The spectrum of neutrons in thermal pseudo-equilibrium with a mixture of partially hydrogenated terphenyls and high-boiling polymers, an organic material known commercially as HB40, has been measured at room temperature. The spectrum was measured in each of seven mixtures of HB40 and a thermal-neutron absorber, trimethyl borate, in various concentrations. The spectra were determined by the time-of-flight method using the University of Toronto linear electron accelerator as a pulsed source of fast neutrons. These spectra were compared with those calculated using several different bound-hydrogen approximations to the actual energy transfer kernel for the mixture. Of these approximations, the best agreement between theory and experiment occurred for a scattering kernel derived using the diphenyl and the polyethylene scattering kernels, combined according to a weighting scheme reflecting the degree of hydrogenation of the organic material.