Compressinal oscillations of nearly constant frequency (period ≲8 min) were observed from L≈5 to L≈10 near local noon over an interval of almost 3 hours during dayside radial pass of the ISEE 1 spacecraft on August 12, 1982. The density fluctuations, measured by the electron density experiment, were in phase with the compressional magnetic oscillations measured by the magnetotmeter. We relate the observations to an analytical model of a global compressional wave reflected at the gradient of the magnetic field and plasma density near the plasmapause and standing in the outer magnetosphere. Qualitative arguments based on the model lead one to expect that conditions in the outer magnetosphere are not normally compatible with the standing wave solution, that when such a solution can be found, only the lowest eigenfrequencies will be present, and that some varion in period with local time may occur.