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A Question for Frank I think,

I have been experimenting with the Thompson lunar clearance  method as described by you:

P1 = HP · sin(Hm) / tan(LD)

P2 = HP · sin(Hs) / sin(LD)

and

P = P1 - P2.

This is the effect of the Moon's parallax

along the lunar arc.

This I have found works perfectly to within a few arc seconds of the full methods, by either calculator or my Fuller 3 slide rule. This is definitely the easiest method for slide rules.(thanks for bringing me to this)

However, I have looked at both Bowditch 1864 and original Thompson  and cannot quite see how you got your formula  from them? (see attached).

Are you able to explain how you got  from that to your formula? ( as usual, apologies if my limited maths make this a simpleton question!).

By the way, the Margetts graphs work well and can easily be checked by calculator using the Thompson formula which uses the same inputs. All great stuff for the winter berth approaching fast.. More to follow. (longitude by "improved polarum"  angle readings of Alkaid LHA, gives very accurate results).

Many thanks 

Francis