AbstractThe variation in film thicknesshwith timetfor the approach of an infinite sphere to a plane horizontal surface (β = 1) or of two infinite spheres (β = 2) is given by:\documentclass[article]\pagestyle[empty]\begin[document]$$ t = (3\pi n^2 \mu a^2 /2\beta ^2 f)\ln (h_o /h)...............................(a) $$\end[document]For finite spherical caps with edge radiusrfthe variation is much more complicated and also involves the parameter S = βr2f/2aho. Fortunately, the gradient\documentclass[article]\pagestyle[empty]\begin[document]$$ - d(\ln h(/dt = (3\pi n^2 \mu a^2 /2\beta ^2 f)..........................(b) $$\end[document]is the same in both cases, providingtis large enough (the critical value oftincreases with decreasingS). A similar result is obtained if the spherical cap is approximated by a parabolic cap with apex curvature 1/aequal to that of the sphere. In both cases the variation in dynamic pressure close to the centre of the draining film is identical and independent of the radial position where the dynamic pressure falls to zero when the film thickness is small.MacKay and Mason (1961) measured the film thickness beneath a sphere of finite size approaching a horizontal plane and experimentally verified Equation (b). This does not however, as they assumed, prove the correctness of Equation (a), which only applies to infinite spheres. The more complicated equations describing the approach of finite spheres and parabolic caps are presented in this pap