344 



The Windings of Rivers 



rivers. Fig. 2 shows one specimen out of many which were 

 exhibited at the meeting of the British Association. 



It is assumed that the rhythmic motion set up in a mass of 



water which is disturbed in its 

 uniform rectilineal motion will be 

 reducible to two reciprocating 

 motions, one in the direction of 

 the fall of the stream and the 

 other at right angles to it. When 

 the gradient of the stream is very 

 steep and the nature of the bed 

 homogeneous, as it is in the case 

 of water flowing down the front of 

 a glacier, the longitudinal oscilla- 

 tion is swamped by the powerful 

 and continuous action of gravity, 

 which does not affect the transverse 

 component. In these circum- 

 stances we often meet with small 

 p- streams which describe an almost 

 g> perfect simple harmonic curve. 



In the ordinary stream of the 

 meandering type the gradient is 

 very small, in the case of the 

 Mississippi from two inches to four 

 inches per mile,. so that the longi- 

 tudinal pulse can produce its full 

 effect. When the two oscillations 

 are simple pendulum motions and 

 have the same period they produce 

 an ellipse, which, when combined 

 with the steady onward flow due to 

 gravity, produces cycloidal sinuosi- 

 ties which are unlike those of actual 

 streams. When the period of the 

 transverse oscillation is twice that 

 of the longitudinal one, their com- 

 bination produces a Lemniscate or 



