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Results from the third season (1992/93) of monitoring the Orion Nebula cluster (including the Trapezium cluster) in the Cousins I band at Van Vleck Observatory are reported. Data were obtained on ten separate fields within the ONC, each one 4.3 arc-minutes on a side. Each field was observed on 28 to 32 nights. A periodogram analysis of the 525 stars in these fields yielded 55 significant periodicities. Of these, 28 are confirmations of periods previously reported by Attridge \& Herbst (ApJ 398, L61) or Mandel \& Herbst (ApJ 383, L75) and 27 are new detections. The total number of rotation periods now known in the ONC (including the Trapezium cluster) is 75. Periods range from about 1.5 to 35 days, more than a factor of twenty! The bimodal period distribution, discovered by Attridge \& Herbst is confirmed. Peaks occur at around 2.5 and 8 days and a gap at about 4.5 days. Spectra and colors are available for a subset of our stars, which allows us to plot them on an HR diagram and infer masses and ages. Focusing on purely convective stars, with periods longward of the gap, we find that, at a given mass, there is no correlation between a star's age and its rotation period. This implies that, as these PMS stars age and contract, they lose angular momentum at just the proper rate to keep their rotation periods nearly constant. The fact that rotation period, rather than angular momentum, is the ``conserved" quantity strongly argues in favor of disk-regulated angular momentum evolution (e.g. Edwards et al. 1993, AJ 106, 372). We also show that all six of the large amplitude periodic variables have periods on the long side of the gap. These are stars which are actively accreting and would be expected to be rotationally locked to their disks, as they appear to be. In addition to the periodic variables, we identify 31 large amplitude (exceeding 0.5 mag) irregular variables in the ONC and display and discuss their light curves.
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