Sometimes a theory is interpreted realistically--i.e., as literally true--whereas sometimes a theory is interpreted instrumentalistically--i.e., as merely a convenient device for summarizing, systematizing, deducing, etc., a given body of observable facts. This paper is part of a program aimed at determining the basis on which scientists decide on which of these interpretations to accept a theory. I proceed by examining one case: the nineteenth-century debates about the existence of atoms. I argue that there was a gradual transition from an instrumentalist (...) to a realistic acceptance of the atomic theory, because of gradual increases in its predictive power, the "testedness" of its hypotheses, the "determinateness" of its quantities, and because of resolutions of doubts about the acceptability of its basic explanatory concepts. (shrink)