  (shortened) From a kinematically unbiased subsample of the Hipparcos
catalogue we have redetermined as a function of colour the kinematics of
main-sequence stars. The stars' mean heliocentric velocity nicely follows the
asymmetric drift relation, except for stars blueward of B-V=0.1. Extrapolating
to zero dispersion yields for the velocity of the Sun w.r.t. the LSR in km/s:
U_0=10.00+/-0.36 (radially inwards), V_0=5.23+/-0.62 (in direction of galactic
rotation), and W_0=7.17+/-0.38 (vertically upwards). A plot of velocity
dispersion vs. colour beautifully shows Parenago's discontinuity: the
dispersion is constant for B-V>0.62 and decreases towards bluer colour.
  We determine the velocity-dispersion tensor sigma^2_ij as function of B-V.
The mixed moments involving vertical motion are zero within the errors, while
sigma^2_xy is non-zero at about (10km/s)^2 independent of colour. The resulting
vertex deviations are about 20 deg for early-type stars and 10+/-4 deg for
old-disc stars. The persistence of the vertex deviation to late-type stars
implies that the Galactic potential is significantly non-axisymmetric at the
solar radius. If spiral arms are responsible for this, they cannot be tightly
wound. Except for stars bluer than B-V=0.1 the ratios of the principal velocity
dispersions are 2.2 : 1.4 :1, while the absolute values increase with colour
from sigma_1=20km/s at B-V=0.2 to sigma_1=38km/s at Parenago's discontinuity
and beyond. These ratios imply significant heating of the disc by spiral
structure and that R_0/R_d=3 to 3.5, where R_d is the scale length of the disc.
