  Though one dimensional self-gravitating $N$-body systems have been studied
for three decade, the nature of relaxation was still unclear. There were
inconsistent results about relaxation time; some initial state relaxed in the
time scale $T\sim N\,t_c$, but another state did not relax even after $T\sim
N^2\,t_c$, where $t_c$ is the crossing time. The water-bag distribution was
believed not to relax after $T\sim N^2\,t_c$. In our previous paper, however,
we found there are two different relaxation times in the water-bag
distribution;in the faster relaxation ( microscopic relaxation ) the
equipartition of energy distribution is attains but the macroscopic
distribution turns into the isothermal distribution in the later relaxation
(macroscopic relaxation). In this paper, we investigated the properties of the
two relaxation. We found that the microscopic relaxation time is $T\sim
N\,t_c$, and the macroscopic relaxation time is proportional to $N\,t_c$, thus
the water-bag does relax. We can see the inconsistency about the relaxation
times is resolved as that we see the two different aspect of relaxations.
Further, the physical mechanisms of the relaxations are presented.
