  The correlation between the Mg absorption index and the velocity dispersion
(sigma) of local elliptical galaxies is very tight. Because the Mg absorption
depends on both metallicity and age of the underlying stellar population the
observed Mg-sigma relation constrains the possible variation in metallicity and
age for a given velocity dispersion. For a time interval with no change in
metallicity any variation of the Mg index is caused only by the aging of the
stars.
  We have measured the Mg absorption and velocity dispersion of ellipticals in
three clusters at a redshift of z=0.37 and established their Mg-sigma relation.
For any given sigma, the measured Mg absorption is weaker than the mean value
for local ellipticals. Since the evolution of bright cluster ellipticals
between z=0.4 and today is most probably only `passive' this reduction in Mg
can be attributed solely to the younger age of the stellar population. The
small weakening of the Mg absorption of the distant galaxies compared to the
local values implies that most of the stars in cluster ellipticals must have
formed at high redshifts (z_f > 2...4).
  The Mg-sigma test is a very robust method to investigate the evolution of
elliptical galaxies and has several advantages over traditional methods using
luminosities. A remaining problem is the aperture correction necessary to
calibrate observations of galaxies at different distances. Here, we show that
our general conclusions about the epoch of formation still hold when aperture
corrections are calculated assuming a dependence of the radial gradient of
sigma on the galaxy's effective radius rather than assuming no dependence as
was done in all previous studies.
