A WEEKLY ILLUSTRATED JOURNAL OF SCIENCE 



' ' To thi solid ground 

 Of .Viitur^ trusts the mind which builds for a_ 



-Wordsworth 



THURSDAY, NOVEMBER 2, 1871 



RIPPLES AND WAVES* 



YOU havealways considered cohesion of water(capillary 

 attraction) as a force which would seriously disturb 

 such experiments as you were making, if on too small a 

 scale. Part of its effect would be to modify the waves 

 generated by towing your models through the water. I 

 have often had in my mind the question of waves as 

 affected by gravity and cohesion jointly, but have only 

 been led to bring it to an issue by a curious phenomenon 

 which we noticed at the surface of the water round a 

 fishing-line one day slipping out of Oban (becalmed) at 

 about half a mile an hour through the water. The speed 

 was so small that the lead kept the line almost vertically 

 downwards ; so that the experimental arrangement was 

 merely a thin straight rod held nearly vertical, and moved 

 through smooth water at speeds from about a quarter to 

 three-quarters of a mile per hour I tried boat-hooks, 

 oars, and other forms of moving solids, but they seemed 

 to give, none of them, so good a result as the fishing-line. 

 The small diameter of thi fishing-line seemed to favour 

 the result, and I do not think its roughness interfered much 

 with it. I shall, however, take another opportunity of trying 

 a smooth round rod like a pencil, kept vertical by a lead 

 weight hanging down under water fron one end, while it 

 is held up by the o:her eni. The fishing-line, however, 

 without any other appliance proved amply sufficient to 

 give very good results. 



What we first noticed was an extremely fine and 

 numerous set of short waves preceding the solid much 

 longer waves following it right in the rear, and oblique 

 waves streaming oft" in the usual manner at a definite 

 angle on each side, into which th: waves in front and the 

 waves in the rear merged so as to form a beautiful and 

 symmetrical pattern, the tactics of which I have not been 

 able thoroughly to follow hitherto. The diameter of the 

 " solid " (that is to say the fishing-line) being only 

 two or three millimetres and the longest of the ob- 

 served waves five or six centimetres, it is clear that 

 the waves at distances in any directions from the solid 



* Extract from a letter to Mr. W. Froude, by Sir W. Thomson. 

 VOL. V. 



exceeding fifteen or twenty centimetres, were sensibly 

 unforced (that is to say moving each as if it were part 

 of an endless series of uniform parallel waves undisturbed 

 by any solid). Hence the waves seen right in front and 

 right in rear showed (what became immediately an obvious 

 result of theory) two different wave-lengths with the same 

 velocity of propagation. The speed of the vessel falling 

 off, the waves in rear of the fishing-line became shorter and 

 those in advance longer, showing another obvious result 

 of theory. The speed further diminishing, one set of waves 

 shorten and the other lengthen, until they become, as 

 nearly as I can distinguish, of the same lengths, and 

 the oblique lines of waves in the intervening pattern open 

 out to an obtuse angle of nearly two right angles. For a 

 very short time a set of parallel waves some before and 

 some behind the fishing-line, and all advancing direct 

 with the same velocity, were seen. The speed further 

 diminishing the pattern of waves disappeared altogether. 

 Then slight tremors of the fishing-line (produced for 

 example by striking it above water) caused circular rings 

 of waves to diverge in all directions, those in front ad- 

 vancing at a greater speed relatively to the water than 

 that of the fishing-line. All these phenomena illustrated 

 very remarkably a geometry of ripples communicated a 

 good many years ago to the PhilosopJiical Magazine by 

 Hirst, in which, however, so far as 1 can recollect, the 

 dynamics of the subject were not discussed. The speed 

 of the sohd which gives the uniform system of parallel 

 waves before and behind it, was clearly an absolute mini- 

 mum wave-velocity, being the limiting velocity to which 

 the common velocity of the larger waves in rear and 

 shorter waves in front was reduced by shortening the 

 former and lengthening the latter to an equality of wave- 

 length. 



Taking '074 of a gramme weight per centimetre of 

 breadth for the cohesive tension of a water surface (cal- 

 culated from experiments by Gay Lussac, contained in 

 Poisson's theory of capillary attraction, for pure water at 

 a temperature, so far as I recollect, of about <f Cent.), 

 and one gramme as the mass of a cubic centimetre, I 

 find, for the minimum velocity of propagation of sur- 

 face waves, 23 centimetres per second.* The mini- 



* One nautical mile per hour, the only other measurement of velocity, 

 except the French metrical reckoning, which ought to be used in any prac- 

 tical measurement, is 51*6 centimetres per second. 



