  We consider the effects of large structures in the Universe on the Hubble
diagram. This problem is treated non-linearly by considering a Swiss Cheese
model of the Universe in which under-dense voids are represented as negatively
curved regions of space-time. Exact expressions for luminosity distances and
redshifts are used to investigate the non-linear effects of structure on the
magnitudes of astrophysical sources. It is found that the intervening voids we
consider, between the observer and source, produce changes in apparent
magnitude of less than 0.012. Sources inside voids, however, can be affected
considerably at redshifts below z~0.5. By averaging observable quantities over
many randomly generated distributions of voids we find that the presence of
these structures has the effect of introducing a dispersion around the mean,
which itself can be displaced the background value. Observers in an
inhomogeneous universe, who take averages of observables along many different
lines of sight, may then introduce systematic biases, and under-estimate
errors, if these effects are not taken into account. Estimates of the potential
size of these effects are made using data from simulated large-scale structure.
