text: In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface:
  where:
  :  = vapor pressure at a curved interface of radius 
  :  = vapor pressure at flat interface () = 
  :  = surface tension
  :  = density of vapor
  :  = density of liquid
  : ,  = radii of curvature along the principal sections of the curved interface.
  In his dissertation of 1885, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) derived the Ostwald–Freundlich equation and showed that Kelvin's equation could be transformed into the Ostwald–Freundlich equation.  The German physical chemist Wilhelm Ostwald derived the equation apparently independently in 1900; however, his derivation contained a minor error which the German chemist Herbert Freundlich corrected in 1909.