The various kinematic effects of special relativity are here treated by considering iterations of the infinitesimal Lorentz transformation. There is only one relativistic effect that appears as a difference between an infinitesimal Lorentz transformation and the corresponding infinitesimal Galilei transformation; this effect is the relative character of simultaneity. When this has been introduced by a physical argument (following Einstein), finite transformations and the other effects are obtained by iteration. Special attention is given to an iteration procedure that reveals the existence of the Thomas precession.