I am not familiar with this technique. I would guess that it involves timing when the eclipse became total. This occurs at a specific Universal Time according to the prediction tables, say 14:23 UT. When you observe the same total eclipse at your location using local time, say at 16:41, you will know that you are located 14:23 - 16:41 = -2:18 to the east of Greenwich's longitude. Since one hour of time corresponds to 15 degrees, this means your longitude is 15 x 2.3 = 34.5 degrees East. This would be my best guess as to a 'method'
Here is a method using a local sun gnomon, for figuring your latitude and longitude:
Copyright 1997 Dr. Sten Odenwald
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