CONSIDER three co-ordinate systems, S, S′, and S″. Let the velocities of the origins of S′ and S′, as observed in S, be SvS′ and SνS″, respectively, and let the velocity of S″, as observed in S′, be S′vS″. Then the remaining possible velocity observations give S′vS = − SvS′, S″vS = − SvS″, and S″vS′ = − S′vS″. In principle, these six velocities can be measured directly (which is what we mean by the words ‘as observed in’). If we wish to use the Lorentz transformation equations to express relations, valid in one co-ordinate system, in terms of another of these co-ordinate systems, then the appropriate one of the foregoing velocities appears in the transformation equations.