Theoretical s-process calculations are presented. Isotopic abundances are summed, so that atomic number Z becomes the independent variable. This form of representation of the calculations has distinct advantages in the interpretation of stellar data, since one generally does not have isotopic information. Predictions based on single neutron exposures as well as exponential exposure distributions are compared with the high-quality observations of Tech for zeta Cap and a few other stars. Tech's data provide a remarkably good fit of theory and observations. For the exposures of relevance to the barium stars, dysprosium and, indeed, heavier lanthanides are expected to be comparable in abundance to samarium and gadolinium. A very low Ce/Ba ratio (< or approx. =10/sup -1/) is not expected if Ba and Sr have comparable abundances. It is concluded that the observations are not yet of high enough quality to allow one to discriminate among several possible exposure models, but that the prospect for doing so with improved observations is good.