  Spin vectors of 60 galaxies in the ``Ursa Major Filament'' are obtained from
CCD images and spectroscopic determinations of the directions of rotation.
These data are used to remove the four-fold degeneracy introduced by the
project ed images of galaxies, making possible the complete reconstruction of
the galaxy spin vectors. Several possible organizations of spin vectors are
investigated by means of statistical analyses of the three-dimensional spin
vector maps. The results indicate that there exists no significant alignment of
galaxy spin vectors with respect to the supergalactic plane, the supergalactic
axis, or the cylindrical axis of the filament itself. No tendency for linear
alignment of spin vectors towards any specific direction was detected. We also
obtain a statistically negative result for azimuthal, radial, and circul
ar-helical orientation of spin vectors.
