 already said, answers only in general to that of the 

 bottom. When the bed is narrowed for a certain 

 distance, so that the water cannot get through 

 with the speed at which it had been flowing, the 

 fall at once increases ; that is, the water is heaped 

 up behind the narrow part of the channel, even 

 when the slant of the bottom remains the same. 

 On the other hand, the effect of the little uneven- 

 nesses in the bed of the river, such as wave-like 

 ridges, and hollows, and even steep slopes, which, 

 when the water is shallow, may cause rapids for 

 short distances, is more and more smoothed down as 

 the level of the water rises. Tor the greater swift- 

 ness with which the stream is now running at the 

 steeper places, must necessarily heap up, as it were, 

 the water in the lower parts of the river, where before 

 the rise it had been running more slowly ; and thus, 

 the more the water rises, over the greater length is 

 its fall spread. Besides, the swiftness of a stream 

 does not depend on the fall alone; for, since the water 

 is always being robbed of part of its motion by 

 the resistance of the ground, and since this loss 

 must ever be made good again by the fall, it is 

 clear that any lessening of the resistance of the 

 ground must enhance the speed of the water, just 

 as does any increase of the fall. In shallow rivers, 



