  We present peculiar velocities for 84 clusters of galaxies in two large
volumes at distances between 6000 and 15000 km/s in the directions of
Hercules-Corona Borealis and Perseus-Pisces-Cetus. These velocities are based
on Fundamental Plane (FP) distance estimates for early-type galaxies in each
cluster. We fit the FP using a maximum likelihood algorithm which accounts for
both selection effects and measurement errors, and yields FP parameters with
smaller bias and variance than other fitting procedures. We find a best-fit FP
with coefficients consistent with the best existing determinations. We measure
the bulk motions of the sample volumes using the 50 clusters with the
best-determined peculiar velocities. We find the bulk motions in both regions
are small, and consistent with zero at about the 5% level. The EFAR results are
in agreement with the small bulk motions found by Dale et al. (1999) on similar
scales, but are inconsistent with pure dipole motions having the large
amplitudes found by Lauer & Postman (1994) and Hudson et al. (1999). The
alignment of the EFAR sample with the Lauer & Postman dipole produces a strong
rejection of a large-amplitude bulk motion in that direction, but the rejection
of the Hudson et al. result is less certain because their dipole lies at a
large angle to the main axis of the EFAR sample. We find the bulk motion of our
sample is consistent with most cosmological models that approximately reproduce
the shape and normalisation of the observed galaxy power spectrum. We conclude
that existing measurements of large-scale bulk motions provide no significant
evidence against standard models for the formation of structure.
