  Understanding the quark and gluon substructure of the nucleon has been a
prime goal of both nuclear and particle physics for more than thirty years and
has led to much of the progress in strong interaction physics. Still the flavor
dependence of the nucleon's spin is a significant fundamental question that is
not understood. Experiments measuring the spin content of the nucleon have
reported conflicting results on the amount of nucleon spin carried by strange
quarks. Quasi-elastic neutrino scattering, observed using a novel detection
technique, provides a theoretically clean measure of this quantity.
  The optimum neutrino beam energy needed to measure the strange spin of the
nucleon is 1 GeV. This is also an ideal energy to search for neutrino
oscillations at high $\Delta m^2$ in an astrophysically interesting region.
Models of the r-process in supernovae which include high-mass sterile neutrinos
may explain the abundance of neutron-rich heavy metals in the universe. These
high-mass sterile neutrinos are outside the sensitivity region of any previous
neutrino oscillation experiments.
  The Booster neutrino beamline at Fermilab provides the world's highest
intensity neutrino beam in the 0.5-1.0 GeV energy range, a range ideal for both
of these measurements. A small detector located upstream of the MiniBooNE
detector, 100 m from the recently commissioned Booster neutrino source, could
definitively measure the strange quark contribution to the nucleon spin. This
detector, in conjunction with the MiniBooNE detector, could also investigate
$\nu_{\mu}$ disappearance in a currently unexplored, cosmologically interesting
region.
