AND OTHER WATER WAVES 271 



is in this case found in the centre of the stream, 

 as may be seen, for example, near the spot, called 

 Bloody Run, opposite Foster's Flats, in the rapids 

 between Niagara Whirlpool and Lewiston. 



In 1896 I noticed some facts relating to waves 

 in rivers of which I found no published explana- 

 tion. The first was that the water of rivers, per- 

 ticularly rapid mountain streams e.g., at Meran, 

 in the Tyrol does not maintain a constant level 

 at any fixed spot, but, on the contrary, oscillates 

 perceptibly with a motion sufficiently rapid and 

 short in period to be readily perceived by the eye. 

 This indicated that there was something of the 

 character of a progressive wave, but I could not 

 at that time see any travelling wave. 



The second observation was that the so-called 

 stationary waves (e.g., on the Eisah, above Botzen, 

 and at the Bingen Rapids, on the Rhine) were not 

 perfectly stationary, but oscillated somewhat about 

 a mean position. Their most noticeable movement 

 was that, from time to time, they charged some- 

 what rapidly a foot or two up-stream ; and in 

 this case the cusped waves broke as waves break 

 on a sea-beach. It appeared to me that the second 

 phenomenon was related to the first in the follow- 

 ing way : granting that the '" stationary " waves 

 are travelling up-stream as fast as the current 



