WHY A FILM OF OIL CAN CALM THE SEA. 501 



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 centi- 

 grammetre 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 cen- 

 timetre, being the sum of '08235 and "02096, the superficial ener- 

 gies 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 derange- 

 ment 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 indi- 

 vidual particles of the liquid, having their centrifugal and cen- 

 tripetal 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 B toward the right by the action of the force <p. If we consider 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 will be formed. Let E represent the 

 superficial energy per unit of area. Then the work done in forming the film will be = 

 Eff{x) dx. But if <\> is the variable force required to draw the ordinate y from the axis 

 B, the same work may be written =f<p dx. Therefore, work =f<p dx =U/f(x) dx (1). 

 Substituting the value <p= Tf(x) in (1), we have Tff(x) dx = Eff(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. 



