The cases of rotations then boosts are similar (no diagrams are shown). Matching up the rotations followed by boosts, in the original setup, an observer in Σ notices Σ′′ to rotate clockwise then move with velocity v ⊕ u, and because of the rotation an observer in Σ′′ notices Σ to rotate anticlockwise then move with velocity − u ⊕ v. If the velocities are exchanged an observer in Σ notices Σ′′ to rotate anticlockwise then move with velocity u ⊕ v, and because of the rotation an observer in Σ′′ notices Σ to rotate clockwise then move with velocity − u ⊕ v.