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Philleo extended the approach of Powers by attempting to quantify the volume fraction of paste within some distance of an air void system (paste-void proximity). Philleo started with an idealized air void system composed of randomly distributed points, the statistics of which are known. Using the Hertz  distribution for the paste-void proximity distribution for zero-radius points, Philleo then modified this distribution to account for finite sized spheres by renormalizing the cumulative distribution to account for the air content. The result, although still only an approximation, characterizes the paste-void spacings for finite-sized air voids. For an air-paste system, the Philleo spacing factor for the volume fraction of paste within a distance s of an air void surface is
where the substitution x=s n1/3 has been made.