  We present new X-ray observations of the X-ray pulsar 1E 2259+586, obtained
during March 1997, with the Rossi X-Ray Timing Explorer (RXTE). We have
measured the pulse frequency derivative $\dot \nu = (-1.08 \pm 0.04) \times
10^{-14}$ Hz s$^{-1}$ from pulse arrival times obtained in a sequence of 5
observations spread over one month. This $\dot\nu$ is consistent with the long
term spin-down trend. We also found that the observed X-ray luminosity is
consistent with that measured at quiescent X-ray flux levels by previous
missions. Our observations imply that 1E 2259+586 was spinning down steadily
without exhibiting any stochastic torque noise fluctuations during the month
covered by our observations.
