We use absolute trigonometric parallaxes from the Hipparcos Catalogue
to determine individual distances to members of the Hyades cluster, fr
om which the 3-dimensional structure of the cluster can be derived. In
ertially-referenced proper motions are used to rediscuss distance dete
rminations based on convergent-point analyses. A combination of parall
axes and proper motions from Hipparcos, and radial velocities from gro
und-based observations, are used to determine the position and velocit
y components of candidate members with respect to the cluster centre,
providing new information on cluster membership: 13 new candidate memb
ers within 20 pc of the cluster centre have been identified. Farther f
rom the cluster centre there is a gradual merging between certain clus
ter members and field stars, both spatially and kinematically. Within
the cluster, the kinematical structure is fully consistent with parall
el space motion of the component stars with an internal velocity dispe
rsion of about 0.3 km s(-1). The spatial structure and mass segregatio
n are consistent with N-body simulation results, without the need to i
nvoke expansion, contraction, rotation, or other significant perturbat
ions of the cluster. The quality of the individual distance determinat
ions permits the cluster zero-age main sequence to be accurately model
led. The helium abundance for the cluster is determined to be Y = 0.26
+/- 0.02 which, combined with isochrone modelling including convectiv
e overshooting, yields a cluster age of 625 +/- 50 Myr. The distance t
o the observed centre of mass (a concept meaningful only in the restri
cted context of the cluster members contained in the Hipparcos Catalog
ue) is 46.34 +/- 0.27 pc, corresponding to a distance modulus m - M =
3.33 +/- 0.01 mag for the objects within 10 pc of the cluster centre (
roughly corresponding to the tidal radius). This distance modulus is c
lose to, but significantly better determined than, that derived from r
ecent high-precision radial velocity studies, somewhat larger than tha
t indicated by recent ground-based trigonometric parallax determinatio
ns, and smaller than those found from recent studies of the cluster co
nvergent point. These discrepancies are investigated and explained.