70 CAPILLARY ACTION velocity of propagation of waves in deep water is that acquired by a heavy body falling through half the radius of the circle whose circumference is the wave-length, or wT This velocity is a minimum when and the minimum value is 4 /~TV = V 4 v o For waves whose length from crest to crest is greater than X, the principal force concerned in the motion is that of gravitation. For waves v hose length is less than A the principal force concerned is l.hat of surface-tension. Sir William Thomson proposes to distinguish the latter kind of waves by the name of ripples. When a small body is partly immersed in a liquid origin ally at rest, and moves horizontally with constant velocity V, waves are propagated through the liquid with various velocities according to their respective wave-lengths. In front of the body the relative velocity of the fluid and the body varies from V where the fluid is at rest, to zero at the cutwater on the front surface of the body. The waves produced by the body will travel forwards faster than the body till they reach a distance from it at which the relative velocity of the body and the fluid is equal to the velocity of propagation corresponding to the wave length. The waves then travel along with the body at a constant distance in front of it. Hence at a certain distance in front of the body there is a series of waves which are stationary with respect to the body. Of these, the waves of minimum velocity form a stationary wave nearest to the front of the body. Between the body and this first wave the surface is comparatively smooth. Then comes the stationary wave of minimum velocity, which is the most marked of the series. In front of this is a double series of stationary waves, the gravitation waves forming a series increasing in wave length with their distance in front of the body, and the surface-tension waves or ripples diminishing in wave-length with their distance from the body, and both sets of waves rapidly diminishing in amplitude with their distance from the body. If the current-function of the water referred to the body considered as origin is l/, then the equation of the form of the crest of a wave of velocity iv, the crest of which travels along with the body, is dty = wds where ds is an element of the length of the crest. To inte grate this equation for a solid of given form is probably diffi cult, but it is easy to see that at some distance on either side of the body, where the liquid is sensibly at rest, the crest of the wave will approximate to an asymptote inclined to the w path of the body at an angle whose sine is , where iv is the velocity of the wave and V is that of the body. The crests of the different kinds of waves will therefore appear to diverge as they get further from the body, and the waves themselves will be less and less perceptible. But those whose wave-length is near to that of the wave of mininum velocity will diverge less than any of the others, so that the most marked feature at a distance from the body will be the two long lines of ripples of minimum velocity. If the angle between these is 20, the velocity of the body is w sec. 0, where w for water is about 23 centi metres per second. TABLES OF SURFACE TENSION. In the following tables the units of length, mass, and time are the centimetre, the gramme, and the second, and the unit of force is that which if it acted on one gramme for one second would communicate to it a velocity of one centimetre per second : Table of Surf ace-Tension at 20 C. (Quincke). Tension of surface separating the liquid Angle of contact with glass in presence of Liquid. SpeciBc Air. Water. Mer cury. Air. Water Mercury Water 1 81 418 25 32 |9R Mercury. ... 13-5432 540 418 51 8 96 8 Bisulphide of ) Carbon ... ) 1-2687 32-1 41-75 372-5 32 16 13 8 Chloroform 1-4878 30-6 29-5 399 Alcohol 0790(3 25-5 399 25 12 Olive Oil 0-9136 1 3fi-9 20-56 335 21 50 17 47 2 Turpentine ... 0-8867 29-7 11-55 250-5 37 44 37 44 47 C 2 Petroleum 0-7977 31-7 27-8 284 36 20 42 46 Hydrochloric ) Acid } 1-1 701 377 .. Solution of Hyposul phite of 1-1248 77"5 442-5 23 20 10 42 Soda Olive Oil and Alcohol, 12 2. Olive oil and aqueous alcohol (sp. g. 9231, tension of free surface 25-5), 6-8, angle 87 48 . Quincke has determined the surface-tension of a great many substances near their point of fusion or solidification. His method was that of observing the form of a large drop standing on a plane surface. If K is the height of the flat surface of the drop, and k that of the point where its tangent plane is vertical, then Surf ace- Tensions of Liquids at their Point of Solidification* From Quincke. Substance. Temperature of Solidification. Surf ace-Tension. Platinum 2000 C. 1658 Gold 1200 983 Zinc 360 860 Tin 230 587 Mercury - 40 577 Lead 330" 448 Silver 1000" 419 Bismuth 265" 382 Potassium 5& 364 Sodium 90* 253 Antimony. 432 244 Borax 1000" 212 Carbonate of Soda Chloride of Sodium Water 1000" 0" 206 114 86-2 Selenium 217 70-4 Sulphur 111 41-3 Phosphorus. . 43 41-1 Wax 68 33-4 Quincke finds that for several series of substances the sur face-tension is nearly proportional to the density, so that if we 2T call (K - kf = the specific cohesion, we may state the 9P general results of his experiments as follows : The bromides and iodides have a specific cohesion about half that of mercury. The nitrates, chlorides, sugars, and
fats, as also the metals, lead, bismuth, and antimony, have