  Because present Monte Carol algorithms for lattice QCD may become trapped in
a given topological charge sector when one approaches the continuum limit, it
is important to understand the effect of calculating at fixed topology. In this
work, we show that although the restriction to a fixed topological sector
becomes irrelevant in the infinite volume limit, it gives rise to
characteristic finite size effects due to contributions from all
$\theta$-vacua. We calculate these effects and show how to extract physical
results from numerical data obtained at fixed topology.
