﻿150 



Mr. J. Rice on the Form of a 



Plateau, in which a drop of oil is suspended in a mixture of 

 water and alcohol having the same density as the oil. If it 

 happens that the evaporation of the alcohol from the surface 

 of the mixture produces a density-gradient in the latter, then 

 the drop of oil flattens into an oval form. 



It is assumed that the density of the surrounding liquid 

 varies continuously with the depth. 



The figure represents a vertical section of the drop (which 

 is of course a surface of revolution) through its highest 

 point. The axes are in the first instance tangent and normal 

 to the section at this point. 



Let a represent the constant density of material of the 

 drop, and p the variable density of the surrounding liquid. 



Then 



p = Pif(y) 



where pi is the liquid-density at the level of 0, and/Q/) is 

 a function of y which approaches the value unity as y 

 approaches zero. 



Let R be the radius of curvature at P, and R t that at 0. 



One easily obtains as the condition of equilibrium 



where T represents surface-tension. If we assume this to be 

 uniform, it is easily shown that the places of maximum 

 surface-curvature lie in the level at which the densities of 

 the drop and the surrounding liquid are equal. 



