The polarization of the fluorescence of anthracene has been measured after two-photon excitation with ruby laser light. The anthracene molecules were rigidly held in a 2×10-3M solution in EPA glass at liquidnitrogen temperatures. For comparison, the polarization of the fluorescence was measured from one-photon excitation at approximately twice the laser frequency. The measured polarization of the two-photon excited light is in satisfactory agreement with the polarization as calculated from the Goeppert-Mayer process involving a transition through an intermediate state. It is in disagreement with the polarization calculated in terms of the process recently suggested involving the A2 term in the Hamiltonian. Thus the measurement of the polarization of the two-photon fluorescent light appears to be one way of experimentally estimating the relative contribution of these two second-order processes. The concentration and intensity independent quantity S, which is the ratio of the cross section to the laser flux, was found experimentally to be 0.9×10-51 cm4·sec/atom- photon for anthracene molecules in a dilute glass.