The 35?day X-ray cycle of Hercules X-1 (Her X-1) has been the subject of intense study since its discovery over 30?years ago. This work summarizes the results of determination of 35?day cycle turn-on (TO) times based on Rossi X-Ray Timing Explorer (RXTE)/All-Sky Monitor (ASM) observations of Her X-1. We apply a cross-correlation method to the entire (RXTE/ASM) Her X-1 database acquired between 1996 February 20 and 2009 December 18. We obtain new TO times for 147 cycles, 94 of which have well-determined times. The results reveal a uniform distribution of TO times with orbital phase. This does not support previous results that suggest TO times cluster around a specific orbital phase, such as 0.2 or 0.7. We also find 35?day cycle lengths ranging from 33.2 days to 36.7?days, and an average cycle length of 34.7 days.
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