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LII. On the Theory of Surface Forces.— III. Effect of Slight 

 Contaminations. By Lord Rayleigh, Sec.R.S* 



OBSERVATION" t having suggested that the lowering 

 of surface-tension of water due to a film of oil falls off 

 more rapidly when the film is attenuated than the thickness of 

 the film itself can he supposed to do, I was led to examine the 

 question theoretically; and the result shows that, according to 

 the principles of Young and Laplace, the lowering of tension 

 due to a very thin film should be in proportion, not to the 

 thickness, but to the square of the thickness of the film. In 

 the calculations which follow the fluids are supposed to be 

 incompressible, a layer of density p and thickness a being 

 interposed between fluids of densities p 2 and p x (fig. 1). The 



thickness a, as well as the range of the forces, is supposed to 

 be negligible in comparison with the radius of curvature R 

 of the surfaces of separation. 



By II. (16)t we have for the difference of pressures in the 

 inner and outer liquids, 



p,- Pl =2K(pi'-p^-r ) Ydp 

 Jm 



=2K( P ^-p^-(p- Pl ) . Y(p, Pl )-( P2 -p) . V( P2 , P ), (1) 



where Y(p, p x ) , V(ps> p) denote the potentials at the surfaces 

 of separation. 



* Communicated by the Author. 



f See, for example, Miss Pockels on Surface Tension, ' Nature,' vol. xliii. 

 p. 437 (1891). 



t Phil. Mag. Feb. 1892. 



