  We establish correlations between equivalent widths of eight diffuse
interstellar bands (DIBs), and examine their correlations with atomic hydrogen,
molecular hydrogen, and EB-V . The DIBs are centered at \lambda\lambda 5780.5,
6204.5, 6283.8, 6196.0, 6613.6, 5705.1, 5797.1, and 5487.7, in decreasing order
of Pearson\^as correlation coefficient with N(H) (here defined as the column
density of neutral hydrogen), ranging from 0.96 to 0.82. We find the equivalent
width of \lambda 5780.5 is better correlated with column densities of H than
with E(B-V) or H2, confirming earlier results based on smaller datasets. We
show the same is true for six of the seven other DIBs presented here. Despite
this similarity, the eight strong DIBs chosen are not well enough correlated
with each other to suggest they come from the same carrier. We further conclude
that these eight DIBs are more likely to be associated with H than with H2, and
hence are not preferentially located in the densest, most UV shielded parts of
interstellar clouds. We suggest they arise from different molecules found in
diffuse H regions with very little H (molecular fraction f<0.01). Of the 133
stars with available data in our study, there are three with significantly
weaker \lambda 5780.5 than our mean H-5780.5 relationship, all of which are in
regions of high radiation fields, as previously noted by Herbig. The
correlations will be useful in deriving interstellar parameters when direct
methods are not available. For instance, with care, the value of N(H) can be
derived from W{\lambda}(5780.5).
