The spectral distribution of the flux of positrons inside a beta radioactive medium was experimentally determined using an anthracene coincidence scintillation spectrometer. Positrons leaving a copper cavity source containing Cu/sup 64/ were absorbed in a thin anthracene crystal. The light pulse from the anthracene was recorded in a 256 channel analyzer if a NaI scintillation spectrometer nearby recorded simultaneously a count under the total absorption peak for annihilation radiation. Thus, discrimination against negative and secondary electrons was obtained which permitted observation of the primary positron slowing down flux. Data were corrected for the non-linear pulse height vs energy relationship in anthracene by a semi-empirical theory due to Birks, the validity of which was demonstrated by its use in obtaining a linear Fermi plot of Pm/sup 147/. Positron spectra were corrected also for Compton absorption of the annihilation radiation in the anthracene. Results were compared with the theoretical continuous-slowing-down model. Over the energy range measured (20-- 650 kev) it was concluded that the continuous-slowing-down model gives the correct shape for the primary slowing-down spectrum. 43 references. (auth)