Dec. 13, 1883] 



NA TURE 



163 



The column is wavy, and the appearance is strikingly lilie that 

 of smol^e rising from a fire in still air. 



The column ascends to a height of ?ome five, ten, or parhaps 

 twenty times the height of the ripple-marks, according to the 

 violence of the agitation. It broidens out at the top on each 

 side, and spreads out into a cloud, until the appearance is exactly 

 like pictures of a volcano :n violent eruption ; but the broad flat 

 cloud dances to and fro relatively to the ascending column. The 

 ink continues to spread out laterally and begins to fall on each 

 side. In this stage if the ink is not thick it is often very like a 

 palm-tree, and fir the sake of a name this appearance is called 

 an ink tree. The branches (as it were) then fall on each side, 

 and the appearance becomes like that of a beech tree, or some- 

 times of an umljrella. The branches reach the ground, and then 

 creep inwards towards the stem, and the ink, which formed the 

 branches, is sometimes seen a cending again i'l a wavy stream 

 parallel to the stem. 



Perhaps a dozen or twenty oscillations are requisite for making 

 llie ink go through the changes from the first growth of the tree. 



The descending column of a pair of trees comes down on to 

 the top of the mu.-hroom, hut the successful manufacture of the 

 tree necessitates an oscillation of sufficient violence to render the 

 simultaneous observation of the mushroom very difficult. 



With violent os:;illation, when the stem of the tree is much 

 convoluted, it cannot be as erted that the mushroom vortices 

 exist, and the author is inclined to believe them to be then 

 evane-cent. 



Each side of the ink tree is clearly a vortex, and the stem is 

 the dividing line between a pair, alo'ig which each vorlex con- 

 tributes its share to the ascending column of fluid. The vortex 

 in half the tree is clearly in the first place generated by the fric- 

 tion of the vortex in its correlated mushroom, and is of cour e 

 endued with the opposite rcation. The ascending stem of the 

 tree is a swift current, i>ut over the mushroom the descending 

 current is slow until close to the mushroom, when the current is 

 seen to be imjielled by pulses. 



If the adjoining crests are of unequal height, the steal of the 

 tree is thrown over sideways away froin the higher crest ; and 

 indeed it requires care to make the growth quite straight. The 

 ink in the stem ascends with a series of pulses, and it is clear 

 that there is a pumping action going on which renders the 

 moli m of each vortex intermittent, and the two halves of the 

 tree are pumped alternately. 



The amount of curvature in the stem of the tree depends on 

 the amplitude of the o dilation of the water. 



The ink is propagated along the convolutions of the stem of 

 the ink tree, but the convolutions are themselves propagated 

 upwards, and each convolution corresponds to one oscillation. 

 The motion of the ink along the convolutions soon becomes 

 slow, but the convolutions become broader and closer. Thus 

 the upper part of the tree is often seen to be most delicately 

 shaded by a series of nearly equidistint black lines. 



In the transition from the mushroom stage to the tree stage it 

 appeared that it was very frequent that only half the ink tree 

 was formed. 



If the agitation is very gentle, the sand on the cre-ts of the 

 ripple-iiiarks i- just moved to and fro ; with slightly more am- 

 plitude, the dance is larger, and particles or visible objects, such 

 as minute air-bubbles in the furrow also dance, but with less 

 amplitude than those on the crests. The dance is not a simple 

 harmonic motion like that of the main body of the water rela- 

 tively 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 da-hed to and fro, 

 forming a spray of sand dancing between two limits. With 

 violent agitation, thi^ dance must have an amplitude of more than 

 half a wave-length. If the agitation be allowed to subside, the 

 dance subides, and when the water is still the ripple-mark is 

 left symmetrical on both sides. With extremely violent oscilla- 

 tion, 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. 



The author illustrates the dance of the vortices by a succession 

 of figures. 



It is hardly possible to explain the series of changes in words, 

 but W'e may here state that the mechanism by which the ripples 



are made and maintained depends on the fact that the upward 

 current of a pair of vortices lingers over the ripple crest, and 

 then darts across with extreme rapidity to the adjoining crest. 

 Thus each pair of vortices is associated with two crests, spend- 

 ing nearly half the time over one, and half the time over the 

 other. 



