Page:Elementary Text-book of Physics (Anthony, 1897).djvu/113

§ 85] upon which the film is stretched be all in one plane, the film will manifestly lie in that plane. When, however, the frame is constructed so that its parts mark the edges of any geometrical volume, the films which are taken up by it often meet. Any three films thus meeting arrange themselves so as to make angles of 120° with one another. This follows as a consequence of the proposition which has already been given to determine the equilibrium of surfaces of separation meeting along a line. If four or more films meet, they always meet at a point.

Plateau also measured the pressure of air in a soap-bubble, and found that it differed from the external pressure by an amount which varied inversely as the radius of the bubble. This follows at once from Laplace's equation. This measurement also gives us a means of determining the surface tension; for, from Laplace's equation, the pressure inwards, due to the outer surface, is $$\frac{T^2}{R}$$, and the pressure in the same direction due to the inner surface is also $$\frac{T^2}{R}$$, for the film is so thin that we may neglect the difference in the radii of the two surfaces: hence the total pressure inwards is $$\frac{4T}{R}$$; and if this be measured by a manometer, we can obtain the value of $$T$$.

85. Liquids influenced by Gravity.—Passing now to consider liquid masses acted on by gravity, we shall treat only a few of the most important cases.

If a glass tube having a narrow bore be immersed perpendicularly in water, the water rises in the tube to a height inversely proportional to the diameter of the tube. This law is known as Jurin's law.

Let Fig. 33 represent the section of a tube of radius $$r$$ immersed in a liquid, the surface of which makes an angle $$\theta$$ with the wall. Then if The the surface tension of the liquid, the tension acting upward is the component of this surface tension parallel to the wall exerted all around the circumference of the tube. This is