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I've discovered a technique that can help us with the timing of certain photos and films captured in the first 15 minutes or later after 12:30. During this time the shadow moves about 3” per minute. The biggest issue I've found is the poor digital resolution of photos and video available to us. As a result, estimated times should be considered to have a possible error up-to plus/minus 1 minute. To be useful the north peristyle wall needs to in-frame, but only a handful of examples exist. Here is a summary of those I've found so far.
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Edit: After viewing the Sixth Floor Museum's DVD copy of the Darnell film the lower left frame is from Darnell.