As above stated, it has seemed that only one of each pair of 

 tree vortices is set up at first, and the author is disposed to regard 

 this as the tran-ilional state from the mode of ojcillation, which 

 produces the h.alf wave-length with small height of ripple-crest, 

 to the fundamental wave-length with considerable height. 



The results of the observations may be summarised as 

 follows :— 



The formation of irregular ripple-marks or dunes by a current 

 is due to tlie vortex which exists on the lee of any superficial in- 

 eqnality of the bottom ; the direct current carries the sand up 

 the weather slope and the vorlex up the lee slope. Thus any 

 existing inequalities are increased, and the surface of sand 

 becomes mot led over with irregular dunes. The velocity of the 

 water must be greater than one limit and less than another, the 

 limiting velocities being dependent on the average size and den- 

 sity of the iiariicles. Existing regular ripple-mark is maintained 

 by a current passing over it perpendicular to the ridges. A slight 

 change in form ensues, the weather .slope becoming less steep 

 and the lee slipe steeper. The ridges are also slowly displaced 

 to leeward. The regular ripple-maik may also thus 1 e somewhat 

 prolonged, so that although a imiform current probably cannot 

 form regular ripple-mark, yet it may increase the area over which 

 it is to be found. 



Regular ripplemark is formed by water which oscillates rela- 

 tively to the bottom. A pair of vortices, or in s >me cases four 

 vortices, are e tablished in the water ; each set of vortices cor- 

 responds to a single ripple crest and the vortices oscillate about 

 a mean position, changing their shapes and intensities periodic- 

 ally, but not with a simple harmonic motion. 



The successive changes in the vortex motion, whilst ripple- 

 mark is being establi-hed, and when the amplitude of oscillation 

 over existing ripple-mark varie-, are cowplev, and we must refer 

 the reader to the original paper for an account of the phenomena. 



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

 mark is established, a wi .e variability of amplitude in the oscil- 

 lation is consi-tent with its maintenance or increase. No explana- 

 tion of ripple-making can be deemed satisfactory which does not 

 satisfy this condition. 



The last section gives some account of the valuable papers of 

 MM. Ilunt,^ Casimir de Candolle,- and Forel'' in this field. 

 The author agrees in the main with these observers, but con- 

 siders that some of their conclusions are open to criticism. 



He next remarks that it is not easy to understand pre- 

 cisely the mode in which the oscillation of the water over the 

 undulating bottom gives rise to vortice-, but that there are 

 familiar instances in which nearly the same kind of fluid motion 

 must occur. 



In the mode of boat propulsion called sculling, the sailor 

 places an oar with a flat blade through a rowlock in the stern el 

 the boat, and, keeping the handle high above the rovilock, waves 

 the oar backwards and forwards with an alternate inclination of 

 the blade in one direction and the other. This action generates 

 a stream of water sternwards. The manner in which the blade 

 meets the water is closcly similar to that in which the slopes of 

 two ri| ple-mnrks alternately meet the oscillating water ; the 

 sternward current in one case, and the upward current in the 

 other are due to similar causes. We may feel confident that in 

 sculling, a pair of vortices are formed with axes vertical, and 

 that the dividing line between them is sinuous. The motion of 

 a fish's tail gives rise to a similar rearward current in almost the 

 same way. These instances may help us to realise the ripple - 

 making vortices. 



Lord Raylei'jh has considered the problem involved in the 

 oscillations of a layer of vortically moving fluid separating two 

 uniform streams.' At the meeting of the British Association at 

 Swansea in 1880 Sir William Thomson read a paper discussing 



vol 



' On the Formation of Ripple-mark." Proc. Roy. Sac, Apri 



Archivis lit! Sciences Physiques et Naturellis Geneve, Ni 

 Marclr 15, 1883. " Rides form^es," &c. 



3 " Les Rides de Fond." Arcttives des Scii 

 Geneve, July 15, iH33. 



* " On tlie Slability or Instability of certain Fluid M^ 

 Math. Sec. (February 11, 1880), vol. xi. p. 57. 



Physiqttes et Naturelles 

 Proc. Lond. 



