Page:Elementary Text-book of Physics (Anthony, 1897).djvu/111

§ 84] If $$T_{ab}$$ be greater than the sum of $$T_{ac}$$ and $$T_{bc}$$, the angle between $$T_{ac}$$ and $$T_{bc}$$ becomes zero, and the fluid $$c$$ spreads itself out in a thin sheet between $$a$$ and $$b$$. Thus, if a drop of oil be placed on water, the tension of the surface of separation between the air and water is greater than the sum of the tensions of the surfaces between the air and oil, and between the oil and water; hence the drop of oil spreads out over the water until it becomes almost indefinitely thin.

In the case of two fluids in contact with a plane solid (Fig. 33), it is evident that the system is in equilibrium when the surface of separation between the fluids $$a$$ and $$b$$ makes the angle $$\theta$$ with the solid $$C$$ given by $$T_{ac} = T_{bc} + T_{ab} \cos \theta$$. The angle of contact is then determined by the equation $$\cos \theta = \frac{T_{ac} - T_{bc}}{T_{ab}}\cdot$$

If $$T_{ac}$$ be greater than $$T_{ab} + T_{bc}$$, the equation gives an impossible value for $$\cos \theta$$. In this case the angle becomes evanescent, the fluid $$b$$ spreads itself out, and wets the whole surface of the solid. In other cases the value of is finite and constant for the same substances. Thus, a drop of water placed on a horizontal glass plate will spread itself over the whole plate; while a small quantity of mercury placed on the same plate will gather together into a drop, the edges of which make a constant angle with the surface.

84. Plateau's Experiments.—The preceding principles will enable us to explain a few of the most important experimental facts of capillarity.

A series of interesting results was obtained by Plateau from the examination of the behavior of a mass of liquid removed from the action of gravity. His method of procedure was to place a mass of oil in a mixture of alcohol and water, carefully mixed so as to have the same specific gravity as the oil. The oil then had no tendency