36 



Prof. (i. H. Darwin. 



[Nov. 22, 



With very violent oscillation the ripple -marks are obliterated, and 

 the water is filled with flying dnst. 



We now revert to the initiation of ripple-mark. 



If the snrface be very even, as when sand is sprinkled on glass, 

 when a uniform oscillation of considerable amplitude be established, 

 the sand is carried backwards and forwards and some of the particles 

 stick in places of greater friction. As soon as there is any superficial 

 inequality, it is probable that a vortex is set up in the lee of the in- 

 equality which tends to establish a dune there. Such vortices are, 

 however, too small to be seen. The return current in the second half 

 of an oscillation maintains the dune, a vortex being established on the 

 other side, now the lee-side. As the sand tends to stick by friction in 

 a great number of positions, the sand agglomerates into elongated 

 patches, and the patches are so near to one another that the vortex 

 on either side of one patch just fails to interfere with the next patch. 

 As the patches elongate and regularise themselves the vortices 

 increase in intensity, and the vortex established on one lee is not 

 obliterated in the return current. The two vortices are then the 

 primary vortices described above. As the ripple increases in height 

 by the obliteration of some of the elongated patches, the primary 

 vortices set up the secondary vortices. Perhaps the normal state of 

 transition is that only one of the secondary vortices is established at 

 first, and that when the other secondary vortex is set up it tends to 

 obliterate every alternate ripple-mark, and thus to generate a ripple 

 of double wave-length. As the ripples increase in height the 

 secondary vortices become more and more important, and the primary 

 less important. The final or stationary condition is that described 

 above as the case of strong oscillation. 



It is to be admitted that this history of the successive stages of 

 the formation of ripple-mark is to some extent speculative, but it is- 

 the only method of formation which appears to accord with the 

 various phenomena observed and described above. 



It is important to note that when once a fairly regular ripple- 

 mark is established, a wide variability of amplitude in the oscillation 

 is consistent with its maintenance or increase. No explanation of 

 ripple-making can be deemed satisfactory which does not satisfy this 

 condition. 



In this summary no attempt has been made to go over again the 

 various peculiarities of the motion, which have been noted above, such 

 as the dance of the crests and of the convolutions of the dividing line 

 of the vortices. We must refer the reader back for the consideration 

 of these points. 



§ 3. The Work of previous Observers and Discussion. 

 Some valuable papers on ripple- mark have been lately published. 



