  A coordinate system is constructed for a general accelerating observer in 1+1
dimensions, and is used to determine the particle density of the massless Dirac
vacuum for that observer. Equations are obtained for the spatial distribution
and frequency distribution of massless fermions seen by this observer, in terms
of the rapidity function of the observer's worldline. Examples that are
considered include the uniformly accelerating observer as a limiting case, but
do not always involve particle horizons. Only the low frequency limit depends
on the possible presence of particle horizons. The rest of the spectrum is
`almost thermal' whenever the observer's acceleration is `almost uniform'.
