  We present a study of the molecular gas of seven early-type galaxies with
high angular resolution data obtained as part of the mm-Wave Interferometric
Survey of Dark Object Masses (WISDOM) project with the Atacama Large
Millimeter/submillimeter Array. Using a fixed spatial scale approach, we study
the mass surface density ($\Sigma$) and velocity dispersion ($\sigma$) of the
molecular gas on spatial scales ranging from $60$ to $120$pc. Given the spatial
resolution of our data ($20$ - $70$pc), we characterise these properties across
many thousands of individual sight lines ($\approx50,000$ at our highest
physical resolution). The molecular gas along these sight lines has a large
range ($\approx2$dex) of mass surface densities and velocity dispersions
$\approx40\%$ higher than those of star-forming spiral galaxies. It has virial
parameters $\alpha_\mathrm{vir}$ that depend weakly on the physical scale
observed, likely due to beam smearing of the bulk galactic rotation, and is
generally super-virial. Comparing the internal turbulent pressure
($P_\mathrm{turb}$) to the pressure required for dynamic equilibrium
($P_\mathrm{DE}$), the ratio $P_\mathrm{turb}$/$P_\mathrm{DE}$ is significantly
less than unity in all galaxies, indicating that the gas is not in dynamic
equilibrium and is strongly compressed, in apparent contradiction to the virial
parameters. This may be due to our neglect of shear and tidal forces, and/or
the combination of three-dimensional and vertical diagnostics. Both
$\alpha_\mathrm{vir}$ and $P_\mathrm{turb}$ anti-correlate with the global
star-formation rate of our galaxies. We therefore conclude that the molecular
gas in early-type galaxies is likely unbound, and that large-scale dynamics
likely plays a critical role in its regulation. This contrasts to the giant
molecular clouds in the discs of late-type galaxies, that are much closer to
dynamical equilibrium.
