No Persistent Pulsations in Aql X-1 as it Fades into Quiescence

We searched for coherent X-ray pulsations from Aql X-1 in a series of RXTE observations taken shortly after a recent outburst. During the course of these observations, Aql X-1 passes through an apparent ``propeller'' phase as its luminosity fades to its quiescent value. No pulsations were detected, and we place upper limits (ranging from 0.52% to 9.0%) on the fractional RMS amplitude of any periodic signal contained in the various data sets searched. This result has implications for the geometry of the system, if the quiescent luminosity is due to continued low-level accretion. Alternatively, our result supports the idea that the quiescent luminosity may be due to thermal emission.