Page:Elementary Text-book of Physics (Anthony, 1897).djvu/107

§ 80] attraction for each other of the molecules lying on either side of a small area taken within the body of the liquid, it is easy to see that, if we suppose the molecules on one side of this surface to be removed, while those on the other side are still acted on by the same forces as those which they experienced before, equilibrium may be maintained by the application of a pressure to all points of the surface. On account of the homogeneity of the liquid this pressure will be the same in all directions; when measured for unit of surface it is called the molecular pressure in the liquid, and is denoted by $$K$$. The condition of things is different in the surface layer included between the planes $$m'n'$$ and $$mn$$. In the first place, the conditions within the range of molecular action around any one molecule, such as $$P$$, are not the same in all directions, and $$P$$ is therefore acted on by a force which is always normal to the surface, and which is greater when $$P$$ is nearer the surface $$mn$$. This appears at once from the figure, which shows that $$P$$ is drawn toward the body of the liquid by the molecules contained within the lower hemisphere determined by the range of molecular action, and is drawn upward by those contained within that portion of the upper hemisphere determined by the surface mn and the parallel plane passing through $$P$$. In the second place, the pressure on a surface containing $$P$$ will not be the same for all positions of the surface. It diminishes as $$P$$ approaches $$mn$$, and vanishes at the surface of the liquid. If we consider a surface perpendicular to $$mn$$, and suppose the molecules on one side of it removed, it is evident that the forces which act on $$P$$ will not be normal to the surface and will tend to displace the molecule at $$P$$ and draw it into the body of the liquid. Such forces give rise to a so-called tension in the surface, which tends to contract it. This tension is best conceived of by considering the surface of the liquid interrupted by a thin rigid rod and the liquid removed from one side of it; a force must then be applied to the rod directed away from the liquid, in order to maintain equilibrium. The ratio of the total force applied to