Transition Layer of a Liquid on its Surface Tension. 883 



k 

 attraction between two molecules is given by . . The ex- 

 pression therefore becomes equal to zero when the density 

 of the substance becomes infinitely small. This holds whether 

 the above expression for the molecular attraction is exactly 

 true or not. Thus suppose that the molecular attraction is 



given by the expression -r. The expression — then becomes 

 -^3, and thus as before becomes equal to zero when the 



density of the substance becomes infinitely small. But the 

 molecular attraction which gives rise to surface-tension must 

 decrease at a much greater rate with the distance of sepa- 

 ration of the molecules than follows from the foregoing- 

 expression *, and ~fe must therefore be equal to zero when 



the density of the substance is infinitely small. On applying 

 the equation under consideration to matter of infinitely small 

 density we obtain C = 0, and thus 



•876x6X 2 = Umi/y/ 3 (14) 



U denotes the energy expended in overcoming the mole- 

 cular attraction on separating the molecules of a gram of 

 substance an infinite distance from one another, and if u 

 denotes the sum of the internal energies of the molecules, 

 the internal heat of evaporation L is given by 



L=Ui— U 2 + wi— u 2 , 



where the suffix 1 refers to the liquid and 2 to the saturated 

 vapour. Let us assume that the internal energy of a molecule 

 is independent of the vicinity of other molecules, in which 

 case i^ — m 2 = 0. If the density of the saturated vapour is 

 small in comparison with that of the liquid, as is the case 

 at low temperatures, U 2 = and consequently Ui = L. 

 Thus, on the above assumption, the values of A 2 can be 

 calculated for low temperatures of the liquid. This has been 

 carried out for four liquids, the results being contained in the 

 table given, which also contains the values of X x obtained by 

 Ramsay & Shields f . The values of L were taken from a 

 paper by Mills {. The values of \ 2 are greater than those 

 of \ 1? as was indicated at the beginning of the paper. The 

 difference (X 3 — \i) is the external work done in the for- 

 mation of the transition layer. It will be seen that it is 



* Phil. Mag. Jan. 1911, pp. 89-90. 



t Phil. Trans, of the Roy. Soc, A, vol. clxxxiv. p. 647 (1898). 



X Journ. of Phys. Ohem. vol. viii. p. 405 (1904\ 



