  In order to test the basic equations believed to dictate the dynamics of disk
galaxies, we present and analyze deep two-dimensional spectral data obtained
using the PPAK integral field unit for the early-type spiral systems NGC 2273,
NGC 2985, NGC 3898 and NGC 5533. We describe the care needed to obtain and
process such data to a point where reliable kinematic measurements can be
obtained from these observations, and a new more optimal method for deriving
the rotational motion and velocity dispersions in such disk systems. The data
from NGC 2273 and NGC 2985 show systematic variations in velocity dispersion
with azimuth, as one would expect if the shapes of their velocity ellipsoids
are significantly anisotropic, while the hotter disks in NGC 3898 and NGC 5533
appear to have fairly isotropic velocity dispersions. Correcting the rotational
motion for asymmetric drift using the derived velocity dispersions reproduces
the rotation curves inferred from emission lines reasonably well, implying that
this correction is quite robust, and that the use of the asymmetric drift
equation is valid. NGC 2985 is sufficiently close to face on for the data,
combined with the asymmetric drift equation, to determine all three components
of the velocity ellipsoid. The principal axes of this velocity ellipsoid are
found to be in the ratio sigma_z:sigma_phi:sigma_R ~ 0.7:0.7:1, which shows
unequivocally that this disk distribution function respects a third integral of
motion. The ratio is also consistent with the predictions of epicyclic theory,
giving some confidence in the application of this approximation to even fairly
early-type disk galaxies.
