The spectra of most non-thermal sources can be closely represented by a simple power law of the form S f , at least between 40 and 1400 Mc/s. The distribution of spectral indices for the sources away from the galactic plane is sharply peaked about a median value of -0.76, while the sources near the plane have a considerably wider dispersion of indices. The small-diameter, relatively weak sources tend to have relatively flat spectra. The most luminous sources, with high surface brightnesses, have normal spectra at decimeter wavelengths but are considerably flatter at meter wavelengths, suggesting that they are younger sources where equilibrium between the rate of injection of relativistic electrons and the rate of radiation loss has not yet been established. The similarity of the spectra among the extragalactic sources and the surprising absence of any sources with very steep spectra are discussed, and it is suggested that these may be understood if intergalactic space provides a common, continuing source of relativistic particles for all extragalactic sources The small differences in the observed spectral indices are explained as a result of variations in the rate at which the relativistic electrons are losing energy.
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K. I. Kellermann (1964) studied this question.