Once the global parameters of galaxies (such as the total luminosity and
the half-luminosity radius) have been determined, it is interesting to look
for possible correlations between them. It is plausible to expect that
luminous galaxies will be also large; a little bit less obvious
is to find out that large galaxies have fainter average surface
brightness. These correlations, or scaling laws, have a twofold
importance. On the one side, they teach us something about the galaxy formation
history. On the other side, they allow us to estimate distance ratios
between clusters. For example, we can write the correlation between 
(in arcsec) and 
(or 
) of the ellipticals in a cluster of known
distance D as:
where a and b (and c and d)
are parameters to be determined from the data
(see point 7 of Sect. 3). If we consider now a second cluster
of galaxies at a distance 
, we may expect its ellipticals to obey a
similar relation as Eq. 22, and derive a coefficient 
. However, surface brightnesses are distance-indipendent
quantities, while half-luminosity radii scale linearly with distance (see
Eq. 25). Therefore, the derived 
coefficient will be
related to b as:
and the distance ratio of the two clusters can be determined. A similar procedure allows one to estimate distance ratios from Eq. 23.
