  Paying attention to the difference of density of states, \Delta ln g(E) = ln
g(E+\Delta E) - ln g(E), we study the convergence of the Wang-Landau method. We
show that this quantity is a good estimator to discuss the errors of
convergence, and refer to the $1/t$ algorithm. We also examine the behavior of
the 1st-order transition with this difference of density of states in
connection with Maxwell's equal area rule. A general procedure to judge the
order of transition is given.
