  In this paper we study the full sample of known Spitzer [$3.6~\mu$m] and
$J$-band variable brown dwarfs. We calculate the rotational velocities, $v\sin
i$, of 16 variable brown dwarfs using archival Keck NIRSPEC data and compute
the inclination angles of 19 variable brown dwarfs.
  The results obtained show that all objects in the sample with mid-IR
variability detections are inclined at an angle $>20^{\circ}$, while all
objects in the sample displaying $J$-band variability have an inclination angle
$>35^{\circ}$. $J$-band variability appears to be more affected by inclination
than \textit{Spitzer} [$3.6~\mu$m] variability, and is strongly attenuated at
lower inclinations. Since $J$-band observations probe deeper into the
atmosphere than mid-IR observations, this effect may be due to the increased
atmospheric path length of $J$-band flux at lower inclinations.
  We find a statistically significant correlation between the colour anomaly
and inclination of our sample, where field objects viewed equator-on appear
redder than objects viewed at lower inclinations. Considering the full sample
of known variable L, T and Y spectral type objects in the literature, we find
that the variability properties of the two bands display notably different
trends, due to both intrinsic differences between bands and the sensitivity of
ground-based versus space-based searches. However, in both bands we find that
variability amplitude may reach a maximum at $\sim7-9~$hr periods. Finally, we
find a strong correlation between colour anomaly and variability amplitude for
both the $J$-band and mid-IR variability detections, where redder objects
display higher variability amplitudes.
