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An upper limit on the Casimir force is found using the dielectric functionsof perfect crystalline materials which depend only on well defined materialconstants. The force measured with the atomic force microscope is larger thanthis limit at small separations between bodies and the discrepancy issignificant. The simplest modification of the experiment is proposed allowingto make its results more reliable and answer the question if the discrepancyhas any relation with the existence of a new force.Comment: 9 pages, LaTeX, 2 Postscript figure

DO THE PRECISE MEASUREMENTS OF THE CASIMIR FORCE AGREE WITH THE EXPECTATIONS?