Recently, Owen(1993) and Owen and Ledlow (1994) have shown that the dividing line between Fanaroff-Riley class~I and class~II Radio Sources is very sharp when the sources are represented as points in the radio-optical luminosity plane. It is shown that if one accepts the propositions that the sources in the vicinity of this dividing line are characterized by (1) transonic Mach numbers and (2) mildly relativistic velocities (consistent with deceleration of an initially moderately relativistic or ultrarelativistic jet), then the slope of the dividing line is readily obtained using simple physical arguments and established empirical relationships between the X-Ray luminosities, core radii, velocity dispersions and absolute magnitudes of elliptical galaxies. The intercept of the dividing line depends upon parameters which are known perhaps to within factors of order unity and agrees with the data to within an order of magnitude. ROSAT observations of elliptical galaxies will be important in constraining the central pressures and X-Ray core radii of radio ellipticals. Knowledge of these two parameters will assist in a more detailed assessment of the physics which is proposed here as being relevant. High resolution observations of jets within a kpc of the radio core will also be useful for determining the spreading rates of jets in this region.