Differences in proper motion between the primary (TGAS) solution and the Tycho-2 catalogue for 1 997 003 sources: a) differences in μ_{α ∗}; b) differences in μ_δ; and c) total differences . Differences are taken in the sense TGAS minus Tycho-2, after rotation of the latter to the Gaia DR1 reference frame. Median differences are shown in cells of about 0.84 deg². Some empty cells are shown in white. The maps use an Aitoff projection in equatorial (ICRS) coordinates, with origin α = δ = 0 at the centre and α increasing from right to left.