The Astrometric technique is unique in that it allows us to do a systematic search of each nearby star to determine whether or not it is the primary star of a planetary system. Both positive and negative results may be expressed with a well defined statistical certainty. Perhaps the best known astrometric study is that of Barnard's star by van de Kamp (1963). That “detection” was later discounted by Gatewood and Eichhorn (1973) but neither study attempted to specify what types (in mass and orbital period) of planets do not orbit Barnard's star. In the following pages we will relate the results of an ongoing study of that object, qualifying what types of bodies are unlikely to orbit Barnard's star, and showing what we believe to be the first step by step illustration of the various astrometric motions that must be analyzed in this study.