  We discuss the effect of the finite size of galaxies on estimating
small-scale relative pairwise peculiar velocity dispersions from the cosmic
virial theorem (CVT). Specifically we evaluate the effect by incorporating the
finite core radius $r_c$ in the two-point correlation function of mass, i.e.
$\xi_\rho(r) \propto (r+r_c)^{-\gamma}$ and the effective gravitational force
softening $r_s$ on small scales. We analytically obtain the lowest-order
correction term for $\gamma <2$ which is in quantitative agreement with the
full numerical evaluation. With a nonzero $r_s$ and/or $r_c$ the cosmic virial
theorem is no longer limited to the case of $\gamma<2$. We present accurate
fitting formulae for the CVT predicted pairwise velocity dispersion for the
case of $\gamma>2$. Compared with the idealistic point-mass approximation
($r_s=r_c=0$), the finite size effect can significantly reduce the small-scale
velocity dispersions of galaxies at scales much larger than $r_s$ and $r_c$.
Even without considering the finite size of galaxies, nonzero values for $r_c$
are generally expected, for instance, for cold dark matter (CDM) models with a
scale-invariant primordial spectrum. For these CDM models, a reasonable force
softening $r_s\le 100 \hikpc$ would have rather tiny effect. We present the CVT
predictions for the small-scale pairwise velocity dispersion in the CDM models
normalized by the COBE observation. The implication of our results for
confrontation of observations of galaxy pair-wise velocity dispersions and
theoretical predictions of the CVT is also discussed.
