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Frank's method requires adjusting each sight for the combined
motion of the vessel and sun toward or away from each other on
a north/south line.  He described it as moving the points before
noon one way, and the points after noon the opposite way.
George asked how "noon" is identified, since that's one of the
unknowns we're looking for.

As far as latitude is concerned, this procedure is no different
from the normal procedure of "advancing all sights to a common
time", so the resulting latitude is the vessel's latitude at the
time chosen for the zero adjustment (which is probably not local
noon).  I hope this much is obvious.  Note that the declination
to be used in computing latitude is the one for the chosen zero
time, not the one where the highest (adjusted) altitude was plotted.

The longitude that results from the paper-folding exercise is the
vessel's longitude when it and the sun were on the same meridian
(i.e., when local noon occurred at the vessel).  If you're traveling
mostly east or west, you could assume the latitude measurement is
also valid for this moment.  Conversely if you're traveling mostly
north or south, you could consider this longitude to be valid for
the moment at which you measured your latitude.  If you're only
moving a mile or two every 10 minutes, you could choose to ignore
the difference.  Or you could advance or retard the longitude or
latitude measurement to the time of the other one.

It's unfortunate (for us pedants) that the the two results don't
naturally correspond to the same time...
        -- Bill

   

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