Fluxes of energetic electrons and protons in Jupiter's outer magnetosphere were observed to be modulated with the 10-hour rotation period of the planet. This modulation is due to the concentration of particles at the magnetic equator; the nonalignment of Jupiter's spin and rotation axes causes Pioneer 10 to oscillate between +2¿ and -19¿ magnetic latitude and hence between regions of stronger and weaker fluxes. In this paper we investigate the relationship between electron and proton fluxes observed off the magnetic equator with those measured at the equatorial crossing radii of the same flux tubes. Liouville's theorem is applied with the assumption that particles move conserving their magnetic moments. A magnetic model which matches the intensity and direction of the magnetic field along the Pioneer 10 trajectory is used for determining the positions of the equatorial crossings. Energetic electrons (1.3 MeV) compared in this way appear to be consistently described. Protons, on the other hand, show much weaker fluxes at the off-equatorial points than would be predicted by this simple application of Liouville's theorem. Violation of the first adiabatic invariant is one explanation; other potential explanations depend on slow magnetic field fluctuations which are not included in the magnetic model and which conserve the first invariant or on a large asymmetry in equatorial proton flux as a function of system III longitude.