1833.] 



On the Formation of Ripple-mark. 



19 



discussion of some phenomena in the vortex motion of air and 

 water. 



§ 1. First Series of Experiments. 



A cylindrical zinc vessel, like a flat bath, with upright sides, 

 2 feet 8 inches in diameter and 9 inches deep, was placed on a table, 

 which was free to turn about a vertical axis. Some fine sand was 

 strewn over the bottom to a depth of about an inch, and water was 

 poured in until it stood three inches deep over the sand. After some 

 trials of simply whirling the bath, in which no regular ripple-mark 

 was formed, I found that rotation al oscillation with a jerking motion 

 of small amplitude gave rise almost immediately to beautiful radial 

 ripples all round the bath. If the jerks were of small amplitude the 

 ripples were small, and if larger they were larger. On one occasion 

 having made large ripple-marks, I oscillated the bath much more 

 rapidly, and a second set of ripples sprang into existence in the 

 furrows of the first set. Another time, when in consequence of 

 irregularity in the motion, a set of radiating waves were generated in 

 the water, a second set of transverse ripples were formed, which pro- 

 duced by interference a beautifully mamellated structure, arranged 

 like a chess-board. In all these experiments the radiating ripples 

 began first to appear at the outer margin of the bath and grew 

 inwards; but the growth stopped after they had extended to a certain 

 distance. If the jerking motion was violent, ripples were not formed 

 near the circumference, and they only began at some distance 

 inwards. After these preliminary trials, arrangements were made for 

 regularising both the frequency and amplitude of oscillation of the 

 bath. An attempt was then made to formulate the laws which govern 

 the generation of ripple-marks. In the following notes of experiments 

 the expression " octave " is used to denote a ripple-length which is 

 one-half of the main or fundamental ripple, and the amplitudes are 

 measured by the displacement of the edge of the bath. 



The water stood 1 inch deep in the bath. 



1. Amplitude 1 inch ; frequency 52 per minute (complete oscil- 

 lations) . 



No ripples formed after four minutes. 



2. Amplitude 2-J- inches; frequency 52. 



55 ripples round the circumference, extending about 4 inches 

 inwards ; somewhat irregular and with a tendency to break into 

 the octave. 



3. Amplitude 6 \ inches ; frequency 52. 



Motion very violent. About 5 large irregular ripples in the circum- 

 ference, breaking at about 9 inches from the outside into about 

 40 ripples. 



4. Amplitude If inches ; frequency 52. 



C 2 



