The source characteristics of southern California earthquakes with local magnitudes ML between 2 and 7 have been estimated from the gross spectral properties of the locally recorded S waves written on broad band torsion seismograph systems that have operated in California since 1932. The seismic moments M0 are consistent with the magnitude-moment relation obtained by M. Wyss and J. N. Brune from surface wave amplitudes, although a single straight line given by log M0 = 1.5 ML + 16.0 fits the data equally well. Source dimensions 2r vary from about 0.6 to 25 km, and stress drops ∆σ lie between 0.3 and 200 bars. Neither parameter is a well-defined function of magnitude, although source size roughly increases with increasing ML. A theoretical relation between ML and source parameters is developed by using Brune's source model and the displacement response of the Wood-Anderson seismograph. The result is ML = log M0 - 32 log r - 17.8, where 3 < ML < 7, M0 is in dynes centimeters, and r is in kilometers. The ML may be accurately obtained by this equation, and the result is used to construct the following relations: log M0 = 2.0 ML + 14.2 - log ∆σ, where ∆σ is in bars, and log 2r = ⅔ ML + 2.9 - ⅔ log ∆σ. Single-valued relations are not expected unless ∆σ is constant. However, all available data are bracketed by these equations if stress drops vary over the range observed in this study. Radiated energies computed by spectrum integration agree with a theoretical result, log Es = 2.0 ML + 8.1, where Es is in ergs. Both are consistent with B. Gutenberg and C. F. Richter's energy-magnitude relation above ML = 4.5 but depart considerably from their result at lower magnitudes. The apparent stress parameter can provide source information that is independent of stress drop only if the high-frequency spectral falloff is a well-determined source property, which is unlikely for most of the data examined in this and other recent spectrum studies. Regional differences in source dimensions and stress drops within the southern California area are suggested by the spectral observations. However, the pattern is complex, and there are significant variations in these source parameters within any one region. Close-in seismic measurements are needed to substantiate the suggested regional differences, and determination of fault zone properties at depth is required to more fully understand the regional and local variations in seismic source parameters suggested by this study.