  First, we have ensured that spherical nonrotating collisionless systems
collapse with almost retaining spherical configurations during initial
contraction phases even if they are allowed to collapse three-dimensionally.
Next, on the assumption of spherical symmetry, we examine the evolution of
velocity dispersions with collapse for the systems which have uniform or
power-law density profiles with Maxwellian velocity distributions by
integrating the collisionless Boltzmann equation directly. The results show
that as far as the initial contraction phases are concerned, the radial
velocity dispersion never grows faster than the tangential velocity dispersion
except at small radii where the nearly isothermal nature remains, irrespective
of the density profiles and virial ratios. This implies that velocity
anisotropy as an initial condition should be a poor indicator for the radial
orbit instability. The growing behavior of the velocity dispersions is briefly
discussed from the viewpoint that phase space density is conserved in
collisionless systems.
