In the three-body theory for period variations in RS CVn systems, the timing residuals are interpreted as light-travel time differences as the eclipsing system moves about the barycenter of the triple. These residuals can require a larger orbit than Kepler's law allows, given the time scale of the period variations. For only two of eight systems investigated, SV Cam and V471 Tau, is the theory plausible in that the inferred barycentric motion of the binary is smaller than the orbit of the third body, and the inferred properties of the third body are both reasonable and consistent with its remaining hidden. The theory is thus not a general theory for period changes. Observational testing of the theory is straightforward and may lead to the detection of "brown dwarfs" associated with eclipsing systems through their kinematic effects.