Page:Elementary Text-book of Physics (Anthony, 1897).djvu/112

98 to move as a mass, and was free to arrange itself entirely under the action of the molecular forces. Referring to the equation of Laplace, already obtained, it is evident that equilibrium can exist only when the sum $$\left(\frac{1}{R'} + \frac{1}{R} \right)$$ is constant for every point on the surface. This is manifestly a property of the sphere, and is true of no other finite surface. Plateau found, accordingly, that the freely floating mass at once assumed a spherical form. If a solid body—for instance, a wire frame—be introduced into the mass of oil, of such a size as to reach the surface, the oil clings to it, and there is a break in the continuity of the surface at the points of contact. Each of the portions of the surface divided from the others by the solid then takes a form which fulfils the condition already laid down, that $$\left(\frac{1}{R'} + \frac{1}{R} \right)$$ equals a constant. Plateau immersed a wire ring in the mass of oil. So long as the ring nowhere reached the surface, the mass remained spherical. On withdrawing a portion of the oil with a syringe, that which was left took the form of two equal calottes, or sections of spheres, forming a double convex lens. A mass of oil, filling a short, wide tube, projected from it at either end in a similar section of a sphere. As the oil was removed, the two end surfaces became less curved, then plane, and finally concave.

Plateau also obtained portions of other figures which fulfil the required condition. For example, a mass of oil was made to surround two rings placed at a short distance from one another. Portions of the oil were then gradually withdrawn, when two spherical calottes formed, one at each ring, and the mass between the rings became a right cylinder. It is evident that the cylinder fulfils the required condition for every point on its surface.

Plateau also studied the behavior of films. He devised a mixture of soap and glycerine, which formed very tough and durable films; and he experimented with them in air. Such films are so light that the action of gravity on them may be neglected in comparison with that of the surface tension. If the parts of the frame