The low energy charged particles (LECP) experiments on the Voyager 1 and 2 spacecraft performed measurements of electrons (~22 keV to ~20 MeV) and ions (~28 keV to ~150 MeV) during the Saturn encounters in 1980 and 1981. Count rate ratios of two of the low energy electron (22 to 35 keV and 183 to 500 keV) and ion (43 to 80 keV and 137 to 215 keV) channels exhibit an approximation 10 hour periodicity in the outer Saturnian magnetosphere beyond the orbit of Titan. Electron ratios vary from ~50 to ~300; ion ratios vary from ~3 to ~20. Similar but less pronounced periodicities are observed for higher and lower energy electron and ion spectral indices. Three complete cycles were observed during the Voyager 2 outbound portion of the encounter from which were determined an electron ratio period of 10h21m¿48m and an ion ratio period of 9h49m¿59m. Using Saturn Kilometric Radiation (SKR) and Saturn Electrostatic Discharge (SED) periods, extrapolation backward from Voyager 2 to Voyager 1 suggests that the periodicities are Saturnian rather than Jovian in nature, and that they persist in phase for time intervals at least as long as 287 days. Ratio minima, or spectral hardenings, occur in the same hemisphere as do auroral brightenings, SKR activity, and spoke enhanement. We interpret the observations as prima facie evidence of an asymmetry in the Saturian magnetic field and the root cause of the observed SKR periodicity.