In a previous paper [J. Colloid Interface Sci. 150, 243 (1992)], one of the authors (D.M.) has shown how, for the contact of elastic spheres, fracture mechanics with a Dugdale model of adhesion forces can lead to a general theory with the Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) theories as limiting cases. The main equations are briefly recalled and the theory is applied to the case of a liquid meniscus around the contact. It is shown that the results are similar to those of Fogden and White [J. Colloid Interface Sci. 138, 414 (1990)]. Experiments with a surface force apparatus are described showing this transition in the presence of a liquid meniscus. The measured profiles are in good agreement with the theory.