  In this paper finite bcc lattices are defined by a triple of vectors in two
different ways - upper triangular lattice form and compact form. In Appendix A
are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The
energy and magnetization of the S = 1/2 XY ferromagnet have been computed on
these bcc lattices in the lowest states for $S_z$ = 0, 1/2, 1 and 3/2. These
data are studied statistically to fit the first three terms of the appropriate
finite lattice scaling equations. Our estimates of the T = 0 energy and
magnetization agree very well with spin wave and series expansion estimates.
