The elastic-photon-scattering cross section for /sup 12/C has been measured at 90/sup 0/ and 135/sup 0/ in the energy range from 23.5 to 39 MeV. These data disagree with the predicted scattering, derived from the measured photonuclear absorption cross section, if only E1 transitions are assumed. To explain the difference in these cross sections, a large component of electric quadrupole absorption between 24 and 40 MeV is inferred.