  We present the first detailed study of the behaviour of the stellar proper
motion across the entire Galactic Anti-centre area visible in the Sloan Digital
Sky Survey data. We use recalibrated SDSS astrometry in combination with
positions from {\it Gaia} DR1 to provide tangential motion measurements with a
systematic uncertainty $<$5 kms$^{-1}$ for the Main Sequence stars at the
distance of the Monoceros Ring. We demonstrate that Monoceros members rotate
around the Galaxy with azimuthal speeds of ~230 kms$^{-1}$, only slightly lower
than that of the Sun. Additionally, both vertical and azimuthal components of
their motion are shown to vary considerably but gradually as a function of
Galactic longitude and latitude. The stellar over-density in the Anti-centre
region can be split into two components, the narrow, stream-like ACS and the
smooth Ring. According to our analysis, these two structures show very similar
but clearly distinct kinematic trends, which can be summarised as follows: the
amplitude of the velocity variation in $v_{\phi}$ and $v_z$ in the ACS is
higher compared to the Ring, whose velocity gradients appear to be flatter.
Currently, no model available can explain the entirety of the data in this area
of the sky. However, the new accurate kinematic map introduced here should
provide strong constraints on the genesis of the Monoceros Ring and the
associated sub-structure.
