ON the basis of rather less restrictive postulates concerning the behaviour of light than are customary in special relativity theory, Capildeo has recently1 given the transformation equations connecting two frames of reference S and S′ (with suitably oriented axes) in uniform relative motion, where, it is suggested, the value of α cannot be uniquely determined without additional evidence. If, however, we consider three frames of reference S, S1, S2, where the velocities of S1, S2 relative to S are V1, V2 along Ox, Oy, respectively, then, with the obvious notation, and and it will be found after rotating the x-axes of S1 and S2 into the direction of their mutual relative velocity that the new co-ordinates in S1 and S2 are connected by equations of the form (1) for all V1 and V2 if, and only if, It thus appears that the Lorentz transformation is the only one consistent with Capildeo's assumptions.