On the lack of a simple relation between RE and mu.e for early-type galaxies.

The direct correlation between effective radius R_e_ and corresponding surface brightness μ_e_, found for early-type galaxies by Kormendy and later confirmed by several studies, is re-examined using a homogeneous photometric data base relative to a luminosity-limited sample of 33 E and S0 Virgo cluster galaxies (M_B_<-17.3). Contrary to previous belief - but in line with the existence of a tight fundamental plane for E galaxies and bulges of SOs - we find that R_e_ and μ_e_ are not simply correlated (apart from the six brightest galaxies) objects with the same total luminosity L_T_ is proportional to I_e_R^2^_e_, but possess surface brightness and sizes which spread over wide ranges (δμ_e_~ 2.5 mag, or equivalently δlog R_e_~0.5). We suspect that the correlations between μ_e_ and R_e_ reported in the literature are due to samples consisting mainly of luminous galaxies. Our data also raise some doubt on the shape of the luminosity function of E + S0 galaxies, indicating the presence of a secondary maximum at the bright end.