  We measure the gas disc thicknesses of the edge-on galaxy NGC 4013 and the
less edge-on galaxies (NGC 4157 and 5907) using CO (CARMA/OVRO) and/or HI
(EVLA) observations. We also estimate the scale heights of stars and/or the
star formation rate (SFR) for our sample of five galaxies using Spitzer IR data
(3.6 $\mu$m and 24 $\mu$m). We derive the average volume densities of the gas
and the SFR using the measured scale heights along with radial surface density
profiles. Using the volume density that is more physically relevant to the SFR
than the surface density, we investigate the existence of a volumetric star
formation law (SFL), how the volumetric SFL is different from the
surface-density SFL, and how the gas pressure regulates the SFR based on our
galaxy sample. We find that the volumetric and surface SFLs in terms of the
total gas have significantly different slopes, while the volumetric and surface
SFLs in terms of the molecular gas do not show any noticeable difference. The
volumetric SFL for the total gas has a flatter power-law slope of 1.26 with a
smaller scatter of 0.19 dex compared to the slope (2.05) and the scatter (0.25
dex) of the surface SFL. The molecular gas SFLs have similar slopes of 0.78
(volume density) and 0.77 (surface density) with the same rms scatter. We show
that the interstellar gas pressure is strongly correlated with the SFR but find
no significant difference between the correlations based on the volume and
surface densities.
