Page:Elementary Text-book of Physics (Anthony, 1897).djvu/106

 another. Young was the first to treat the subject satisfactorily, though others had given partial and imperfect demonstrations before him. He showed that a liquid can be dealt with as if it were covered at the bounding surface with a stretched membrane, in which is a constant tension tending to contract it. From this basis he proceeded to deduce some of the most important of the experimental laws. Laplace, proceeding directly from the law of the attraction which we have already given, considered the attraction of a mass of liquid on a filament of the liquid terminating at the surface, and obtained an expression for the pressure within the mass at the interior end of the filament. He also was able, not only to account for already observed laws, but to predict, in at least one instance, a subsequently verified result. Some years later, Gauss, dissatisfied with Laplace's assumption, without a priori demonstration, of a known experimental fact, treated the subject from the basis of the principle of virtual velocities, which in this case is the equivalent of that of the conservation of energy. He proved that, if any change be made in the form of a liquid mass, the work done or the energy recovered is proportional to the change of surface, and hence deduced a proof of the fact which Laplace assumed, and also an expression for the pressure within the mass of a liquid identical with his. For purposes of elementary treatment the earliest method is still the best. We shall accordingly employ the idea of surface tension, after having shown that it may be obtained from the hypothesis of molecular attraction.

80. Surface Tension.—Consider any liquid bounded by a plane surface, of which the line $$mn$$ (Fig. 28) is the trace, and let the line $$m'n'$$ be the trace of a parallel plane at the distance $$\epsilon$$ from the plane of $$mn$$. Beneath the plane $$m'n'$$ the liquid will be homogeneous at all points, and the attraction on any one molecule of it due to the surrounding molecules will be the same in all directions. If we consider the