  Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical
potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon
screening mass decreases linearly as $\mu$ increases predicting a critical
chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation.
The meson spectrum does not change as $\mu$ increases over the same range, from
zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that
there is phase transition at $\mu = m_\pi/2$. We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to
$m_N/3$. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.
