176 



KNOWLEDGE 



[August 1, 189G. 



WAVES-VIII. 



CAPILLARY WAVES. 



(ll'((/i iiifdiiiitilion iijion Breakinij and S]Tiii/in'j, anil upon 

 the Use of Oil at Sea.) 



By Vauoiian Cornish, M.Sc. 



A snip on her course leaves a wave track bpliind, 

 whilst in front there is scarcely any vifiblo dis- 

 turbance except the foaming,' surge at the bow. 

 It is otherwise with a small body moviiifj; slowly 

 through the water, which niiikos thn principal dis- 

 turbance in front. If, when walking slowly by the edge of 

 a pond, one trails his walking stick in the water, little 

 ship-waves of the familiar pattern follow in its wake, but 

 in front of the stick there is a novel appearance not seen 

 with the ship. This is an arrow-head pattern of wavelets 

 or capillary waves, such as is shown in Fig. 1, the pattern 



Fio. 1.— The Wavelet Pattern, after Scott Eussel. (The Section 

 shows also the Waves on the lee side which are omitted from the Plan.) 



moving as a whole through the water, preserving its 

 position relatively to the stick. The pattern is seen even 

 better with a fishing line, especially if the line be kept 

 nearly vertical by a weight ; the ship waves bthind are 

 not so conspicuous with the smaller body, but the pattern 

 of wavelets in front is better defined. The appearance is 

 seen equally well when fishing from a river bank or from a 

 boat slowly drifting on a smooth sea. All that is neces- 

 sary is that there should be a slow relative motion of, say, 

 a half to one mile per hour between the obstacle and the 

 water ; dozens of ridges can then be counted in front of 

 the fishing line. When the motion is more rapid the 

 pattern closes up, and at the same time the angle of the 

 arrow-head becomes sharper. On slowing down again 

 the arrow-head flattens out, until at a very slow speed, 

 about nine inches per second, the obstacle is preceded and 

 followed by one or two nearly straight parallel ridges 

 separated by intervals of about two-thirds of an inch. 

 This phase is difiicult to catch, for if the motion becomes 

 ever so little slower the ridges vanish altogether, the surface 

 of the water being smooth and unwrinkled. .\bout nine 

 inches per second is the lowest velocity possible for a wave 



of water, and there is one definite wave-length, about two- 

 thirds of an inch, corresponding to this speed. As soon, 

 however, as the speed of the moving body is decreased, two 

 seta of uiidula'ions of dillereiit wave-length accompany the 

 body, and it therefore appears that for any speed greater 

 than nine inches per second there are two wave-lengths, 

 one greater and one loss than two-thirds of an inch. The 

 latter are the wavelets or capillary waves (which L ird 

 Kelvin calls ripples) which form the fore part of the visible 

 wave pattern of a small moving body. Those furthest in 

 front are the shortest, the wave-length increasing as 

 we go backwards through the pattern, 'i'hese wave- 

 lets which run by capillarity move quicker the shorter 

 their wave-length. Waves which run by gravitation 

 move quicker the longer their wave-length. Tlio wave of 

 minimum velocity is controlled equally by the two forces of 

 gravitation and capillarity. Wavelets a little shorter are 

 mainly controlled by capillarity ; waves a little longer are 

 mainly controlled by gravity ; and if the wave-length is 

 much shorter or much greater than two-thirds of an inch, 

 the one or the other force has complete control. Clerk 

 Maxwell treats the case of a small body moving slowly 

 through water in the following manner. In front of the 

 body the relative velocity of the water and the body varies 

 from V, the velocity of the body, where the fluid is at rest, 

 to zero at the cutwater, where the fluid is forced to move 

 with the body. The waves produced by the body roll 

 away from the cutwater until they reach distances from it 

 at which the relative velocity of the body and the fluid is 

 equil to the several velocities corresponding to the wave- 

 length of the several disturbances. Nearest the body is 

 the wave of minimum velocity. Now what does theory 

 indicate that there should be in front of this, where the 

 relative velocity of the water and the body is greater ? 

 TIteofeticidly there is a doable series of undulations — 

 capillary waves and gravitation waves, the former getting 

 shorter, the latter getting longer, the further they are in 

 front of the body. Practicallij we do not notice the gravi- 

 tation waves in front, because they are too flat, whereas 

 the little wrinklings of the capillary waves are rendered 

 conspicuous by the play of light and shadow upon their 

 steep sides. The wave of minimum velocity diverges least 

 on either side of the path of the moving body, and at a 

 distance on either side it is the most conspicuous part of 

 the pattern. When the body moves quickly, even though 

 it be small, the amplitude of the disturbances is so much 

 increased that the gravitation wave nearest the body 

 becomes steep enough to be conspicuous. This corre- 

 sponds to the great bow wave of a steamer. Now these 

 gravitation waves drop their energy behind them, as was 

 explained in the article upon the force of the waves, so 

 that the bow wave makes a group of waves behind it, and 

 these are the waves which follow in the track of the ship 

 althoiTgh originating in front. Directly in the wake of the 

 ship or moving body they appear as a procession of waves 

 following the ship, each keeping its place relatively to the 

 ship. Their outer border on either side of the ship's path 

 is a series of short billows, stepped back one behind the 

 other en echelon, as described in the article upon ship 

 waves. Each line of the capillary waves, on the contrary, 

 presents an unbroken front— a continuous arrow-head. 

 This, I suppose, indicates that the energy of the capillary 

 waves does not lose itself in the depths of the water, 

 but keeps in the skin of the liquid : that is to say, 

 the surface film of capillary thickness. If this be so, 

 the form of the wave front of the capillary waves 

 created by a moving body is readily explained. Let us 

 think for a moment of the pattern formed by the drops 

 falling from the blade of an oar when swung back slowly 



