Experimental studies of the relative atomic mu --meson capture probabilities in the constituents of chemical compounds are described. Fermi and Teller had predicted that the atomic-capture probability is proportional to the nuclear charge of the atomic species weighted by its atomic concentration. This is sometimes referred to as the Fermi-Teller Z law.'' Previous experiments indicated no clear systematics to this capture process, and there are conflicts between the results of several measurements made with the same or similar compounds. In these experiments the capturing atom was identified by detection of either mesic x rays or decay electrons from mu /sup -/ mesons bound in the mesic K shell in the atomic species, In these experiments oxides and sulfides of some medium- and high-Z elements as well as two metallic solutions were used, and a nuclear capture product (neutron) rather than the decay electrons was detected. Results show that among the substances examIned, namely CuO, Sb/sub 2/O/sub 3, PbO, CuS, Sb/sub 2/S/sub 3/, PbS AgLi, and CuAu, the Z law'' behavior is not indicated either in insulators or in metals, although in all cases there is a preference for capturing in the atom of higher Z. If the atomic-capture probability is …