every square centimetre of film torn asunder there will be destroyed ·05856 centigrammetre of potential energy, being the sum of ·03760 and ·02096, the potential or surface energies, in centigram-metres per square centimetre, of the surfaces separating air from oil and oil from water; and there will be generated for every square centimetre of free surface of water formed, ·08235 centigrammetre of potential energy. The mere fact of breaking the film of oil causes an expenditure of energy, because it lays bare a surface having a tension greater than the sum of the tensions of the surfaces separating air from oil and oil from water. But there is a further loss of energy in these circumstances. Suppose after a "break" has occurred, a layer of water glides over a layer of oil. The superficial energy in the surface separating the oil from the air, amounting to ·03760 centigrammetres per square centimetre, is replaced by ·10331 centigrammetre per square centimetre, being the sum of ·08235 and ·02096, the superficial energies per square centimetre of the surfaces separating air from water and water from oil respectively. Therefore, when water breaks over an oily film, there is required for the formation of each square centimetre of a layer of water on the oily film, ·10331 minus ·03760, or ·06571 centigrammetre of work.
The film of oil also acts as a shield to prevent the derangement of the wave mechanism and to prevent the growth of waves and the formation of sharp crests. It has been pointed out that, when waves are propagated across any body of liquid, the individual particles of the liquid, having their centrifugal and centripetal forces in equilibrium, describe closed orbits. At the highest points of these orbits, or in the crests of the waves, the particles are moving in the direction of propagation of the waves.
When the wind is blowing over the waves with a velocity greater than the velocity of propagation, and in the same direction with it, the moving air tends to impart to the particles of water a velocity additional to the normal velocity of revolution in their orbits, causing the distortion of the orbits and the disintegration of the crests of the waves. The force which the moving air exerts to draw the water along with it is due to the viscosity of air.
between the curve and the two axes is produced by drawing the ordinate y away from the axis O B toward the right by the action of the force Φ. If we consider O B and D C, which is equal to y, to be two rods wet with oil and placed between the curve and the axis of X, and then drawn asunder, the oily film B C A D O will be formed. Let E represent the superficial energy per unit of area. Then the work done in forming the film will be = E∫f(x)dx. But if Φ is the variable force required to draw the ordinate y from the axis O B, the same work may be written = ∫ Φ dx. Therefore, work = ∫ Φ dx = E∫f(x)dx(1). Substituting the value Φ = Tf(x) in (1), we have T∫f(x)dx = E∫f(x)dx, or T = E, or that the numerical value of the superficial tension per unit of length is equal to the superficial energy per unit of area.