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Data from the CYGNUS experiment has been used to examine ultra high energy (UHE) radiation associated with the X-ray binary star system Hercules X-1. A search for both pulsed, and unpulsed emission over time scales ranging from minutes to years has failed to yield a result of comparable significance to that of the previously published observation of July 24, 1986. A reassessment of this result in light of the number of hypotheses that have been examined for Hercules X-1 yields a probability estimate of 0.44% that the data is consistent with background fluctuations. If the number of independent source hypotheses is also accounted for, an overall chance probability of 1.8% is assessed for the observations of the CYGNUS experiment. The extensive air showers corresponding to the episode of July 24, 1986 contain a substantial muon content, in contradiction with traditional predictions for primary gamma-rays. No satisfactory theory has yet been put forward to explain this phenomenon. A further analysis of shower characteristics for events associated with this episode indicates a steeper radial dependence of the showerfront timing width at a chance probability level of 0.16%. This property might be explained by a model that invokes a forward-peaked and/or a deeply interacting component of the hadronic interaction in the atmosphere. The potential importance of UHE observations of Hercules X-1 is great. however the evidence is not yet compelling. Further observations will be necessary, to confirm the potential properties of associated UHE radiation.