AuorsT 1, 1896.] 



KNOWLEDGE. 



177 



Fig. i. — The Arrow-Head. 



for a stroke. The wavelets from the falling drops ring out 

 thus (Fig. 2), and the dotted line shows the arrow-head 

 wave-front which would be produced if the disturbance 

 were continuous instead of intermittent. 



The arrow-head pattern of diminishing wavelets is a 

 decorative tracery of singular delicacy worth knowing for 

 its beauty, apart even from its scientific interest. The 

 pattern can be seen on the 

 up-stream side of every 

 pebble which raises a 

 wave in a brook, and on 

 the lee side of every small 

 wave raised by the wind 

 on a calm sea, or on a 

 river, lake, or pond. In 

 front of the breast of a 

 duck, when swimming 



quietly, the broad pattern is visible ; and the little duck- 

 lings show it almost better, for they cannot swim fast 

 enough to obliterate the pattern. Those insects from 

 whose feet the water shrinks so that they stand in 

 little holes, make an arrow-headed track when they dart 

 about on the surface of a pond. 



Capillary waves are also formed by other means than 

 those which give the arrow-headed pattern, as, for instance, 

 when a catspaw of wind suddenly darkens the surface of 

 still water, covering it with fairly uniform wavelets, the 

 wrinkled surface smoothing itself once more the moment 

 the gust has passed. 



An exquisitely fine pattern of stationary wavelets is seen 

 on the water in a finger-glass when the wetted finger is 

 drawn round the rim so as to cause the glass to vibrate 

 and emit a musical note. The vibrating prongs of a tuning- 

 fork in the same way will produce minute wavelets, which 

 are finer in pattern the higher the note. A special device 

 for showing capillary waves was recently exhibited by 

 Professor Boys at the Royal Institution. A circular glass 

 dish with vertical sides is placed upon a whirling table, 

 and the surface of the whirling water is touched with the 

 point of a needle. The arrow-head takes the form shown in 

 Fig. 3, the wavelets vanishing towards the centre where 



the velocity is less 

 than that of the 

 slowest wave. Any- 

 thing which dimin- 

 ishes the tightness of 

 the skin of the water 

 will enable the wave 

 pattern to extend 

 nearer to the centre, 

 for when the surface 

 is not so taut, less 

 force is needed to 

 wrinkle it and the 

 corresponding velo- 

 city is less. A little 

 soap added to the 

 water has this elt'ect. 

 The skin of alcohol is 

 not so tight as the 

 skin of water, and if the basin be filled with alcohol 

 instead of water and the vessel be started whirling, the 

 capillary wave pattern appears sooner than with water, 

 and the wavelets are longer from crest to crest. The 

 same is the case with wavelets in mercury, for although 

 mercury has a tight skin the liquid is so much heavier 

 than water that the force required to propagate a wave 

 is provided by a slower motion of the liquid. Capillary 

 waves on liquid metals such as mercury (or molten alu- 



FlG. 3. — The Arrow-IIeacl iu a 

 Whirling Dish. 



minium) are very beautiful owing to the perfection of the 

 surface reflection. 



The force called " capillary," which gives a liquid a tight 

 skin, requiring an appreciable force to wrinkle or ruffle it, 

 is due to the strong attraction exercised between the 

 neighbouring particles of a body, and between those parts 

 of different bodies which are so close that, to our senses, 

 they appear in actual contact. At very small distances 

 attraction can be very much stronger than is accounted 

 for by the lux of gravitation — the law which states that 

 attraction is proportional to the square of the nearness. 

 This law appears to hold good from the greatest distances 

 down to, say, the hundredth or the thousandth of an inch, 

 but at much closer quarters the law no longer holds. Not 

 that any new agency necessarily comes into play, but that 

 the law of its action is changed. Perhaps, as Lord Kelvin 

 has pointed out, if we could locate each molecule we 

 should be able to account for the increased attraction at 

 close quarters, simply by the arrangement of the discon- 

 tinuous matter. A spot may be eo hemmed in by the 

 contiguous molecules that their attraction is far greater 

 there than that of all the distant parts of the body., 

 however large it may be. It is this which constitutes the 

 strength of materials. 



Obviously, the conditions with regard to such short- 

 distance actions must change abruptly at the surface of a 

 body. Indeed, the surface of a solid body is the boundary 

 of a universe, on the two sides of which are two different 

 laws of being. At present, however, we are concerned with 

 the surface of a liquid. If Fig. 4 represent a vessel con- 

 taining a liquid and its own vapour, the horizontal line 

 representing the sur- 

 face of separation, 

 and if we consider 

 the attractions upon 

 a particle C of all 

 other particles which 

 are very near to it ; 

 we see, in the first 

 place, that as there 

 are fewer particles 

 above than below 

 ( the vapour being less 

 dense than the 

 liquid), it will require 

 work to carry the 

 particle C into the 

 upper part of the 

 vessel. This is a 

 familiar fact ; energy 



Fio. 4. — The Surface of a Liquid. 



of 

 to 



is taken up, -m/., in the form 

 heat, when a liquid is made to evaporate. Secondly, 

 pull C down into the depths of the liquid wiU similarly 

 require the supply of external energy, because the attraction 

 of all particles below the dotted line is as nothing compared 

 with the attraction of the neighbouriug particles in the 

 thin film above the dotted line. On the whole, therefore, 

 there is a resultant force along the surface of the liquid, 

 which makes the surface behave something like a stretched 

 sheet of india-rubber, for it always tries to shrink so as to 

 make itself as small as possible. It requires force to 

 wrinkle it because wrinkling increases the extent of 

 surface ; and, if the compulsion be withdrawn, the crests 

 fall smartly down, and the troughs jump nimbly up; 

 inertia carries crest and trough past the middle line, 

 vibration goes on with diminishing amplitude, and 

 presently the surface comes to rest. This is the vibration 

 of a capillary wave, surface tension wave, or ripple. 



It is the shrinking of the surface which makes liquids 

 tend to form spherical drops, the sphere being the figure 



