ORIGIN OF THE SMALL BUBBLES OF FROTH. 211 



a more distinctive designation is desirable, the quantity 

 may be referred to as the surface excess of mechanical 

 potential energy. In connection with solids the magnitude 

 of the quantity cannot be directly ascertained, but for liquids 

 an expression for the value of the surface energy at any 

 temperature was found by Lord Kelvin in 1858. x Suppose 

 the area of a surface increased by dS; by the change 

 additional restraint is created for the molecules which 

 constitute the new part of the surface layer; they thus 

 acquire increased potential energy, but at the same moment 

 lose kinetic energy, on the whole, owing to the variation 

 of the restraint within the stratum. The work done in 

 increasing the surface is sdS, where s is the surface tension, 

 here its mean value, so we may write, 



gain of potential energy — loss of kinetic energy = sdS. 



Lord Kelvin shows, in the paper to which the reference 

 has been given, that the energy which must be added during 

 the extension of the surface to keep the temperature 

 constant, that is to maintain the kinetic energy, of the 

 molecules under consideration, at its original value, is 

 - (6ds/d6)dS, where represents the absolute temperature. 

 This term, then, measures the loss of kinetic energy that 

 would have occurred in the adiabatic case had the surface 

 tension remained constant, so that for extension at the 

 tempereture we may put, 



gain of potential energy + (Ods/dO)dS = sdS. 

 Therefore the additional molecular potential energy associ- 

 ated with the surface layer, per unit area of surface, due 

 to the extra restraint which molecules experience in the 

 stratum, is, for the temperature 0, 



s - eds/dO. 

 This is the expression for what is known as the surface 

 energy, per unit area of surface, at the temperature 0. 



1 W. Thomson, Proc. Eoy. Soc, Vol. ix, p. 255, 1857-9. 



