  By systematically applying ten inequivalent two-part relations between
hypergeometric sums 3F2(1) to the published database of all such sums, 66 new
sums are obtained. Many results extracted from the literature are shown to be
special cases of these new sums. In particular, the general problem of finding
elements contiguous to Watson's, Dixon's and Whipple's theorem is reduced to a
simple algorithm suitable for machine computation. Several errors in the
literature are corrected or noted.
