The hot protons of the outer magnetosphere typically exhibit a temperature anisotropy such that T⊥/T∥>1, where perpendicular and parallel symbols denote directions relative to the background magnetic field. If this anisotropy is sufficiently large, the electromagnetic proton cyclotron anisotropy instability may be excited. This instability is studied using linear Vlasov theory and one-dimensional hybrid simulations for a homogeneous plasma model representative of conditions in the outer magnetosphere with a hot anisotropic proton component (denoted by the subscript h) and a cool, initially isotropic proton component (subscript c). Linear theory yields an instability threshold condition on the hot proton temperature anisotropy whereas the simulations imply an upper bound on T⊥h/T∥h; both the threshold and the upper bound have similar scalings with the maximum growth rate &ggr;m, the parallel &bgr; of the hot component, &bgr; ∥h, and the relative density of the hot component n h/ne. An analysis of plasma observations from the Los Alamos magnetospheric plasma analyzer (MPA) in geosynchronous orbit finds that the maximum value of the hot proton temperature anisotropy approximately satisfies the predicted scalings with &bgr;∥h and h /ne and yields the proportionality factor that quantifies this upper bound. The simulations are also used to examine the heating of the cool protons by the proton cyclotron instability. The simulations yield a scaling for the dimensionless late-time cool proton average temperature Tc/T∥h as (nh/ne)/&bgr;∥h0.5. Analysis of MPA data shows that the observed values of Tc/T∥h have similar scalings and again yield the proportionality factor which quantifies this relationship. ¿ American Geophysical Union 1994