1883.] 



On the Formation of Ripple-mark. 



31 



that of the crests is '7, and the breadth of the convolutions of the tree- 

 is *3. The sum of the amplitude of oscillation of the crest, with 

 the breadth of the convolutions, and the wave-length of ripple- 

 mark is equal to 2, and this is very nearly equal to the amplitude of 

 oscillation of the water, as it ought to be. 



The law which governs the intensity of the vortices must be a 

 matter of inference, since I found the motion too rapid to be sure of 

 anything save that the vortices are driven alternately by pulses, and 

 that the motion was most energetic near the elongations. 



In i the right hand vortex of a pair must be at its maximum of 

 intensity, and it seems probable that the left hand vortex has a sub- 

 maximum in consequence of the friction of the water along the 

 dividing line. During the return motion from i to vii, the left 

 hand vortex must be increasing in intensity, so that it is at its 

 maximum in vii. Probably the right hand vortex diminishes in 

 intensity from i to v, and then increases to its sub-maximum in vii. 



I am not able to say from observation that the vortices which have 

 been described as giving rise to the ink mushrooms actually exist in 

 this state of oscillation, but if they are there, one of them should be 

 found at the point marked with an asterisk in iv. 



The figures tell better than words the mechanism by which the 

 ripple-mark is made and maintained, and the cause of the dance of 

 the crests. The only difficulty is in stage iv, where the root of the 

 tree is in the state of transference from one crest to the next. In this 

 stage the vortices would seem to be in the act of degrading the ripple- 

 mark, but they are not then either of them at their maximum of 

 intensity, and the time during which this holds good is exceedingly 

 short compared with the whole semi-period of oscillation. It seems 

 somewhat likely that small vortices are called into existence at the 

 points marked with asterisks in iv, which serve to protect the ripple- 

 marks from degradation during the transference. 



Fig. 11, i to vii, exhibits the dance of the vortices when the oscilla- 

 tion of the water is considerably less in amplitude than the wave- 

 length of ripple-mark. 



Here the crests of the ripple-mark are scarcely sensibly disturbed. 

 Above the crest is drawn the pair of mushroom vortices, the carved 

 arrows showing the direction of rotation being placed outside of the 

 mushrooms ; but I am not able to satisfy myself that they are both 

 in existence during the whole oscillation. Fig. 8 above exhibits an 

 appearance which I have sometimes seen, which seems to show that 

 they may both exist together with an ink tree. 



We must now draw attention to the manner in which the convolu- 

 tions are added to the ink tree, and thus show the continuity of this 

 tig. 11 for gentle oscillation with fig. 10 for violent oscillation. 



In fig. 10, in ii, iii, iv, a convolution is added, which is unwrapped 



