A novel Fourier-transform spectroscopic method using two-photon polarization to determine the spectral distribution of the two photons emitted in the spontaneous decay of metastable atomic hydrogen is described. The method uses birefringent retardation plates and takes advantage of the subtle interplay between the spectral properties and the entangled polarization properties of the radiation emitted in the decay. Assuming the validity of the theoretical spectral distribution, it is shown that the experimental results agree well with theory. On the other hand, success in solving the inverse problem of determining the spectral distribution from the experimental results is limited by the small number of experimental points. However, making reasonable assumptions it is deduced that the observed spectrum is characterized by a broadband signal of width and centre angular frequency in good agreement with the predictions of and , respectively, obtained from the theoretical spectral distribution modified to take account of the absorption of the two-photon radiation in air. The values of 1.5 fs for the coherence time and 440 nm for the coherence length for single photons of the two-photon pair which are obtained from the measured bandwidth imply that, in the ideal case, these values are determined by the essentially zero lifetime of the virtual intermediate state of the decay process rather than the long lifetime of the metastable state which, it is suggested, determines the coherence time and coherence length appropriate to certain types of fourth-order interference experiments.