  To understand physical properties of the interstellar medium (ISM) on various
scales, we investigate it at parsec resolution on the kiloparsec scale. Here,
we report on the sub-kpc scale Gas Density Histogram (GDH) of the Milky Way.
The GDH is a density probability distribution function (PDF) of the gas volume
density. Using this method, we are free from an identification of individual
molecular clouds and their spatial structures. We use survey data of $^{12}$CO
and $^{13}$CO ($J$=1-0) emission in the Galactic plane ($l =
10^{\circ}$-$50^{\circ}$) obtained as a part of the FOREST Unbiased Galactic
plane Imaging survey with the Nobeyama 45m telescope (FUGIN). We make a GDH for
every channel map of $2^{\circ} \times 2^{\circ}$ area, including the blank sky
component, and without setting cloud boundaries. This is a different approach
from previous works for molecular clouds. The GDH fits well to a single or
double log-normal distribution, which we name the low-density log-normal (L-LN)
and high-density log-normal (H-LN) components, respectively. The
multi-log-normal components suggest that the L-LN and H-LN components originate
from two different stages of structure formation in the ISM. Moreover, we find
that both the volume ratios of H-LN components to total ($f_{\mathrm{H}}$) and
the width of the L-LN along the gas density axis ($\sigma_{\rm{L}}$) show
coherent structure in the Galactic-plane longitude-velocity diagram. It is
possible that these GDH parameters are related to strong galactic shocks and
other weak shocks in the Milky Way.
