40 



Prof. G. EL Darwin. 



[Nov. 22, 



the ratio of amplitude to period, we should have the wave-length for 

 any one sand varying as the frequency multiplied by the square of 

 the amplitude. The few fairly consistent experiments recorded in 

 § 1, do not accord with this view, for it seemed that wave-length 

 varied as v, which is proportional to frequency multiplied by 

 amplitude. This I understand to accord with M. de Candolle's law. 

 As to the law that the finer the sand the longer the wave-length, M. 

 Ford justly observes that it is in contradiction with the fact that small 

 ripples are formed by fine sand, and large ripples by coarse sand. But 

 he endeavours to remove the apparent inconsistency by remarking in 

 effect that the larger limiting velocity for fine sand is smaller than the 

 smaller limiting velocity for coarse sand. There must undoubtedly 

 be truth in this view, but I hesitate to accept it as the whole truth. 



Noticing that, in the same sites in the Lake of Geneva, the ripples 

 are always of the same length, he says, " de ces observations il 

 semblerait resulter que l'intensite des vagues a bien peu d'influence 

 sur la largeur des rides ; que la nature du sol est le seul facteur 

 important." 



It appears to me that M. Ford's view as to the wave-length of 

 ripple-mark cannot be accepted as final, but he has certainly 

 thrown much light on the subject in his interesting paper. 



The following considerations bear upon the laws of wave- 

 length : — 



It appeared that in the initial stages of ripple-making, the wave- 

 length is at first only half as long as it becomes ultimately, and 

 that when the layer of sand is thin, the wave-length always remains 

 shorter than if it is thick. Hence if a little sand is dusted on to the 

 oscillating sheet of glass, it is found that the wave-length of ripple is 

 long in the middle of the. patch of sand, and short near the margins. 

 Thus the patch when ripple-marked presents such an appearance 



Fig. 12. 



as fig. 12. If the sand is thin, this appearance often persists 

 however long the oscillation is maintained. This shows that wave- 



