AND OTHER WATER WAVES 299 



comes the dominant factor in determining the rate 

 of flow. If this small depth be increased, the rate 

 of flow is at once greatly accelerated, for the upper 

 layers flow with considerable freedom upon a couch 

 of water, whereas the lowest layer clings to the 

 bed. Thus a momentary retardation of flow at 

 any spot, by increasing the depth there, enables 

 the water which then arrives to flow with much 

 greater speed. The excrescence caused by any 

 momentary check therefore dashes down-stream. 

 Thus every retardation quickly causes acceleration. 

 This condition necessitates the substitution of a 

 gushing for a continuous flow. The more highly 

 developed are the down -stream progressive waves, 

 or roll -waves, the more gushy is the stream. 



I shall now give some account of observations 

 of these spontaneous roll -waves in shallow streams 

 (generally artificial conduits) which I made in 

 Switzerland during 1904 and 1905. The waves in 

 the conduits, which are much easier to observe 

 than the corresponding waves in natural channels, 

 throw some light upon occurrences which are con- 

 fused and obscured under natural conditions. 



When looking at water flowing past in a shallow 

 channel, I find that the eye is generally fixed by 

 stationary features of the surface, such as diagonal 

 standing waves originating from the banks. When 



