1883.] 



On the Formation of Ripple-mark. 



29 



furrow appears to be in a different phase from that on the crest, with 

 more violent rocking I did not observe the difference of phase. The 

 dance is not a simple harmonic motion like that of the main body of 

 the water relatively to the bottom, but the particles dash from one 

 elongation to the other, pause there, and then dash back again. 



As the amplitude further increases the furrows are completely 

 scoured out, and the sand on the crests is dashed to and fro, forming 

 a, spray dancing between two limits. With violent agitation this 

 dance must have an amplitude of more than half a wave-length. 

 If the agitation be allowed to subside the dance subsides, and when 

 the water is still the ripple-mark is left symmetrical on both sides. 

 With extremely violent oscillation all the water becomes filled with 

 flying dust, and it is no longer possible to see what is happening. 

 This seems to be the condition when the agitation is too strong for 

 the formation of ripple-mark. It is probable that the rush of water 

 sweeps away the existing ripple-mark, and there is then no longer 

 anything to produce a systematic arrangement of vortices. 



In fig. 10 I have tried to exhibit the dance of the vortices by the 

 succession of figs, i to vii. When the amplitude of oscillation is the 

 same as when the ripple-mark is generated, the series of changes is 

 of the kind shown. The figures succeed one another in time, but 

 they do not pretend to such accuracy as to represent the stages at 

 rigorously equal intervals. 



The dotted waves show a mean contour of the ripple-mark ; they 

 are introduced to show the displacements of the crests relatively to 

 the mean position. A perfectly symmetrical ripple -mark does not, 

 however, present a simple harmonic outline, for the hollows are flat 

 and the crests rather sharp. 



The convoluted line is the stem of the ink tree, which forms the 

 dividing line of the two vortices ; the curved arrows show the direc- 

 tion of rotation. 



In i the water is at its elongation to the right. The crest of the 

 ripple-mark is also at its extreme to the right, and the right hand 

 slopes are steep, whilst the left are gentle. Here the water is at rest 

 oxcept for the vortices, which both tend to carry sand up to the 

 crest. 



In ii the general mass of water is beginning its movement to the 

 left ; it carries with it the upper convolutions of the ink tree, but 

 leaves the root very nearly in the same position as in i. The crest of 

 the ripple-mark is but little displaced. In iii the crest has begun its 

 displacement, so that although the root of the ink tree has begun 

 moving to the left, it is still over the crest. The convoluted stem 

 continues to move to the left with increasing velocity, leaving the 

 root behind it over the crest. 



Just before the convolutions reach the position over the middle of 



