  We present an analysis of long term X-ray monitoring observations of Circinus
X-1 (Cir X-1) made with four different instruments: Vela 5B, Ariel V ASM, Ginga
ASM, and RXTE ASM, over the course of more than 30 years. We use Lomb-Scargle
periodograms to search for the ~16.5 day orbital period of Cir X-1 in each of
these data sets and from this derive a new orbital ephemeris based solely on
X-ray measurements, which we compare to the previous ephemerides obtained from
radio observations. We also use the Phase Dispersion Minimization (PDM)
technique, as well as FFT analysis, to verify the periods obtained from
periodograms. we obtain dynamic periodograms (both Lomb-Scargle and PDM) of Cir
X-1 during the RXTE era, showing the period evolution of Cir X-1, and also
displaying some unexplained discrete jumps in the location of the peak power.
