  On the basis of near-infrared imaging observations, we derived visual
extinction (Av) distribution toward ten Bok globules through measurements of
both the color excess (E_{H-K}) and the stellar density at J, H, and Ks (star
count). Radial column density profiles for each globule were analyzed with the
Bonnor-Ebert sphere model. Using the data of our ten globules and four globules
in the literature, we investigated the stability of globules on the basis of
xi_max, which characterizes the Bonnor-Ebert sphere as well as the stability of
the equilibrium state against the gravitational collapse. We found that more
than half of starless globules are located near the critical state (xi_max =
6.5 +/- 2). Thus, we suggest that a nearly critical Bonnor-Ebert sphere
characterizes the typical density structure of starless globules. Remaining
starless globules show clearly unstable states (xi_max > 10). Since unstable
equilibrium states are not long maintained, we expect that these globules are
on the way to gravitational collapse or that they are stabilized by non-thermal
support. It was also found that all the star-forming globules show unstable
solutions of xi_max >10, which is consistent with the fact that they have
started gravitational collapse. We investigated the evolution of a collapsing
gas sphere whose initial condition is a nearly critical Bonnor-Ebert sphere. We
found that the column density profiles of the collapsing sphere mimic those of
the static Bonnor-Ebert spheres in unstable equilibrium. The collapsing gas
sphere resembles marginally unstable Bonnor-Ebert spheres for a long time. We
found that the frequency distribution of xi_max for the observed starless
globules is consistent with that from model calculations of the collapsing
sphere.
