We describe observations made by GEOS 1, ISEE 1, and ISEE 2 of a hydromagnetic wave with a period ~90 s observed near 0200 LT between L=9 and L=6, close to the measured inner boundary of the plasma sheet. The wave magnetic perpendicular to and along the ambient field had similar amplitudes. Using primarily the transverse magnetic components, we show that the wave is a second harmonic resonance of the local geomagnetic lines. ISEE 1 and 2 observed the opposite sense of polarization for about 30 min, although the spacecraft were separated by only 9 min in their orbit; this remarkable feature cannot be explained by either a stationary spatial boundary or a simple temporal boundary but could result from a rapid movement of the resonant region. We argue that the most likely energy source is bounce resonance with medium energy (~ 5 keV) ions. Calculations of the wave Poynting vector at ISEE 1 support this conclusion.