62 CAPILLARY ACTION attractive force. Hence we may consider 11 very small compared with L. If we neglect M altogether, /A-K i"-V L If we assume a quantity a such that a 2 K = 2L, we may call a the average range of the molecular forces. If we also take b, so that bnl, we may call b the modulus of the variation of the density near the surface. Our calculation hitherto has been made on the hypothesis that a is small when compared with b, and in that case we have found that a 2 :& 2 :: A-K : K. But it appears from experiments on liquids that A-K is in general large when compared with K, and sometimes very large. Hence we conclude, first, that the hypothesis of our calculation is incorrect, and, secondly, that the phenomena of capillary action do not in any very great degree depend on the variation of density near the surface, but that the principal part of the force depends on the finite range of the molecular action. In the following table, Ap is half the ciibical elasticity of the liquid, and Kp the molecular pressure, both expressed in atmo spheres (the absolute value of an atmosphere being one million in centimetre-gramme-second measure, see below, p. 70). p is the density, T the surface-tension, and a the average range of the molecular action, as calculated by Von der Waals from the values of T and K. The unit in which a is expressed is 1 cm x 10 ~ 9 ; a is therefore the twenty-millionth part of a centimetre for mercury, the thirty- millionth for water, and the forty-millionth part for alcohol. Quincke, however, found by direct experiment that certain molecu lar actions were sensible at a distance of a two-hundred-thousandth part of a centimetre, so that we cannot regard any of these num bers as accurate. A p Kp p T a Ether 4(100 1300 73 18 29 Alcohol 5500 100 79 25 5 25 Bisulphide of Carbon... Water 16000 22200 2900 5000 1-27
321 81 23 "1 Mercurv 542000 22500 540 49 ON SUEF ACE-TENSION. Definition. The tension of a liquid surface across any line draivn on the surface is normal to the line, and is the same for all directions of the line, and is measured by the force across an element of the line divided by the length of that element. Experimental Laws of Surface-tension. 1. For any given liquid surface, as the surface which separates water from air. or oil from water, the surface- tension is the same at every point of the surface and in every direction. It is also practically independent of the curvature of the surface, although it appears from the mathematical theory that there is a slight increase of tension where the mean curvature of the surface is concave, and a slight diminution where it is convex. The amount of this increase and diminution is too small to be directly measured, though it has a certain theoretical importance in the explanation of the equilibrium of the superficial layer of the liquid where it is inclined to the horizon. 2. The surface-tension diminishes as the temperature rises, and when the temperature reaches that of the critical point at which the distinction between the liquid and its vapour ceases, it has been observed by Andrews that the capillary action also vanishes. The early writers on capillary action supposed that the diminution of capillary action was due simply to the change of density corresponding to the rise of temperature, and, therefore, assuming the surface- tension to vary as the square of the density, they deduced s variations from the observed dilatation of the liquid by eat. This assumption, however, does not appear to be verified by the experiments of Brunner and Wolff on the rise of water in tubes at different temperatures Fig. 3. 3. The tension of the surface separating two liquids which do not mix cannot be deduced by any known method from the tensions of the surfaces of the liquids when separately in contact with air. When the surface is curved, the effect of the surface- tension is to make the pressure on the concave side exceed the pressure on the convex side by T ( ^- +ir), where T is
-Kj R--J
the intensity of the surface-tension and R 1( R. 2 are the radii of curvature of any two sections normal to the surface and to each other. If three fluids which do not mix are in contact with each other, the three surfaces of separation meet in a line, straight or curved. Let (fig. 3) be a point in this line, and let the plane of the paper be supposed to be normal to the line at the point 0. The three angles between the tan gent planes to the three sur faces of separation at the point are completely deter mined by the tensions of the three surfaces. For if in the triangle abc the side ab is taken so as to represent on a given scale the tension of the surface of contact of the fluids a and b, and if the other sides be and ca are taken so as to represent on the same scale the tensions of the surfaces between b and c and between c and a respectively, then the condition of equilibrium at O for the corresponding tensions R, P, and Q is that the angle ROP shall be the supplement of abc, POQ of bca, and, there fore, QOR of cab. Thus the angles at which the surfaces of separation meet are the same at all parts of the line of concourse of the three fluids. When three films of tho same liquid meet, their tensions are equal, and, therefore, they make angles of 120 with each other. The froth of soap-suds or beat-up eggs consists of a multitude of small films which meet each other at angles of 120. If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron ABCD is formed so that its edge AB repre sents the tension of the surface of contact of the liquids a and b, BC that of b andc, and so on ; then if we place this tetrahedron so that the face ABC is normal to the tangent at O to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at O to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at O to the other three lines of concourse of the liquids, and the other five edges of the tetrahedron will be normal to the tangent planes at O to the other five surfaces of contact. If six films of the same liquid meet in a point the corre sponding tetrahedron is a regular tetrahedron, and each film, where it meets the others, has an angle v, hose cosine is - -ij. Hence if we take two nets of wire with hexagonal meshes, and place one on the other so that the point of concourse of three hexagons of one net coincides with the middle of a hexagon of the other, and if we then, after dipping them in Plateau s liquid, place them horizontally, and gently raise the upper one, we shall develop a system of plane laminae arranged as the walls and floors of the cells are arranged in a honeycomb. We must not, how ever, raise the upper net too much, or the system of films will become unstable. When a drop of one liquid, B, is placed on the surface of another, A, the phenomena which take place depend on the relative magnitude of the three surface-tensions corre
sponding to the surface between A and air, between B