  Harmonic slicing has in recent years become a standard way of prescribing the
lapse function in numerical simulations of general relativity. However, as was
first noticed by Alcubierre (1997), numerical solutions generated using this
slicing condition can show pathological behaviour. In this paper, analytic and
numerical methods are used to examine harmonic slicings of Kasner and Gowdy
cosmological spacetimes. It is shown that in general the slicings are prevented
from covering the whole of the spacetimes by the appearance of coordinate
singularities. As well as limiting the maximum running times of numerical
simulations, the coordinate singularities can lead to features being produced
in numerically evolved solutions which must be distinguished from genuine
physical effects.
