Page:Encyclopædia Britannica, Ninth Edition, v. 5.djvu/75

CAPILLARY ACTION 63 and air, and between A and B. If no one of these ten sions is greater than the sum of the other two, the drop will assume the form of a lens, the angles which the upper and lower surfaces of the lens make with the free surface of A and with each other being equal to the external angles of the triangle of forces. Such lenses are often seen formed by drops of fat floating on the surface of hot water, soup, or gravy. But when the surface-tension of A exceeds the sum of the tensions of the surfaces of contact of B with air and with A, it is impossible to construct the triangle of forces, so that equilibrium becomes impossible. The edge, of the drop is drawn out by the surface-tension of A with a force greater than the sum of the tensions of the two surfaces of the drop. The drop, therefore, spreads itself out, with great velocity, over the surface of A till it covers an enormous area, and is reduced to such extreme tenuity that it is not probable that it retains the same pro perties of surface-tension which it has in a large mass. Thus a drop of train oil will spread itself over the surface of the sea till it shows the colours of thin plates. These rapidly descend in Newton s scale and at last disappear, showing that the thickness of the film is less than the tenth part of the length of a wave of light. But even when thus attenuated, the film may be proved to be present, since the surface-tension of the liquid is considerably less than that of pure water. This may be shown by placing another drop of oil on the surface. This drop will not spread out like the first drop, but will take the form of a flat lens with a distinct circular edge, showing that the surface-tension of what is still apparently pure water is now less than the sum of the tensions of the surfaces separating oil from air and water. The spreading of drops on the surface of a liquid has formed the subject of a very extensive series of experiments by Mr Tomlinson. M. Van der Mensbrugghe has also written a very complete memoir on this subject. 1 When a solid body is in contact with two fluids, the surface of the solid cannot alter its form, but the angle at which the surface of contact of the two fluids meets the surface of the solid depends on the values of the three surface- tensions. If a and b are the two fluids and c the solid then the equilibrium of the ten sions at the point O depends only on that of thin components parallel to the surface, bo- cause the surface-tensions normal to the sur face are balanced by the resistance of the solid. Hence if the angle EOQ (fig. 4) at which the surface of contact OP meets the solid is denoted by a, Fig. 4. whence T 6( .-T, a -T a6 cos. a-0, be ~ * ca As an experiment on the angle of contact only gives us the difference of the surf ace -tensions at the solid surface, we cannot determine their actual value. It is theoretically probable that they are often negative, and may be called surface-pressures. The constancy of the angle of contact between the surface of a fluid and a solid was first pointed out by Dr Young, who states that the angle of contact between mercury and glass is about 140. Quincke makes it 128 52 . If the tension of the surface between the solid and one of the fluids exceeds the sum of the other two tensions, the point of contact will not be in equilibrium, but will be dragged towards the side on which the tension is greatest. If the quantity of the first fluid is small it will stand in a Tension Superficielle des Liquides, Bruxelles, 1873. drop on the surface of the solid without wetting it. If the quantity of the second fluid is small it will spread itself over the surface and wet the solid. The angle of contact of the first fluid is 180 and that of the second is [o. If a drop of alcohol be made to touch one side of a drop of oil on a glass plate, the alcohol will appear to chase the oil over the plate, and if a drop of water and a drop of bisulphide of carbon be placed in contact in a horizontal capillary tube, the bisulphide of carbon will chase the water along the tube. In both cases the liquids move in the direction in which the surface-pressure at the solid is least. ON THE RISE OF A LIQUID IN A TUBE. Let a tube (fig. 5) whose internal radius is r, made of a solid substance c, be dipped into a liquid a. Let us suppose that the angle of contact for this liquid with the solid c is an acute angle. This im plies that the ten sion of the free surface of the solid c is greater than that of the sur face of contact of the solid with the liquid a. Now consider the ten- pjg. 5. sion of the free surface of the liquid a. All round its edge there is a tension T acting at an angle a with the vertical. The circumference of the edge is 2irr, so that the resultant of this tension is a force 27H-T cos. a acting vertically upwards on the liquid. Hence the liquid will rise in the tube till the weight of the vertical column between the free surface and the level of the liquid in the vessel balances the resultant of the surface- tension. The upper surface of this column is not level, so that the height of the column cannot be directly measured, but let us assume that h is the mean height of the column, that is to say, the height of a column of equal weight, but with a flat top. Then if r is the radius of the tube at the top of the column, the volume of the suspended column is irr-h, and its weight is irpgrVi, when p is its density and g the intensity of gravity. Equating this force with the resultant of the tension cos. a, or 2T cos. a Hence the mean height to which the fluid rises is inversely as the radius of the tube. For water in a clean glass tube the angle of contact is zero, and 2T h = W- For mercury in a glass tube the angle of contact is 128 52 , the cosine of which is negative. Hence when a glass tube is dipped into a vessel of mercury, the mercury within the tube stands at a lower level than outside it. EISE OF A LIQUID BETWEEN Two PLATES. When two parallel plates are placed vertically in a liquid the liquid rises between them. If we now suppose fig. 5 to represent a vertical section perpendicular to the plates, we may calculate the rise of the liquid. Let I be the

breadth of the plates measured perpendicularly to the