  We find that dim gamma-ray bursts (GRBs) are softer than bright GRBs, as
indicated on average by data from the Burst and Transient Source Experiment
(BATSE) on board the Compton Gamma Ray Observatory. We show that this
correlation is statistically significant with respect to variations due to
random differences between GRBs. This effect is discernable using a variety of
methods and data sets, including public domain data. We analyze several types
of systematic errors and selection effects in the BATSE data and conclude that
the observed effect is not dominated by any of them. We therefore assert that
this dim/soft effect is a real property of GRBs. It is possible that this
correlation is a consequence of the time dilation detected by Norris et al.
(1994) and that this is additional evidence that burst sources are located at
cosmological distances.
