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We have investigated the correlations between the equivalent widths of 21 selected diffuse interstellar bands (DIBs) and the corresponding interstellar column densities N(C2), N(CN), and N(CH), toward 53 stars with color excesses 0:11 EðBVÞ 1:99. The observational data were derived primarily from echelle spectra acquired at R 38; 000 as part of our extensive, continuing survey of the bands. All but six of the 53 final spectra show signal-to-noise ratios800 at 5780 Å. The principal result presented here is that seven of the 21 bands prove to be examples of ‘ ‘ the C2 DIBs,’ ’ a class of weak, narrow bands whose normalized equivalent widthsW(X)/W (6196) are well correlated specifically with N(C2)/EðBVÞ via power laws. In contrast, the similarly normalized equivalent widths of the 14 other, well-known DIBs analyzed here are uncorrelated, or weakly anticorrelated, with N(C2)/EðBVÞ, to within the observational uncertainties. Thus, the polyatomic molecule(s) presumed to cause these seven C2 DIBs may bear a direct chemical relation to C2 that is not shared by the polyatomic molecules putatively responsible for the other 14 bands. The C2 DIBs also show positive correlations with N(CN)/EðBVÞ and N(CH)/EðBVÞ in our particular sample of light paths, although generally with shallower slopes in the case of N(CN) and with greater scatter in the case of N(CH). Eleven additional C2 DIBs are also identified but are not analyzed here. Among the 18 C2 DIBs identified, four apparently have not been previously detected. The 4963 band is generally the strongest of the 18 C2 DIBs, while the 4734 band shows the most sensitive correlation withN(C2). Subject headings: ISM: lines and bands — ISM: molecules 1