  We review a sample of the early literature in which the reality of the
expansion is discussed, explain Hubble's reticence to accept the expansion as
real, and contrast the Tolman surface brightness test with three other modern
tests. We search for the Tolman surface brightness depression with redshift
using the Hubble Space Telescope (HST) data from Paper III for 34 early-type
galaxies from the three clusters Cl 1324+3011 (z=0.76), Cl 1604+4304 (z=0.90),
and Cl 1604+4321 (z=0.92). Depressions of the surface brightness relative to
the zero-redshift fiducial lines in the mean surface brightness, log linear
radius diagrams of Paper I are found for all three clusters. Expressed as the
exponent, n, in 2.5 log (1 + z)^n mag, the value of n for all three clusters is
n = 2.59 +/- 0.17 in the R band and 3.37 +/- 0.13 in the I band for a q_o = 1/2
model. The sensitivity of the result to the assumed value of q_o is shown to be
less than 23% between q_o = 0 and +1. For a true Tolman signal with n = 4, the
luminosity evolution in the look-back time, expressed as the exponent in 2.5
log (1+z)^(4-n) mag, must then be between 1.72 to 1.19 in the R band and 0.94
to 0.45 in the I band. We show that this is precisely the range expected from
the evolutionary models of Bruzual & Charlot. We conclude that the Tolman
surface brightness test is consistent with the reality of the expansion. We
have also used the high-redshift HST data to test the ``tired light''
speculation for a non-expansion model for the redshift. The HST data rule out
the ``tired light'' model at a significance level of better than 10 sigma.
