1883.] 



On the Formation of Ripple-mark. 



21 



2 , the least and greatest velocities of the water compatible with the 

 formation of ripple-mark. 



The following are the results : — 



•0031 

 •0027 to -0028 

 •0024 

 •0021 

 •0023 

 •002; 



Mean '00245 min. 

 or "147 second. 



Feet per sec. ©j. 

 •51 to -56 

 •46 to -51 

 •43 to -49 

 -43 to -52 



•50 



•56 



more than -42 

 •503 



Feet pe* see. v%. 



1 2 

 1 12 



1 2 



It appears therefore that ripples are not formed if the maximum 

 velocity of the water relatively to this particular sand, estimated on 

 the above hypothesis, is less than half a foot or greater than a foot 

 per second ; and that if v be that maximum velocity in inches per 

 minute, the wave-length of ripples generated is "002450, or '147^ when 

 v is measured in inches per second. The results seem as fairly con- 

 sistent with one another as could be expected. It will appear from 

 section 2 that the maximum velocity of the water, as estimated on 

 the hypothesis; that the water as a whole executes a simple harmonic 

 oscillation relatively to the bottom, does not give the maximum 

 velocity of the water in contact with the sand relatively thereto. 

 The quantity called v is not in reality the maximum velocity of the 

 water in contact with the bottom relatively thereto, but it is in fact 

 6*283 times the amplitude multiplied by the frequency. Thus we 

 cannot conclude that a current of half a foot per second is just 

 sufficient to stir the sand. In the state of oscillation corresponding 

 to Vi, it is probable that part of the water at the bottom is moving 

 with a velocity much greater than half a foot per second relatively to 

 the sand. The number of the experiments analysed is insufficient 

 for the accurate determination of the law connecting wave-length, 

 amplitude, and frequency; but this branch of the subject was not 

 pursued further because other observers, whose work is referred to in 

 § 3, have made a number of experiments with this object. 



It was after making this set of experiments that I hit on what 

 appears to be the key-note of the whole phenomenon. 



A series of ripples extending inwards for some distance having 

 been made by oscillation, and the water having come to rest, the bath 

 was turned slowly and nearly uniformly round. The ripples were 

 then observed to prolong themselves towards the centre ; this shows 

 that a uniform current is competent to prolong existing ripples. The 



