NavList:

Evangelos,

Glad you found the NavList message boards. Now that you have phrased your question differently, I can see why this seems like a puzzle to you. I would suggest that you're thinking about this too theoretically. In a practical circumstance, a navigator is never lost. You always have at least a rough estimate of your longitude and you can convert that into GMT. We don't start from complete ignorance of our position. Even if a navigator has somehow become thoroughly confused about the date, the observation of the lunar itself fills you in on the approximate GMT within an hour or so even if you do not use the correct HP. For example, suppose you're sailing in the Pacific next month, and you have the misfortune of spending a few days in stormy weather. The clouds clear late in the afternoon as the storm subsides, and you see the Sun about 40° high in the west and the Moon about 50° high in the east. You measure the angle from the Moon to the Sun --necessarily a "near limb" lunar. Suppose that the observed distance is 91° 12' and increasing. From this information you can readily determine the date and you can estimate the GMT within 15 minutes or so with almost no calculation by doing a very rough clearing of the lunar (in your head, or graphically). Try it out. See if you can work this example with the data given, but without doing a full clearing of the lunar. What is the approximate GMT? With that rough GMT in hand, you would then do a proper clearing of the lunar to deduce a more exact value of GMT. 

-FER