  At which height will a prominence inclined to be unstable, or where is the
most probable critical height for the prominence destabilization? This question
is statistically studied based on 362 solar limb prominences well-recognized by
SLIPCAT from 2007 April to the end of 2009. We found that there are about 71%
disrupted prominences (DPs), among which about 42% of them did not erupt
successfully and about 89% of them experienced a sudden destabilization (SD)
process. After a comprehensive analysis of the DPs, the following findings are
discovered. (1) Most DPs become unstable at the height of 0.06 -- 0.14
R$_\odot$ from the solar surface, and there are two most probable critical
heights, at which a prominence is much likely to get unstable; the primary one
is 0.13 R$_\odot$ and the secondary one is 0.19 R$_\odot$. (2) There exists
upper limit for the erupting velocity of eruptive prominences (EPs), which
decreases following a power law with increasing height and mass; the kinetic
energy of EPs accordingly has an upper limit too, which decreases as critical
height increases. (3) Stable prominences (SPs) are generally longer and heavier
than DPs, and not higher than 0.4 R$_\odot$. (4) About 62% of EPs were
associated with CMEs; but there is no difference in apparent properties between
EPs associated with and without CMEs.
