Average radial, azimuthal, and vertical velocity (⟨ V_R ⟩, ⟨ V_φ ⟩ , and ⟨ V_Z ⟩) as a function of the [Fe/H] ratio. The [Mg/Fe] bins are colour-coded, and the average values of each one are written in the legend. The thin and thick discs are represented by open squares (□) and filled circles (•), respectively. The error bars correspond to the standard errors on the mean velocity for each bin. The derived thin- and thick-disc gradients are shown as full and dashed lines, respectively.