  An upper limit on the Casimir force is found using the dielectric functions
of perfect crystalline materials which depend only on well defined material
constants. The force measured with the atomic force microscope is larger than
this limit at small separations between bodies and the discrepancy is
significant. The simplest modification of the experiment is proposed allowing
to make its results more reliable and answer the question if the discrepancy
has any relation with the existence of a new force.
