Page:Elementary Text-book of Physics (Anthony, 1897).djvu/110

96 negative, and the pressure is directed outwards. This pressure is to be added to the constant molecular pressure which we have already seen exists everywhere in the mass. If we denote this constant molecular pressure by $$K$$, the expression for the total pressure within the mass is $$K + T \left(\frac{1}{R'} + \frac{1}{R} \right)$$, where the convention with regard to the signs of $$R'$$ and $$R$$ must be understood. For a plane surface, the radii of curvature are infinite, and the pressure under such a surface reduces to $$K$$.

This equation is known as Laplace's equation.

83. Angles of Contact.—Many of the capillary phenomena appear when different liquids, or liquids and solids, are brought in contact with one another. It becomes, therefore, necessary to know the relations of the surface tensions and the angles of contact. They are determined by the following considerations:

Consider first the case when three liquids meet along a line. Let $$O$$ represent the point where this line cuts a plane drawn at right angles to it (Fig. 31). Then the tension $$T_{ab}$$ of the surface of separation of the liquid $$a$$ from the liquid $$b$$, acting normal to this line, is counterbalanced by the tensions $$T_{ac}$$ and $$T_{bc}$$ of the surfaces of separation of $$a$$ and $$c$$, $$b$$ and $$c$$. These tensions are always the same for the three liquids under similar conditions of temperature and purity. Knowing the value of the tensions, the angles which they make with one another are determined at once by the parallelogram of forces; and these angles are always constant.

Similar relations arise if one of the liquids be replaced by a gas. Indeed, some experiments by Bosscha indicate that capillary phenomena occur at surfaces of separation between gases. We need, therefore, in the subsequent discussions, make no distinction between gases and liquids, and may use the general term fluids.