This paper is concerned with the effects that density fluctuations in different regions of a liquidndash;vapor interface have on the interfacial thermodynamic and structural properties. The total volumeVis divided into a square array of columns whose width is the order of the bulk correlation length. The canonical partition function is written as a sum of constrained partition functions, each describing a system with a given number of particles in each column. Changes in the occupation number of each column (i.e., density fluctuations) are related to changes in position of the local Gibbs dividing surface, and the free energy of such distortions of the Gibbs surface is estimated using macroscopic ideas similar to those used in the capillary wave theory by Buff, Lovett, and Stillinger. Corrections to the interface tension as calculated for a single column with periodic boundary conditions are given. We make a selfhyphen;consistent choice of the column width which yields a scaling law originally porposed by Widom. Fluctuations in position of the local Gibbs surfaces of widely separated columns cause the total interface width to depend on the system size and strength of an external field while the local width in a single column is proportional to the bulk correlation length. These fluctuations also cause the very longhyphen;ranged correlations parallel to the interface predicted by Wertheim. Both the singlet and the pair distributions functions are calculated. An extension of Wertheimrsquo;s analysis is given.
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