The direct correlation between effective radius Re and corresponding surface brightness mu-e, found for early-type galaxies by Kormendy (1977) and later confirmed by several studies, is reexamined using a homogeneous photometric data base relative to a luminosity-limited sample of 33 E and SO Virgo cluster galaxies. Contrary to previous belief, but in line with the existence of a tight fundamental plane for E galaxies and bulges of SOs, it is found that Re and mu-e are not simply correlated objects with the same total luminosity L(T) proportional to Ie Re-squared, but possess surface brightness and sizes which spread over wide ranges. It is suspected that the correlations between mu-e and Re reported in the literature are due to samples consisting mainly of luminous galaxies.