Function lnf(θ) given by Eq. (11) against the colatitude θ, calculated for η = 0.2 and 0.8, with both functions Υ(θ) given in Eq. (5), differential-rotation parameters α = − 0.5, 0.0, and 0.5, and for powers k = 0.5, 2.0 and 6.0. Blocks (a) and (b) are for Υ(θ) = cos^kθ. Blocks (c) and (d) are for Υ(θ) = sin^kθ. Colours indicate the power k and they are the same for all blocks. The line-styles identify the values of α and they are the same for α′ = − α/ (1 + α) where α are the same as in (a) and (b).