The Astrometric technique is unique in that it allows us to do a syste
matic search of each nearby star to determine whether or not it is the
primary star of a planetary system. Both positive and negative result
s may be expressed with a well defined statistical certainty. Perhaps
the best known astrometric study is that of Barnard's star by van de K
amp (1963). That ''detection'' was later discounted by Gatewood and Ei
chhorn (1973) but neither study attempted to specify what types (in ma
ss 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 illu
stration of the various astrometric motions that must be analyzed in t
his study.