  We present harmonic decompositions of the velocity fields of 19 galaxies from
THINGS (The \HI Nearby Galaxy Survey) which quantify the magnitude of the
non-circular motions in these galaxies and yield observational estimates of the
elongations of the dark matter halo potentials. Additionally, we present
accurate dynamical center positions for these galaxies. We show that the
positions of the kinematic and photometric centers of the large majority of the
galaxies in our sample are in good agreement. The median absolute amplitude of
the non-circular motions, averaged over our sample, is $6.7 \kms$, with $\sim
90$ percent of the galaxies having median non-circular motions of less than
$\sim 9\kms$. As a fraction of the total rotation velocity this translates into
4.5 percent on average. The mean elongation of the gravitational potential,
after a statistical correction for an unknown viewing angle, is $0.017\pm
0.020$, i.e., consistent with a round potential. Our derived non-circular
motions and elongations are smaller than what is needed to bring Cold Dark
Matter (CDM) simulations in agreement with the observations. In particular, the
amplitudes of the non-circular motions are not high enough to hide the steep
central mass-density profiles predicted by CDM simulations. We show that the
amplitudes of the non-circular motions decrease towards lower luminosities and
later Hubble types.
