  The extensive CCD photometry by Postman & Lauer (1995, ApJ, 440, 28) in the
Cape/Cousins R photometric band for first ranked cluster elliptical and S0
galaxies in 118 low redshift clusters is analyzed for the correlations between
average surface brightness, linear radius, and absolute magnitude. The purpose
is to calibrate the correlations between these three parameters in the limit of
zero redshift. These local correlations provide the comparisons to be made in
Paper IV with the sample of early-type galaxies at high redshift in search of
the Tolman surface brightness signal of (1 + z)^4 if the expansion is real.
Surface brightness averages are calculated at various metric radii in each
galaxy in the sample. The definition of such radii by Petrosian (1976, ApJ,
209, L1) uses ratios of observed surface photometric data. The observed surface
brightnesses are listed for 118 first ranked cluster galaxies at Petrosian eta
radii of 1.0, 1.3, 1.5, 1.7, 2.0, and 2.5 mag. The three local diagnostic
correlation diagrams are defined and discussed. We review the Tolman test and
show that, although recipes from the standard cosmological model that already
have the Tolman signal incorporated are required to calculate linear radii and
absolute magnitudes from the observed data, the test is nevertheless free from
the hermeneutical circularity dilemma occasionally claimed in the literature.
The reasons are the observed mean surface brightness (1) is independent of any
assumptions of cosmological model, (2) does not depend on the existence of a
Tolman signal because it is calculated directly from the data using only
angular radii and apparent magnitudes, and (3) can be used to search for the
Tolman signal because it carries the bulk of that signal.
